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  THE MODES

  OF

  ANCIENT GREEK MUSIC

  _MONRO_
  London

  HENRY FROWDE

  OXFORD UNIVERSITY PRESS WAREHOUSE
  AMEN CORNER, E.C.

  [Illustration]

  New York

  MACMILLAN & CO., 66, FIFTH AVENUE

  _The Modes
  of
  Ancient Greek Music_

  BY

  D. B. MONRO, M.A.

  PROVOST OF ORIEL COLLEGE, OXFORD
  HONORARY DOCTOR OF LETTERS IN THE UNIVERSITY OF DUBLIN

  Oxford

  AT THE CLARENDON PRESS

  1894
  Oxford

  PRINTED AT THE CLARENDON PRESS

  BY HORACE HART, PRINTER TO THE UNIVERSITY
  DEDICATED
  TO THE
  PROVOST AND FELLOWS
  OF TRINITY COLLEGE DUBLIN

  [Greek: xeinosynes heneka]


[Blank Page]

PREFACE


The present essay is the sequel of an article on Greek music which
the author contributed to the new edition of _Smith's Dictionary of
Greek and Roman Antiquities_ (London, 1890-91, art. MUSICA). In that
article the long-standing controversy regarding the nature of the
ancient musical Modes was briefly noticed, and some reasons were
given for dissenting from the views maintained by Westphal, and now
very generally accepted. A full discussion of the subject would have
taken up more space than was then at the author's disposal, and he
accordingly proposed to the Delegates of the Clarendon Press to treat
the question in a separate form. He has now to thank them for
undertaking the publication of a work which is necessarily addressed
to a very limited circle.

The progress of the work has been more than once delayed by the
accession of materials. Much of it was written before the author had
the opportunity of studying two very interesting documents first made
known in the course of last year in the _Bulletin de correspondance
hellenique_ and the _Philologus_, viz. the so-called Seikelos
 inscription from Tralles, and a fragment of the _Orestes_ of
Euripides. But a much greater surprise was in store. The book was
nearly ready for publication last November, when the newspapers
reported that the French scholars engaged in excavating on the site
of Delphi had found several pieces of musical notation, in particular
a hymn to Apollo dating from the third century B.C. As the known
remains of Greek music were either miserably brief, or so late as
hardly to belong to classical antiquity, it was thought best to wait
for the publication of the new material. The French School of Athens
must be congratulated upon the good fortune which has attended their
enterprise, and also upon the excellent form in which its results
have been placed, within a comparatively short time, at the service
of students. The writer of these pages, it will be readily
understood, had especial reason to be interested in the announcement
of a discovery which might give an entirely new complexion to the
whole argument. It will be for the reader to determine whether the
main thesis of the book has gained or lost by the new evidence.

Mr. Hubert Parry prefaces his suggestive treatment of Greek music by
some remarks on the difficulty of the subject. 'It still seems
possible,' he observes, 'that a large portion of what has passed into
the domain of "well-authenticated fact" is complete misapprehension,
as Greek scholars have not time for a thorough study of music up to
the standard required to judge securely of the matters in question,
and musicians as a rule are not extremely intimate with Greek' (_The
Art of Music_, p. 24). To the present writer, who has no claim to the
title of musician, the scepticism expressed in these words appears to
be well founded. If his interpretation of the ancient texts furnishes
musicians like Mr. Parry with a somewhat more trustworthy basis for
their criticism of Greek music as an art, his object will be fully
attained.




                        TABLE OF CONTENTS

        Sec. 1.  _Introductory._                                      PAGE
Musical forms called [Greek: harmoniai] or [Greek: tropoi]            1


        Sec. 2. _Statement of the question._
The terms Dorian, Phrygian, Lydian, &c.                               3


        Sec. 3. _The Authorities._
Aristoxenus--Plato--Aristotle--Heraclides Ponticus--the
    Aristotelian _Problems_                                           4


        Sec. 4. _The Early Poets._
Pratinas--Telestes--Aristophanes                                      5


        Sec. 5. _Plato._
The [Greek: harmoniai] in the _Republic_--The _Laches_                7


        Sec. 6. _Heraclides Ponticus._
The three Hellenic [Greek: harmoniai]--the Phrygian and Lydian--the
    Hypo-dorian, &c.                                                  9


        Sec. 7. _Aristotle--The Politics._
The [Greek: harmoniai] in the _Politics_                             12


        Sec. 8. _The Aristotelian Problems._
Hypo-dorian and Hypo-phrygian                                        14


        Sec. 9. _The Rhetoric._
The [Greek: harmonia] of oratory                                     15


        Sec. 10. _Aristoxenus._
The [Greek: topoi] or keys                                           16

        Sec. 11.  _Names of keys._
The prefix Hypo- --the term [Greek: tonos]                           19


        Sec. 12. _Plutarch's Dialogue on Music._
The Platonic modes--Lydian--Mixo-lydian and Syntono-lydian--the
    Mixo-lydian octave--the keys of Sacadas--[Greek: tonos]
    and [Greek: harmonia]                                            20


        Sec. 13. _Modes employed on different instruments._
Modes on wind-instruments--on the water-organ--on the
    cithara--on the flute                                            27


        Sec. 14. _Recapitulation._
Equivalence of [Greek: harmonia] and [Greek: tonos]                  28


        Sec. 15._ The Systems of Greek music._
The musical System ([Greek: systema emmeles])                        30


        Sec. 16. _The standard Octachord System._
The scale in Aristotle and Aristoxenus                               31


        Sec. 17. _Earlier Heptachord Scales._
Seven-stringed scales in the _Problems_--Nicomachus                  33


        Sec. 18. _The Perfect System._
The Greater and Lesser Perfect Systems--Aristoxenus--enlargement
    of the scale--Timotheus--Pronomus--the
    Proslambanomenos--the Hyperhypate                                35


        Sec. 19. _Relation of System and Key._
The standard System and the 'modes'--the multiplicity of
    [Greek: harmoniai]                                               40


        Sec. 20. _Tonality of the Greek musical scale._
The Mese as a key-note--the close on the Hypate--[Greek: arche] in
    the _Metaphysics_                                                42


        Sec. 21. _The Species of a Scale._
The seven Species ([Greek: schemata, eide]) of the Octave--connexion
    with the Modes                                                   47

        Sec. 22. _The Scales as treated by Aristoxenus._
Advance made by Aristoxenus--diagrams of the Enharmonic
    genus--reference in Plato's _Republic_--Aristides
    Quintilianus--the _Philebus_                                     48


        Sec. 23. _The Seven Species._
Aristoxenus--the _Introductio Harmonica_                             56


        Sec. 24. _Relation of the Species to the Keys._
Use of the names Dorian, &c.--treatment of musical scales
    in Aristoxenus--Species in the different genera                  58


        Sec. 25. _The Ethos of Music._
Regions of the voice--branches of lyrical poetry--kinds of
    ethos                                                            62


        Sec. 26. _The Ethos of the Genera and Species._
Ethos depending on pitch--on the genus                               66


        Sec. 27. _The Musical Notation._
The instrumental notes--original form and date                       67


        Sec. 28. _Traces of the Species in the Notation._
Westphal's theory                                                    75


        Sec. 29. _Ptolemy's Scheme of Modes._
Reduction of the Modes to seven--nomenclature according
    to _value_ and according to _position_                           78


        Sec. 30. _Nomenclature by Position._
The term [Greek: thesis] in Aristoxenus--in the Aristotelian
    _Problems_                                                       81


        Sec. 31. _Scales of the Lyre and Cithara._
The scales on the lyre--on the cithara (viz. [Greek: tritai, tropoi,
    parypatai, lydia, hypertropa, iastiaioliaia])                    83


        Sec. 32. _Remains of Greek Music._
The hymns of Dionysius and Mesomedes--instrumental
    passages in the _Anonymus_--Mr. Ramsay's inscription--melody
    and accent--fragment of the _Orestes_                            87


        Sec. 33. _Modes of Aristides Quintilianus._
The six Modes of Plato's _Republic_                                  94

        Sec. 34. _Credibility of Aristides Quintilianus._
Date of Aristides--genuineness of his scales                         95


        Sec. 35. _Evidence for Scales of different species._
The Hypo-dorian or common species--the Dorian--the
    Mixo-lydian--the Phrygian and the Hypo-phrygian--Aristotle
    on Dorian and Phrygian--the dithyramb                           101


        Sec. 36. _Conclusion._
Early importance of genus and key only--change in
    Ptolemy's time in the direction of the mediaeval Tones          108


        Sec. 37. _Epilogue--Speech and Song._
Musical nature of Greek accent--relation of musical and
    ordinary utterance--agreement of melody and accent in
    the Seikelos inscription--rhythm of music and of prose--the
    stress accent (_ictus_)--music influenced by language--words
    and melody--want of harmony--the
    non-diatonic scales                                             113


                        APPENDIX.

Table I. Scales of the seven oldest Keys, with the species
    of the same name                                                127
Table II. The fifteen Keys                                          128
Music of the _Orestes_ of Euripides                                 130
Musical part of the Seikelos inscription                            133
The hymns recently discovered at Delphi:
Hymn to Apollo--the scale--the changes of genus
    and key--the 'mode' identical with the modern Minor--the
    other fragments--the agreement of melody and
    accent                                                          134
Index of passages discussed or referred to                          142


THE MODES OF ANCIENT GREEK MUSIC.




Sec. 1. _Introductory._


The modes of ancient Greek music are of interest to us, not only as
the forms under which the Fine Art of Music was developed by a people
of extraordinary artistic capability, but also on account of the
peculiar ethical influence ascribed to them by the greatest ancient
philosophers. It appears from a well-known passage in the _Republic_
of Plato, as well as from many other references, that in ancient
Greece there were certain kinds or forms of music, which were known
by national or tribal names--Dorian, Ionian, Phrygian, Lydian and the
like: that each of these was believed to be capable, not only of
expressing particular emotions, but of reacting on the sensibility in
such a way as to exercise a powerful and specific influence in the
formation of character: and consequently that the choice, among these
varieties, of the musical forms to be admitted into the education of
the state, was a matter of the most serious practical concern. If on
a question of this kind we are inclined to distrust the imaginative
temper of Plato we have only to turn to the discussion of the same
subject in the _Politics_ of Aristotle, and we shall find the
Platonic view criticised in some important details, but treated in
the main as being beyond controversy.

The word [Greek: harmonia], 'harmony,' applied to these forms of
music by Plato and Aristotle, means literally 'fitting' or
'adjustment,' hence the 'tuning' of a series of notes on any
principle, the formation of a 'scale' or 'gamut.' Other ancient
writers use the word [Greek: tropos], whence the Latin _modus_ and
our mood or 'mode,' generally employed in this sense by English
scholars. The word 'mode' is open to the objection that in modern
music it has a meaning which assumes just what it is our present
business to prove or disprove about the 'modes' of Greek music. The
word 'harmony,' however, is still more misleading, and on the whole
it seems best to abide by the established use of 'mode' as a
translation of [Greek: harmonia], trusting that the context will show
when the word has its distinctively modern sense, and when it simply
denotes a musical scale of some particular kind.

The rhythm of music is also recognized by both Plato and Aristotle as
an important element in its moral value. On this part of the subject,
however, we have much less material for a judgement. Plato goes on to
the rhythms after he has done with the modes, and lays down the
principle that they must not be complex or varied, but must be the
rhythms of a sober and brave life. But he confesses that he cannot
tell which these are ([Greek: poia de poiou biou mimemata ouk echo
legein]), and leaves the matter for future inquiry[1].

[Footnote 1: Plato, _Rep._ p. 400 _b_ [Greek: alla tauta men, en d'
ego, kai meta Damonos bouleusometha, tines te aneleutherias kai
hybreos e manias kai alles kakias prepousai baseis, kai tinas tois
enantiois leipteon rhythmous.]]

Sec. 2. _Statement of the question._


What then are the musical forms to which Plato and Aristotle ascribe
this remarkable efficacy? And what is the source of their influence
on human emotion and character?

There are two obvious relations in which the scales employed in any
system of music may stand to each other. They may be related as two
keys of the same mode in modern music: that is to say, we may have to
do with a scale consisting of a fixed succession of intervals, which
may vary in pitch--may be 'transposed,' as we say, from one pitch or
key to another. Or the scales may differ as the Major mode differs
from the Minor, namely in the order in which the intervals follow
each other. In modern music we have these two modes, and each of them
may be in any one of twelve keys. It is evidently possible, also,
that a name such as Dorian or Lydian might denote a particular mode
taken in a particular key--that the scale so called should possess a
definite pitch as well as a definite series of intervals.

According to the theory which appears now to prevail among students
of Greek music, these famous names had a double application. There
was a Dorian mode as well as a Dorian key, a Phrygian mode and a
Phrygian key, and so on. This is the view set forth by Boeckh in the
treatise which may be said to have laid the foundations of our
knowledge of Greek music (_De Metris Pindari_, lib. III. cc.
vii-xii). It is expounded, along with much subsidiary speculation, in
the successive volumes which we owe to the fertile pen of Westphal;
and it has been adopted in the learned and excellent _Histoire et
Theorie de la Musique de l'Antiquite_ of M. Gevaert. According to
these high authorities the Greeks had a system of key ([Greek:
tonoi]), and also a system of modes ([Greek: harmoniai]), the former
being based solely upon difference of pitch, the latter upon the
'form' or species ([Greek: eidos]) of the octave scale, that is to
say, upon the order of the intervals which compose it.




Sec. 3. _The Authorities._


The sources of our knowledge are the various systematic treatises
upon music which have come down to us from Greek antiquity, together
with incidental references in other authors, chiefly poets and
philosophers. Of the systematic or 'technical' writers the earliest
and most important is Aristoxenus, a pupil of Aristotle. His treatise
on _Harmonics_ ([Greek: harmonike]) has reached us in a fragmentary
condition, but may be supplemented to some extent from later works of
the same school. Among the incidental notices of music the most
considerable are the passages in the _Republic_ and the _Politics_
already referred to. To these we have to add a few other references
in Plato and Aristotle; a long fragment from the Platonic philosopher
Heraclides Ponticus, containing some interesting quotations from
earlier poets; a number of detached observations collected in the
nineteenth section of the Aristotelian _Problems_; and one or two
notices preserved in lexicographical works, such as the _Onomasticon_
of Pollux.

In these groups of authorities the scholars above mentioned find the
double use which they believe to have been made of the names Dorian,
Phrygian, Lydian and the rest. In Aristoxenus they recognise that
these names are applied to a series of keys ([Greek: tonoi]), which
differed in pitch only. In Plato and Aristotle they find the same
names applied to scales called [Greek: harmoniai], and these scales,
they maintain, differed primarily in the order of their intervals. I
shall endeavour to show that there was no such double use: that in
the earlier periods of Greek music the scales in use, whether called
[Greek: tonoi] or [Greek: harmoniai], differed primarily in _pitch_:
that the statements of ancient authors about them, down to and
including Aristoxenus, agree as closely as there is reason to expect:
and that the passages on which the opposite view is based--all of
them drawn from comparatively late writers--either do not relate to
these ancient scales at all, or point to the emergence in
post-classical times of some new forms or tendencies of musical art.
I propose in any case to adhere as closely as possible to a
chronological treatment of the evidence which is at our command, and
I hope to make it probable that the difficulties of the question may
be best dealt with on this method.




Sec. 4. _The Early Poets._


The earliest of the passages now in question comes from the poet
Pratinas, a contemporary of Aeschylus. It is quoted by Heraclides
Ponticus, in the course of a long fragment preserved by Athenaeus
(xiv. cc. 19-21, p. 624 _c_-626 _a_). The words are:

    [Greek: mete syntonon dioke mete tan aneimenan
    Iasti mousan, alla tan messan neon
    arouran aiolize to melei.]

'Follow neither a highly-strung music nor the low-pitched Ionian, but
turning over the middle plough-land be an Aeolian in your melody.'
Westphal takes the word [Greek: 'Iasti] with [Greek: syntonon] as
well as with [Greek: aneimenan], and infers that there were two kinds
of Ionian, a 'highly-strung' and a 'relaxed' or low-pitched. But this
is not required by the words, and seems less natural than the
interpretation which I have given. All that the passage proves is
that in the time of Pratinas a composer had the choice of at least
three scales: one (or more) of which the pitch was high ([Greek:
syntonos]); another of low pitch ([Greek: aneimene]), which was
called _Ionian_; and a third, intermediate between the others, and
known as _Aeolian_. Later in the same passage we are told that
Pratinas spoke of the 'Aeolian harmony' ([Greek: prepei toi pasin
aoidolabraktais Aiolis harmonia]). And the term is also found, with
the epithet 'deep-sounding,' in a passage quoted from the hymn to
Demeter of a contemporary poet, Lasus of Hermione (Athen. xiv. 624
_e_):

    [Greek: Damatra melpo Koran te Klymenoio alochon Meliboian,
    hymnon anagon Aiolid' hama barybromon harmonian.]

With regard to the Phrygian and Lydian scales Heraclides (_l. c._)
quotes an interesting passage from Telestes of Selinus, in which
their introduction is ascribed to the colony that was said to have
followed Pelops from Asia Minor to the Peloponnesus:

    [Greek: protoi para krateras Hellenon en aulois
    synopadoi Pelopos matros oreias phrygion aeison nomon;
    toi d' oxyphonois pektidon psalmois krekon
    Dydion hymnon.]

'The comrades of Pelops were the first who beside the Grecian cups
sang with the flute ([Greek: aulos]) the Phrygian measure of the
Great Mother; and these again by shrill-voiced notes of the _pectis_
sounded a Lydian hymn.' The epithet [Greek: oxyphonos] is worth
notice in connexion with other evidence of the high pitch of the
music known as Lydian. The Lydian mode is mentioned by Pindar, _Nem._
4. 45:

    [Greek: exyphaine glykeia kai tod' autika phorminx
    Lydia syn harmonia melos pephilemenon.]

The Dorian is the subject of an elaborate jest made at the expense of
Cleon in the _Knights_ of Aristophanes, ll. 985-996:

    [Greek: alla kai tod' ego ge thaumazo tes hyomousias
    autou phasi gar auton hoi paides hoi xynephoiton
    ten Doristi monen enarmottesthai thama ten lyran,
    allen d' ouk ethelein labein; kata ton kitharisten
    orgisthent' apagein keleuein, hos harmonian ho pais
    outos ou dynatai mathein en me Dorodokesti.]




Sec. 5. _Plato._

Following the order of time, we come next to the passage in the
_Republic_ (p. 398), where Socrates is endeavouring to determine the
kinds of music to be admitted for the use of his future 'guardians,'
in accordance with the general principles which are to govern their
education. First among these principles is the condemnation of all
undue expression of grief. 'What modes of music ([Greek:
harmoniai]),' he asks, are plaintive ([Greek: threnodeis])?' 'The
_Mixo-lydian_,' Glaucon replies, 'and the _Syntono-lydian_, and
such-like.' These accordingly Socrates excludes. 'But again,
drunkenness and slothfulness are no less forbidden to the guardians;
which of the modes are soft and convivial ([Greek: malakai te kai
sympotikai])?' '_Ionian_,' says Glaucon, 'and _Lydian_, those which
are called slack ([Greek: chalarai]).' 'Which then remain?'
'Seemingly _Dorian_ and _Phrygian_.' 'I do not know the modes,' says
Socrates, 'but leave me one that will imitate the tones and accents
of a brave man enduring danger or distress, fighting with constancy
against fortune: and also one fitted for the work of peace, for
prayer heard by the gods, for the successful persuasion or
exhortation of men, and generally for the sober enjoyment of ease and
prosperity.' Two such modes, one for Courage and one for Temperance,
are declared by Glaucon to be found in the Dorian and the Phrygian.
In the _Laches_ (p. 188) there is a passing reference in which a
similar view is expressed. Plato is speaking of the character of a
brave man as being metaphorically a 'harmony,' by which his life is
made consonant to reason--'a Dorian harmony,' he adds--playing upon
the musical sense of the word--'not an Ionian, certainly not a
Phrygian or a Lydian, but that one which only is truly Hellenic'
([Greek: atechnos Doristi, all' ouk Iasti, oiomai de oude Phrygisti
oude Lydisti, all' he per mone Hellenike estin harmonia]). The
exclusion of Phrygian may be due to the fact that the virtue
discussed in the _Laches_ is courage; but it is in agreement with
Aristotle's opinion. The absence of Aeolian from both the Platonic
passages seems to show that it had gone out of use in his time (but
cp. p. 11).

The point of view from which Plato professes to determine the right
modes to be used in his ideal education appears clearly in the
passage of the _Republic_. The modes first rejected are those which
are high in pitch. The Syntono-lydian or 'high-strung Lydian' is
shown by its name to be of this class. The Mixo-lydian is similar, as
we shall see from Aristotle and other writers. The second group which
he condemns is that of the 'slack' or low-pitched. Thus it is on the
profoundly Hellenic principle of choosing the mean between opposite
extremes that he approves of the Dorian and Phrygian pitch. The
application of this principle was not a new one, for it had been
already laid down by Pratinas: [Greek: mete syntonon dioke mete tan
aneimenan].

The three chapters which Aristotle devotes to a discussion of the use
of music in the state (_Politics_ viii. cc. 5-7), and in which he
reviews and criticises the Platonic treatment of the same subject,
will be found entirely to bear out the view now taken. It is also
supported by the commentary of Plutarch, in his dialogue on Music
(cc. 15-17), of which we shall have something to say hereafter.
Meanwhile, following the chronological order of our authorities, we
come next to the fragment of Heraclides Ponticus already mentioned
(Athen. xiv. p. 624 _c_-626 _a_).




Sec. 6. _Heraclides Ponticus._

The chief doctrine maintained by Heraclides Ponticus is that there
are three modes ([Greek: harmoniai]), belonging to the three Greek
races--Dorian, Aeolian, Ionian. The Phrygian and Lydian, in his view,
had no right to the name of mode or 'harmony' ([Greek: oud' harmonian
phesi dein kaleisthai ten Phrygion, kathaper oude ten Lydion]). The
three which he recognized had each a marked ethos. The Dorian
reflected the military traditions and temper of Sparta. The Aeolian,
which Heraclides identified with the Hypo-dorian of his own time,
answered to the national character of the Thessalians, which was bold
and gay, somewhat overweening and self-indulgent, but hospitable and
chivalrous. Some said that it was called Hypo-dorian because it was
below the Dorian on the [Greek: aulos] or flute; but Heraclides
thinks that the name merely expressed likeness to the Dorian
character ([Greek: Dorion men auten ou nomizein, prosemphere de pos
ekeine]). The Ionian, again, was harsh and severe, expressive of the
unkindly disposition fostered amid the pride and material welfare of
Miletus. Heraclides is inclined to say that it was not properly a
distinct musical scale or 'harmony,' but a strange aberration in the
form of the musical scale ([Greek: tropon de tina thaumaston
schematos harmonias]). He goes on to protest against those who do not
appreciate differences of kind ([Greek: tas kat' eidos diaphoras]),
and are guided only by the high or low pitch of the notes ([Greek: te
ton phthongon exyteti kai baryteti]); so that they make a
Hyper-mixolydian, and another again above that. 'I do not see,' he
adds, 'that the Hyper-phrygian has a distinct ethos; and yet some say
that they have discovered a new mode ([Greek: harmonia]), the
Hypo-phrygian. But a mode ought to have a distinct moral or emotional
character ([Greek: eidos echein ethous he pathous]), as the Locrian,
which was in use in the time of Simonides and Pindar, but went out of
fashion again.' The Phrygian and Lydian, as we have seen, were said
to have been brought to the Peloponnesus by the followers of Pelops.

The tone as well as the substance of this extract makes it evident
that the opinions of Heraclides on questions of theoretical music
must be accepted with considerable reserve. The notion that the
Phrygian and Lydian scales were 'barbarous' and opposed to Hellenic
ethos was apparently common enough, though largely due (as we may
gather from several indications) to national prejudice. But no one,
except Heraclides, goes so far as to deny them the name of [Greek:
harmonia]. The threefold division into Dorian, Aeolian and Ionian
must also be arbitrary. It is to be observed that Heraclides obtains
his Aeolian by identifying the Aeolian of Pratinas and other early
poets with the mode called Hypo-dorian in his own time. The
circumstance that Plato mentions neither Aeolian nor Hypo-dorian
suggests rather that Aeolian had gone out of use before Hypo-dorian
came in. The conjecture of Boeckh that Ionian was the same as the
later Hypo-phrygian (_De Metr. Pind._ iii. 8) is open to a similar
objection. The Ionian mode was at least as old as Pratinas, whereas
the Hypo-phrygian was a novelty in the time of Heraclides. The
protest which Heraclides makes against classifying modes merely
according to their pitch is chiefly valuable as proving that the
modes were as a matter of fact usually classified from that point of
view. It is far from proving that there was any other principle which
Heraclides wished to adopt--such, for example, as difference in the
intervals employed, or in their succession. His 'differences of kind'
([Greek: tas kat' eidos diaphoras]) are not necessarily to be
explained from the technical use of [Greek: eidos] for the 'species'
of the octave. What he complains of seems to be the multiplication of
modes--Hyper-mixolydian, Hyper-phrygian, Hypo-phrygian--beyond the
legitimate requirements of the art. The Mixo-lydian (_e.g._) is
high-pitched and plaintive: what more can the Hyper-mixolydian be?
The Hypo-phrygian is a new mode: Heraclides denies it a distinctive
ethos. His view seems to be that the number of modes should not be
greater than the number of varieties in temper or emotion of which
music is capable. But there is nothing to show that he did not regard
pitch as the chief element, or one of the chief elements, of musical
expression.

The absence of the name Hypo-lydian, taken with the description of
Hypo-dorian as 'below the Dorian,' would indicate that the
Hypo-dorian of Heraclides was not the later mode of that name, but
was a semitone below the Dorian, in the place afterwards occupied by
the Hypo-lydian. This is confirmed, as we shall see, by Aristoxenus
(p. 18).




Sec. 7. _Aristotle--the Politics._

Of the writers who deal with music from the point of view of the
cultivated layman, Aristotle is undoubtedly the most instructive. The
chapters in his _Politics_ which treat of music in its relation to
the state and to morality go much more deeply than Plato does into
the grounds of the influence which musical forms exert upon temper
and feeling. Moreover, Aristotle's scope is wider, not being confined
to the education of the young; and his treatment is evidently a more
faithful reflexion of the ordinary Greek notions and sentiment. He
begins (_Pol._ viii. 5, p. 1340 _a_ 38) by agreeing with Plato as to
the great importance of the subject for practical politics. Musical
forms, he holds, are not mere _symbols_ ([Greek: semeia]), acting
through association, but are an actual _copy_ or reflex of the forms
of moral temper ([Greek: en de tois melesin autois esti mimemata ton
ethon]); and this is the ground of the different moral influence
exercised by different modes ([Greek: harmoniai]). By some of them,
especially by the Mixo-lydian, we are moved to a plaintive and
depressed temper ([Greek: diatithesthai odyrtikoteros kai
synestekotos mallon]); by others, such as those which are called the
'relaxed' ([Greek: aneimenai]), we are disposed to 'softness' of mind
([Greek: malakoteros ten dianoian]). The Dorian, again, is the only
one under whose influence men are in a middle and settled mood
([Greek: mesos kai kathestekotos malista]): while the Phrygian makes
them excited ([Greek: enthousiastikous]). In a later chapter (Pol.
viii. 7, p. 1342 _a_ 32), he returns to the subject of the Phrygian.
Socrates, he thinks, ought not to have left it with the Dorian,
especially since he condemned the flute ([Greek: aulos]), which has
the same character among instruments as the Phrygian among modes,
both being orgiastic and emotional. The Dorian, as all agree, is the
most steadfast ([Greek: stasimotate]), and has most of the ethos of
courage; and, as compared with other modes, it has the character
which Aristotle himself regards as the universal criterion of
excellence, viz. that of being the mean between opposite excesses.
Aristotle, therefore, certainly understood Plato to have approved the
Dorian and the Phrygian as representing the mean in respect of pitch,
while other modes were either too high or too low. He goes on to
defend the use of the 'relaxed' modes on the ground that they furnish
a music that is still within the powers of those whose voice has
failed from age, and who therefore are not able to sing the
high-pitched modes ([Greek: oion tois apeirekosi dia chronon ou
rhadion adein tas syntonous harmonias, alla tas aneimenas he physis
hypoballei tois telikoutois]). In this passage the meaning of the
words [Greek: syntonos] and [Greek: aneimenos] is especially clear.

In the same discussion (c. 6), Aristotle refers to the distinction
between music that is ethical, music suited to action, and music that
inspires religious excitement ([Greek: ta men ethika, ta de praktika,
ta ho enthousiastika]). The last of these kinds serves as a
'purification' ([Greek: katharsis]). The excitement is calmed by
giving it vent; and the morbid condition of the ethos is met by music
of high pitch and exceptional 'colour' ([Greek: ton harmonion
parekbaseis kai ton melon ta syntona kai parakechrosmena]).

In a different connexion (_Pol._ iv. 3, p. 1290 _a_ 20), dealing with
the opinion that all forms of government are ultimately reducible to
two, viz. oligarchy and democracy, Aristotle compares the view of
some who held that there are properly only two musical modes, Dorian
and Phrygian,--the other scales being mere varieties of these two.
Rather, he says, there is in each case a right form, or two right
forms at most, from which the rest are declensions ([Greek:
parekbaseis]),--on one side to 'high-pitched' and imperious
oligarchies, on the other to 'relaxed' and 'soft' forms of popular
government ([Greek: oligarchikas men tas syntonoteras kai
despotikonteras, tas d' aneimenas kai malakas demotikas]). This is
obviously the Platonic doctrine of two right keys, holding the mean
between high and low.




Sec. 8. _The Aristotelian Problems._

Some further notices of the [Greek: harmoniai] or modes are contained
in the so-called _Problems_,--a collection which is probably not the
work of Aristotle himself, but can hardly be later than the
Aristotelian age. What is said in it of the modes is clearly of the
period before the reform of Aristoxenus. In one place (_Probl._ xix.
48) the question is asked why the Hypo-dorian and Hypo-phrygian are
not used in the _chorus_ of tragedy. One answer is that the
Hypo-phrygian has the ethos of action ([Greek: ethos echei
praktikon]), and that the Hypo-dorian is the expression of a lofty
and unshaken character; both of these things being proper to the
heroic personages on the stage, but not to the chorus, which
represents the average spectator, and takes no part in the action.
Hence the music suited to the chorus is that of emotion venting
itself in passive complaint:--a description which fits the other
modes, but least of all the exciting and orgiastic Hypo-phrygian. On
the contrary (the writer adds) the passive attitude is especially
expressed by the Mixo-lydian. The view here taken of the Hypo-dorian
evidently agrees with that of Heraclides Ponticus (_supra_, p. 10).

The relation which Plato assumes between high pitch and the
excitement of passion, and again between lowness of pitch and
'softness' or self-indulgence ([Greek: malakia kai argia]), is
recognized in the _Problems_, xix. 49 [Greek: epei de ho men barys
phthongos malakos kai eremaios estin, ho de oxys kinetikos, k.t.l.]:
'since a deep note is soft and calm, and a high note is exciting,
&c.'




Sec. 9. _The Rhetoric._

The word [Greek: tonos] occurs several times in Aristotle with the
sense of 'pitch,' but is not applied by him to the keys of music. The
nearest approach to such a use may be found in a passage of the
_Rhetoric_ (iii. 1, p. 1403 _b_ 27).

Speaking of the rise of acting ([Greek: hypokrisis]), which was
originally the business of the poet himself, but had grown into a
distinct art, capable of theoretical as well as practical treatment,
he observes that a similar art might be formed for oratory. 'Such an
art would lay down rules directing how to use the voice so as to suit
each variety of feeling,--when it should be loud, when low, when
intermediate;--and how to use the keys, when the pitch of the voice
should be high or low or middle ([Greek: kai pos tois tonois, oion
oxeia kai bareia kai mese], sc. [Greek: phone]); and the rhythms,
which to use for each case. For there are three things which men
study, viz. quantity (_i. e._ loudness of sound), tune, and rhythm
([tria gar esti peri hon skopousi, tauta d' esti megethos, harmonia,
rhythmos]).' The passage is interesting as showing the value which
Aristotle set upon pitch as an element of effect. And the use of
[Greek: harmonia] in reference to the pitch of the voice, and as
virtually equivalent to [Greek: tonos], is especially worthy of note.




Sec. 10. _Aristoxenus._

Our next source of information is the technical writer Aristoxenus, a
contemporary and pupil of Aristotle. Of his many works on the subject
of music three books only have survived, bearing the title [Greek:
harmonika otoicheia][1]. In the treatment adopted by Aristoxenus the
chapter on keys follows the chapter on 'systems' ([Greek:
systemata]). By a [Greek: systema] he means a scale consisting of a
certain succession of intervals: in other words, a series of notes
whose relative pitch is determined. Such a system may vary in
absolute pitch, and the [Greek: tonoi] or keys are simply the
different degrees of pitch at which a particular system is taken
([Greek: tous tonous eph' on tithemena ta systemata melodeitai]).
When the system and the key are both given it is evident that the
whole series of notes is determined.

Aristoxenus is the chief authority on the keys of Greek music. In
this department he is considered to have done for Greece what Bach's
_Wohltemperirtes Clavier_ did for modern Europe. It is true that the
scheme of keys which later writers ascribe to him is not given in the
_Harmonics_ which we have: but we find there what is in some respects
more valuable, namely, a vivid account of the state of things in
respect of tonality which he observed in the music of his time.

[Footnote 1: It is foreign to our purpose to discuss the critical
problems presented by the text of Aristoxenus. Of the three extant
books the first is obviously a distinct treatise, and should probably
be entitled [Greek: peri archon]. The other two books will then bear
the old title [Greek: harmonika stoicheia]. They deal with the same
subjects, for the most part, as the first book, and in the same
order,--a species of repetition of which there are well-known
instances in the Aristotelian writings. The conclusion is abrupt, and
some important topics are omitted. It seems an exaggeration, however,
to describe the _Harmonics_ of Aristoxenus as a mere collection of
excerpts, which is the view taken by Marquard (_Die harmonischen
Fragmente des Aristoxenus_, pp. 359-393). See Westphal's _Harmonik
und Melopoeie der Griechen_ (p. 41, ed. 1863), and the reply to
Marquard in his _Aristoxenus von Tarent_ (pp. 165-170).]

'No one,' says Aristoxenus (p. 37 Meib.), 'has told us a word about
the keys, either how they are to be arrived at ([Greek: tina tropon
lepteon]), or from what point of view their number is to be
determined. Musicians assign the place of the keys very much as the
different cities regulate the days of the month. The Corinthians, for
example, will be found counting a day as the tenth of the month,
while with the Athenians it is the fifth, and in some other place the
eighth. Some authorities on music ([Greek: harmonikoi]) say that the
Hypo-dorian is the lowest key, the Mixo-lydian a semitone higher, the
Dorian again a semitone higher, the Phrygian a tone above the Dorian,
and similarly the Lydian a tone above the Phrygian. Others add the
Hypo-phrygian flute [_i. e._ the scale of the flute so called] at the
lower end of the list. Others, again, looking to the holes of the
flute ([Greek: pros ten ton aulon trupesin blepontes]), separate the
three lowest keys, viz. the Hypo-phrygian, Hypo-dorian, and Dorian,
by the interval of three-quarters of a tone ([Greek: trisi
diesesin]), but the Phrygian from the Dorian by a tone, the Lydian
from the Phrygian again by three-quarters of a tone, and the
Mixo-lydian from the Lydian by a like interval. But as to what
determines the interval between one key and another they have told us
nothing.'

It will be seen that (with one marked exception) there was agreement
about the order of the keys in respect of pitch, and that some at
least had reduced the intervals to the succession of tones and
semitones which characterises the diatonic scale. The exception is
the Mixo-lydian, which some ranked immediately below the Dorian,
others above the Lydian. Westphal attributes this strange discrepancy
to the accidental displacing of some words in the MSS. of
Aristoxenus[1]. However this may be, it is plain that in the time of
Aristoxenus considerable progress had been made towards the scheme of
keys which was afterwards connected with his name. This may be
represented by the following table, in which for the sake of
comparison the later Hypo-lydian and Hypo-dorian are added in
brackets:


                   Mixo-lydian
      semitone - {
                   Lydian
        tone   - {
                   Phrygian
        tone   - {
                   Dorian
      semitone - {
                   Hypo-dorian [Hypo-lydian]
        tone   - {
                   Hypo-phrygian
        tone   - {
                   [Hypo-dorian]


[Footnote 1: _Harm._ p. 37, 19 Meib. [Greek: houto gar hoi men ton
harmonikon legousi barytaton men ton Hypodorion ton tonon, hemitonio
de oxyteron toutou ton Mixolydion, toutou de hemitonio ton Dorion,
tou de Doriou tono ton Phrygion: hosautos de kai tou Phrygiou ton
Lydion hetero tono.] Westphal (_Harmonik und Melopoeie_ p. 165) would
transfer the words [Greek: hemitonio ... Mixolydion] to the end of
the sentence, and insert [Greek: oxyteron] before [Greek: ton
Dorion]. The necessity for this insertion shows that Westphal's
transposition is not in itself an easy one. The only reason for it is
the difficulty of supposing that there could have been so great a
difference in the pitch of the Mixo-lydian scale. As to this,
however, see p. 23 (note).

The words [Greek: Hypophrygion aulon] have also been condemned by
Westphal (_Aristoxenus_, p. 453). He points out the curious
contradiction between [Greek: pros ten ton aulon trypesin blepontes]
and the complaint [Greek: ti d' esti pros ho blepontes ... ouden
eirekasin]. But if [Greek: pros ten ... blepontes] was a marginal
gloss, as Westphal suggests, it was doubtless a gloss on [Greek:
aulon], and if so, [Greek: aulon] is presumably sound. Since the
[Greek: aulos] was especially a Phrygian instrument, and regularly
associated with the Phrygian mode (as we know from Aristotle, see p.
13), nothing is more probable than that there was a variety of flute
called Hypo-phrygian, because tuned so as to yield the Hypo-phrygian
key, either by itself or as a modulation from the Phrygian.]

In this scheme the important feature--that which marks it as an
advance on the others referred to by Aristoxenus--is the conformity
which it exhibits with the diatonic scale. The result of this
conformity is that the keys stand in a certain relation to each
other. Taking any two, we find that certain notes are common to them.
So long as the intervals of pitch were quite arbitrary, or were
practically irrational quantities, such as three-quarters of a tone,
no such relation could exist. It now became possible to pass from one
key to another, _i. e._ to employ _modulation_ ([Greek: metabole]) as
a source of musical effect. This new system had evidently made some
progress when Aristoxenus wrote, though it was not perfected, and had
not passed into general use.




Sec. 11. _Names of Keys_ ([Greek: hypo-]).

A point that deserves special notice at this place is the use of the
prefix _Hypo-_ ([Greek: hypo-]) in the names of keys. In the final
Aristoxenean system _Hypo-_ implies that a key is lower by the
interval of a Fourth than the key to whose name it is prefixed. This
convention served to bring out the special relation between the two
keys, viz. to show that they are related (to use modern language) as
the keys of a tonic and dominant. In the scheme of keys now in
question there is only one instance of this use of _Hypo-_, namely in
the Hypo-phrygian, the most recently introduced. It must have been on
the analogy of this name that the term Hypo-dorian was shifted from
the key immediately below the Dorian to the new key a Fourth below
it, and that the new term Hypo-lydian was given to the old
Hypo-dorian in accordance with its similar relation to the Lydian. In
the time of Aristoxenus, then, this technical sense of _Hypo-_ had
not yet been established, but was coming into use. It led naturally
to the employment of _Hyper-_ in the inverse sense, viz. to denote a
key a Fourth higher (the key of the sub-dominant). By further steps,
of which there is no record, the Greek musicians arrived at the idea
of a key for every semitone in the octave; and thus was formed the
system of thirteen keys, ascribed to Aristoxenus by later writers.
(See the scheme at the end of this book, Table II.) Whether in fact
it was entirely his work may be doubted. In any case he had formed a
clear conception--the want of which he noted in his predecessors--of
the principles on which a theoretically complete scheme of keys
should be constructed.

In the discussions to which we have been referring, Aristoxenus
invariably employs the word [Greek: tonos] in the sense of 'key.' The
word [Greek: harmonia] in his writings is equivalent to 'Enharmonic
genus' ([Greek: genos enarmonion]), the _genus_ of music which made
use of the Enharmonic _diesis_ or quarter-tone. Thus he never speaks,
as Plato and Aristotle do, of the Dorian (or Phrygian or Lydian)
[Greek: harmonia], but only of the [Greek: tonoi] so named. There is
indeed one passage in which certain octave scales are said by
Aristoxenus to have been called [Greek: harmoniai]: but this, as will
be shown, is a use which is to be otherwise explained (see p. 54).




Sec. 12. _Plutarch's Dialogue on Music._

After the time of Aristoxenus the technical writers on music make
little or no use of the term [Greek: harmonia]. Their word for 'key'
is [Greek: tonos]; and the octachord scales which are distinguished
by the succession of their intervals are called 'species of the
octave' ([Greek: eide tou dia] [Greek: pason]). The modes of the
classical period, however, were still objects of antiquarian and
philosophic interest, and authors who treated them from this point of
view naturally kept up the old designation. A good specimen of the
writings of this class has survived in the _dialogus de musica_ of
Plutarch. Like most productions of the time, it is mainly a
compilation from earlier works now lost. Much of it comes from
Aristoxenus, and there is therefore a special fitness in dealing with
it in this place, by way of supplement to the arguments drawn
directly from the Aristoxenean _Harmonics_. The following are the
chief passages bearing on the subject of our enquiry:

(1) In cc. 15-17 we find a commentary of some interest on the
Platonic treatment of the modes. Plutarch is dwelling on the
superiority of the older and simpler music, and appeals to the
opinion of Plato.

'The Lydian mode ([Greek: harmonia]) Plato objects to because it is
high ([Greek: oxeia]) and suited to lamentation. Indeed it is said to
have been originally devised for that purpose: for Aristoxenus tells
us, in his first book on Music, that Olympus first employed the
Lydian mode on the flute in a dirge ([Greek: epikedeion aulesai
Lydisti]) over the Python. But some say that Melanippides began this
kind of music. And Pindar in his paeans says that the Lydian mode
([Greek: harmonia]) was first brought in by Anthippus in an ode on
the marriage of Niobe. But others say that Torrhebus first used that
mode, as Dionysius the Iambus relates.'

'The Mixo-lydian, too, is pathetic and suitable to tragedy. And
Aristoxenus says that Sappho was the inventor of the Mixo-lydian, and
that from her the tragic poets learned it. They combined it with the
Dorian, since that mode gives grandeur and dignity, and the other
pathos, and these are the two elements of tragedy. But in his
Historical Treatise on Music ([Greek: historika tes harmonias
hypomnemata]) he says that Pythoclides the flute-player was the
discoverer of it. And Lysis says that Lamprocles the Athenian,
perceiving that in it the disjunctive tone ([Greek: diazeuxis]) is
not where it was generally supposed to be, but is at the upper end of
the scale, made the form of it to be that of the octave from Paramese
to Hypate Hypaton ([Greek: toiouton autes apergasasthai to schema
hoion to apo parameses epi hypaten hypaton]). Moreover, it is said
that the relaxed Lydian ([Greek: epaneimenen Lydisti]), which is the
opposite of the Mixo-lydian, being similar to the Ionian ([Greek:
paraplesian ousan te Iadi]), was invented by Damon the Athenian.'

'These modes then, the one plaintive, the other relaxed ([Greek:
eklelymene]), Plato properly rejected, and chose the Dorian, as
befitting warlike and temperate men.'

In this passage the 'high-pitched Lydian' ([Greek: Syntonolydisti])
of Plato is called simply Lydian. There is every reason to suppose
that it is the mode called Lydian by Aristotle and Heraclides
Ponticus[1]. If this is so, it follows almost of necessity that the
Lydian of Plato, called slack ([Greek: chalara]) by him--Plutarch's
[Greek: epaneimene Lydisti]--is to be identified with the later
Hypo-lydian.

[Footnote 1: An objection to this identification has been based on
the words of Pollux, _Onom._ iv. 78 [Greek: kai harmonia men auletike
Doristi, Phrygisti, Lydios kai Ionike, kai syntonos Lydisti en
Anthippos exeure]. The source of this statement, or at least of the
latter part of it, is evidently the same as that of the notice in
Plutarch. The agreement with Plato's list makes it probable that this
source was some comment on the passage in the _Republic_. If so, it
can hardly be doubted that Pollux gives the original terms, the
Platonic [Greek: Lydisti] and [Greek: Syntonolydisti], and
consequently that the later Lydian is not to be found in his [Greek:
Lydios] (which is a 'relaxed' mode), but in his [Greek: syntonos
Lydisti]. There is no difficulty in supposing that the mode was
called [Greek: syntonos] merely in contrast to the other.]

The point, however, is not free from difficulty: for (as we have
seen, p. 18), the name Hypo-lydian is not in the list of keys given
by Aristoxenus--the key which was ultimately called Hypo-lydian being
known to him as the Hypo-dorian. If, however, the confusion in the
nomenclature of the keys was as great as Aristoxenus himself
describes, such a contradiction as this cannot be taken to prove
much[1].

The statement that the 'relaxed Lydian' was the opposite of the
Mixo-lydian, and similar to the Ionian, has given rise to much
speculation. In what sense, we naturally ask, can a key or a mode be
said to be 'opposite' or 'similar' to another? I venture to think
that it is evidently a mere paraphrase of Plato's language. The
relaxed Lydian is opposed to the Mixo-lydian because it is at the
other end of the scale in pitch; and it is similar to the Ionian
because the two are classed together (as [Greek: chalarai]) by Plato.

The Mixo-lydian, according to Aristoxenus, was employed by the tragic
poets in close union with the Dorian mode ([Greek: labontas syzeuxai
te Doristi]). The fact that the Mixo-lydian was just a Fourth higher
than the Dorian must have made the transition from the one to the
other a natural and melodious one. As Aristoxenus suggested, it would
be especially used to mark the passage from grandeur and dignity to
pathos which is the chief characteristic of tragedy ([Greek: he men
to megaloprepes kai axiomatikon apodidosin, he de to pathetikon,
memiktai de dia touton tragodia]). It is worth noticing that this
relation obtained in the scheme of the musicians who did not arrange
the keys according to the diatonic scale, but in some way suggested
by the form of the flute ([Greek: hoi pros ten ton aulon trypesin
blepontes]). It may therefore be supposed to have been established
before the relative pitch of other keys had been settled.

[Footnote 1: It seems not impossible that this difficulty with regard
to the 'slack Lydian' and Hypo-lydian may be connected with the
contradiction in the statement of Aristoxenus about the schemes of
keys in his time (p. 18). According to that account, if the text is
sound, some musicians placed the Mixo-lydian a semitone below the
Dorian--the Hypo-dorian being again a semitone lower. In this scheme,
then, the Mixo-lydian held the place of the later Hypo-lydian. The
conjecture may perhaps be hazarded, that this lower Mixo-lydian
somehow represents Plato's 'slack Lydian,' and eventually passed into
the Hypo-lydian.]

So far the passage of Plutarch goes to confirm the view of the
Platonic modes according to which they were distinguished chiefly, if
not wholly, by difference of pitch. We come now, however, to a
statement which apparently tends in the opposite direction, viz. that
a certain Lamprocles of Athens noticed that in the Mixo-lydian mode
the Disjunctive Tone ([Greek: diazeuxis]) was at the upper end of the
scale ([Greek: epi to oxy]), and reformed the scale accordingly. This
must refer to an octave scale of the form _b c d e f g a b_,
consisting of the two tetrachords _b-e_ and _e-a_, and the tone
_a-b_. Such an octave may or may not be in the Mixo-lydian key: it is
certainly of the Mixo-lydian species (p. 57).

In estimating the value of this piece of evidence it is necessary to
remark, in the first place, that the authority is no longer that of
Aristoxenus, but of a certain Lysis, of whom nothing else seems to be
known. That he was later than Aristoxenus is made probable by his way
of describing the Mixo-lydian octave, viz. by reference to the notes
in the Perfect System by which it is exemplified (Hypate Hypaton to
Paramese). In Aristoxenus, as we shall see (p. 31), the primitive
octave (from Hypate to Nete) is the only scale the notes of which are
mentioned by name. But even if the notice is comparatively early, it
is worth observing that the Mixo-lydian scale thus ascribed to
Lamprocles consists of two tetrachords of the normal type, viz. with
the semitone or [Greek: pyknon] at the lower end of the scale
(Diatonic _e f g a_, Enharmonic _e e* f a_). The difference is that
they are conjunct, whereas in the primitive standard octave (_e - e_)
the tetrachords are disjunct (_e-a b-e_). This, however, is a variety
which is provided for by the tetrachord Synemmenon in the Perfect
System, and which may have been allowed in the less complete scales
of earlier times. In any case the existence of a scale of this
particular form does not prove that the octaves of other species were
recognised in the same way.

(2) In another passage (c. 6) Plutarch says of the ancient music of
the cithara that it was characterised by perfect simplicity. It was
not allowed, he tells us, to change the mode ([Greek: metapherein tas
harmonias]) or the rhythm: for in the primitive lyrical compositions
called 'Nomes' ([Greek: nomoi]) they preserved in each its proper
pitch ([Greek: ten oikeian tasin]). Here the word [Greek: tasis]
indicates that by [Greek: harmoniai] Plutarch (or the older author
from whom he was quoting) meant particular _keys_. This is fully
confirmed by the use of [Greek: tonos] in a passage a little further
on (c. 8), where Plutarch gives an account of an innovation in this
matter made by Sacadas of Argos (fl. 590 B.C.). 'There being three
keys ([Greek: tonoi]) in the time of Polymnastus and Sacadas, viz.
the Dorian, Phrygian and Lydian, it is said that Sacadas composed a
strophe in each of these keys, and taught the chorus to sing them,
the first in the Dorian, the second in the Phrygian, and the third in
the Lydian key: and this composition was called the "three-part Nome"
([Greek: nomos trimeres]) on account of the change of key.' In
Westphal's _Harmonik und Melopoeie_ (ed. 1863, p. 76, cp. p. 62) he
explains this notice of the ancient modes ([Greek: harmoniai],
_Tonarten_), observing that the word [Greek: tonos] is there used
improperly for what the technical writers call [Greek: eidos tou dia
pason].

(3) In a somewhat similar passage of the same work (c. 19) Plutarch
is contending that the fewness of the notes in the scales used by the
early musicians did not arise from ignorance, but was characteristic
of their art, and necessary to its peculiar ethos. Among other points
he notices that the tetrachord Hypaton was not used in Dorian music
([Greek: en tois Doriois]), and this, he says, was not because they
did not know of that tetrachord--for they used it in other keys
([Greek: tonoi])--but they left it out in the Dorian key for the sake
of preserving its ethos, the beauty of which they valued ([Greek: dia
de ten tou ethous phylaken apheroun tou Doriou tonou, timontes to
kalon autou]). Here again Westphal (_Aristoxenus_, p. 476) has to
take [Greek: tonos] to mean [Greek: harmonia] or 'mode' (in his
language _Tonart_, not _Transpositionsscala_). For in the view of
those who distinguish [Greek: harmonia] from [Greek: tonos] it is the
[Greek: harmonia] upon which the ethos of music depends. Plutarch
himself had just been saying (in c. 17) that Plato preferred the
Dorian [Greek: harmonia] on account of its grave and elevated
character ([Greek: epei poly to semnon estin en te Doristi, tauten
proutimesen]). On the other hand the usual sense of [Greek: tonos] is
supported by the consideration that the want of the tetrachord
Hypaton would affect the pitch of the scale rather than the
succession of its intervals.

It seems to follow from a comparison of these three passages that
Plutarch was not aware of any difference of meaning between the words
[Greek: tonos] and [Greek: harmonia], or any distinction in the
scales of Greek music such as has been supposed to be conveyed by
these words. Another synonym of [Greek: tonos] which becomes very
common in the later writers on music is the word [Greek: tropos][1].
In the course of the passage of Plutarch already referred to (_De
Mus._ c. 17) it is applied to the Dorian mode, which Plutarch has
just called [Greek: harmonia]. As [Greek: tropos] is always used in
the later writers of the keys ([Greek: tonoi]) of Aristoxenus, this
may be added to the places in which [Greek: harmonia] has the same
meaning.




Sec. 13. _Modes employed on different Instruments._

In the anonymous treatise on music published by Bellermann[2] (c.
28), we find the following statement regarding the use of the modes
or keys in the scales of different instruments:

'The Phrygian mode ([Greek: harmonia]) has the first place on
wind-instruments: witness the first discoverers--Marsyas, Hyagnis,
Olympus--who were Phrygians. Players on the water-organ ([Greek:
hydraulai]) use only six modes ([Greek: tropoi]), viz. Hyper-lydian,
Hyper-ionian, Lydian, Phrygian, Hypo-lydian, Hypo-phrygian. Players
on the cithara tune their instrument to these four, viz.
Hyper-ionian, Lydian, Hypo-lydian, Ionian. Flute-players employ
seven, viz. Hyper-aeolian, Hyper-ionian, Hypo-lydian, Lydian,
Phrygian, Ionian, Hypo-phrygian. Musicians who concern themselves
with orchestic (choral music) use seven, viz. Hyper-dorian, Lydian,
Phrygian, Dorian, Hypo-lydian, Hypo-phrygian, Hypo-dorian.

[Footnote 1: Aristides Quintilianus uses [Greek: tropos] as the
regular word for 'key:' e.g. in p. 136 [Greek: en te ton tropon, hous
kai tonous ekalesamen, ekthesei]. So Alypius (p. 2 Meib.) [Greek:
dielein eis tous legomenous tropous te kai tonous, ontas pentekaideka
ton arithmon]. Also Bacchius in his catechism (p. 12 Meib.) [Greek:
hoi tous treis tropous adontes tinas adousi; Lydion, Phrygion,
Dorion; hoi de tous hepta tinas; Mixolydion, Lydion, Phrygion,
Dorion, Hypolydion, Hypophrygion, Hypodorion, touton poios estin
oxyteros? ho Mixolydios, k.t.l.] And Gaudentius (p. 21, l. 2) [Greek:
kath' hekaston tropon he tonon]. Cp. Dionys. Hal. _De Comp. Verb._ c.
19.]

[Footnote 2: _Anonymi scriptio de Musica_ (Berlin. 1841).]

In this passage it is evident that we have to do with keys of the
scheme attributed to Aristoxenus, including the two (Hyper-aeolian
and Hyper-lydian) which were said to have been added after his time.
The number of scales mentioned is sufficient to prove that the
reference is not to the seven species of the octave. Yet the word
[Greek: harmonia] is used of these keys, and with it, seemingly as an
equivalent, the word [Greek: tropos].

Pollux (_Onom._ iv. 78) gives a somewhat different account of the
modes used on the flute: [Greek: kai harmonia men auletike Doristi,
Phrygisti, Lydios kai Ionike, kai syntonos Lydisti hen Anthippos
exeure]. But this statement, as has been already pointed out (p. 22),
is a piece of antiquarian learning, and therefore takes no notice of
the more recent keys, as Hyper-aeolian and Hyper-ionian, or even
Hypo-phrygian (unless that is the Ionian of Pollux). The absence of
Dorian from the list given by the _Anonymus_ is curious: but it seems
that at that time it was equally unknown to the cithara and the
water-organ. There is therefore no reason to think that the two lists
are framed with reference to different things. That is to say,
[Greek: harmonia] in Pollux has the same meaning as [Greek: harmonia]
in the _Anonymus_, and is equivalent to [Greek: tonos].




Sec. 14. _Recapitulation--[Greek: harmonia] and [Greek: tonos]._

The inquiry has now reached a stage at which we may stop to consider
what result has been reached, especially in regard to the question
whether the two words [Greek: harmonia] and [Greek: tonos] denote two
sets of musical forms, or are merely two different names for the same
thing. The latter alternative appears to be supported by several
considerations.

1. From various passages, especially in Plato and Aristotle, it has
been shown that the modes anciently called [Greek: harmoniai]
differed in pitch, and that this difference in pitch was regarded as
the chief source of the peculiar ethical character of the modes.

2. The list of [Greek: harmoniai] as gathered from the writers who
treat of them, viz. Plato, Aristotle, and Heraclides Ponticus, is
substantially the same as the list of [Greek: tonoi] described by
Aristoxenus (p. 18): and moreover, there is an agreement in detail
between the two lists which cannot be purely accidental. Thus
Heraclides says that certain people had found out a new [Greek:
harmonia], the Hypo-phrygian; and Aristoxenus speaks of the
Hypo-phrygian [Greek: tonos] as a comparatively new one. Again, the
account which Aristoxenus gives of the Hypo-dorian [Greek: tonos] as
a key immediately below the Dorian agrees with what Heraclides says
of the Hypo-dorian [Greek: harmonia], and also with the mention of
Hypo-dorian and Hypo-phrygian (but not Hypo-lydian) in the
Aristotelian _Problems_. Once more, the absence of Ionian from the
list of [Greek: tonoi] in Aristoxenus is an exception which proves
the rule: since the name of the Ionian [Greek: harmonia] is similarly
absent from Aristotle.

3. The usage of the words [Greek: harmonia] and [Greek: tonos] is
never such as to suggest that they refer to different things. In the
earlier writers, down to and including Aristotle, [Greek: harmonia]
is used, never [Greek: tonos]. In Aristoxenus and his school we find
[Greek: tonos], and in later writers [Greek: tropos], but not [Greek:
harmonia]. The few writers (such as Plutarch) who use both [Greek:
tonos] and [Greek: harmonia] do not observe any consistent
distinction between them. Those who (like Westphal) believe that
there was a distinction, are obliged to admit that [Greek: harmonia]
is occasionally used for [Greek: tonos] and conversely.

4. If a series of names such as Dorian, Phrygian, Lydian and the rest
were applied to two sets of things so distinct from each other, and
at the same time so important in the practice of music, as what we
now call modes and keys, it is incredible that there should be no
trace of the double usage. Yet our authors show no sense even of
possible ambiguity. Indeed, they seem to prefer, in referring to
modes or keys, to use the adverbial forms [Greek: doristi], [Greek:
phrygisti], &c., or the neuter [Greek: ta doria], [Greek: ta
phrygia], &c., where there is nothing to show whether 'mode' or
'key,' [Greek: harmonia] or [Greek: tonos], is intended.




Sec. 15. _The Systems of Greek Music._

The arguments in favour of identifying the primitive national Modes
([Greek: harmoniai]) with the [Greek: tonoi] or keys may be
reinforced by some considerations drawn from the history and use of
another ancient term, namely [Greek: systema].

A System ([Greek: systema]) is defined by the Greek technical writers
as a group or complex of intervals ([Greek: to ek pleionon e henos
diastematon synkeimenon] Ps. Eucl.). That is to say, any three or
more notes whose _relative_ pitch is fixed may be regarded as forming
a particular System. If the notes are such as might be used in the
same melody, they are said to form a _musical_ System ([Greek:
systema emmeles]). As a matter of abstract theory it is evident that
there are very many combinations of intervals which in this sense
form a musical System. In fact, however, the variety of systems
recognised in the theory of Greek music was strictly limited. The
notion of a small number of scales, of a particular compass,
available for the use of the musician, was naturally suggested by the
ancient lyre, with its fixed and conventional number of strings. The
word for _string_ ([Greek: chorde]) came to be used with the general
sense of a _note_ of music; and in this way the several strings of
the lyre gave their names to the notes of the Greek gamut[1].




Sec. 16. _The Standard Octachord System._

In the age of the great melic poets the lyre had no more than seven
strings: but the octave was completed in the earliest times of which
we have accurate information. The scale which is assumed as matter of
common knowledge in the Aristotelian _Problems_ and the _Harmonics_
of Aristoxenus consists of eight notes, named as follows from their
place on the lyre:


      Nete ([Greek: neate] or [Greek: nete], lit. 'lowest,' our 'highest').
      Paranete  ([Greek: paranete], 'next to Nete').
      Trite ([Greek: trite], _i.e._ 'third' string).
      Paramese ([Greek: paramese] or [Greek: paramesos], 'next to Mese').
      Mese ([Greek: mese], 'middle string').
      Lichanos ([Greek: lichanos], _i.e._ 'forefinger' string).
      Parhypate ([Greek: parypate]).
      Hypate ([Greek: hypate], lit. 'uppermost,' our 'lowest').


It will be seen that the conventional sense of high and low in the
words [Greek: hypate] and [Greek: neate] was the reverse of the
modern usage.

The musical scale formed by these eight notes consists of two
_tetrachords_ or scales of four notes, and a major tone. The lower of
the tetrachords consists of the notes from Hypate to Mese, the higher
of those from Paramese to Nete: the interval between Mese and
Paramese being the so-called _Disjunctive Tone_ ([Greek: tonos
diazeuktikos]). Within each tetrachord the intervals depend upon the
_Genus_ ([Greek: genos]). Thus the four notes just mentioned--Hypate,
Mese, Paramese, Nete--are the same for every genus, and accordingly
are called the 'standing' or 'immoveable' notes ([Greek: phthongoi
hestotes, akinetoi]), while the others vary with the genus, and are
therefore 'moveable' ([Greek: pheromenoi]).

[Footnote 1: This is especially evident in the case of the Lichanos;
as was observed by Aristides Quintilianus, who says (p. 10 Meib.):
[Greek: hai kai to genei lichanoi prosegoreuthesan, homonymos to
plettonti daktylo ten echousan autas chorden onomastheisai]. But
Trite also is doubtless originally the 'third string' rather than the
'third note.']

In the ordinary Diatonic genus the intervals of the tetrachords are,
in the ascending order, semitone + tone + tone: _i.e._ Parhypate is a
semitone above Hypate, and Lichanos a tone above Parhypate. In the
Enharmonic genus the intervals are two successive quarter-tones
([Greek: diesis]) followed by a ditone or major Third: consequently
Parhypate is only a quarter of a tone above Hypate, and Lichanos
again a quarter of a tone above Parhypate. The group of three notes
separated in this way by small intervals (viz. two successive
quarter-tones) is called a [Greek: pyknon]. If we use an asterisk to
denote that a note is raised a quarter of a tone, these two scales
may be represented in modern notation as follows:


        _Diatonic._              _Enharmonic._

      e  =Nete=      \           e  =Nete=      \
      d  Paranete          }        ( c  Paranete          }
      c  Trite             }    +---( b* Trite             }
      b  =Paramese=  /     |   ( b  =Paramese=  /
      a  =Mese=      \     |     a  =Mese=      \
      g  Lichanos          }    |   ( f  Lichanos          }
      f  Parhypate         }    | +-( e* Parhypate         }
      e  =Hypate=    /     | | ( e  =Hypate=    /
                                | |
                  [Greek: pyknon] [Greek: pyknon]


In the Chromatic genus and its varieties the division is of an
intermediate kind. The interval between Lichanos and Mese is more
than one tone, but less than two: and the two other intervals, as in
the enharmonic, are equal.

The most characteristic feature of this scale, in contrast to those
of the modern Major and Minor, is the place of the small intervals
(semitone or [Greek: pyknon]), which are always the lowest intervals
of a tetrachord. It is hardly necessary to quote passages from
Aristotle and Aristoxenus to show that this is the succession of
intervals assumed by them. The question is asked in the Aristotelian
_Problems_ (xix. 4), why Parhypate is difficult to sing, while Hypate
is easy, although there is only a diesis between them ([Greek: kaitoi
diesis hekateras]). Again (_Probl._ xix. 47), speaking of the old
heptachord scale, the writer says that the Paramese was left out, and
consequently the Mese became the lowest note of the upper [Greek:
pyknon], _i.e._ the group of 'close' notes consisting of Mese, Trite,
and Paranete. Similarly Aristoxenus (_Harm._ p. 23) observes that the
'space' of the Lichanos, _i.e._ the limit within which it varies in
the different genera, is a tone while the space of the Parhypate is
only a diesis, for it is never nearer Hypate than a diesis or further
off than a semitone.




Sec. 17. _Earlier Heptachord Scales._

Regarding the earlier seven-stringed scales which preceded this
octave our information is scanty and somewhat obscure. The chief
notice on the subject is the following passage of the Aristotelian
_Problems_:


     _Probl._ xix. 47 [Greek: dia ti hoi archaioi heptachordous
     poiountes tas harmonias ten hypaten all' ou ten neten
     katelipon: he ou ten] [Greek: hypaten] (leg. [Greek: neten]),
     [Greek: alla ten nyn paramesen kaloumenen apheroun kai to
     toniaion diastema; echronto de te eschate mese tou epi to oxy
     pyknou; did kai mesen auten proseloreusan [he] oti en tou men
     ano tetrachordon teleute, tou de kato arche, kai meson eiche
     logon tono ton akron?]

     'Why did the ancient seven-stringed scales include Hypate but
     not Nete? Or should we say that the note omitted was not Nete,
     but the present Paramese and the interval of a tone (_i.e._
     the disjunctive tone)? The Mese, then, was the lowest note of
     the upper [Greek: pyknon]: whence the name [Greek: mese],
     because it was the end of the upper tetrachord and beginning
     of the lower one, and was in pitch the middle between the
     extremes.'


This clearly implies two conjunct tetrachords--

[Music: _e f g a a# c d_ \---- /\----- /]

In another place (_Probl._ xix. 32) the question is asked, why the
interval of the octave is called [Greek: dia pason], not [Greek: di'
okto],--as the Fourth is [Greek: dia tessaron], the Fifth [Greek: dia
pente]. The answer suggested is that there were anciently seven
strings, and that Terpander left out the Trite and added the Nete.
That is to say, Terpander increased the compass of the scale from the
ancient two tetrachords to a full Octave; but he did not increase the
number of strings to eight. Thus he produced a scale like the
standard octave, but with one note wanting; so that the term [Greek:
di okto] was inappropriate.

Among later writers who confirm this account we may notice
Nicomachus, p. 7 Meib. [Greek: mese dia tessaron pros amphotera en te
heptachordo kata to palaion diestosa]: and p. 20 [Greek: te toinyn
archaiotropo lyra toutesti te heptachordo, kata synaphen ek duo
tetrachordon synestose k.t.l.]

It appears then that two kinds of seven-stringed scales were known,
at least by tradition: viz. (1) a scale composed of two conjunct
tetrachords, and therefore of a compass less than an octave by one
tone; and (2) a scale of the compass of an octave, but wanting a
note, viz. the note above Mese. The existence of this incomplete
scale is interesting as a testimony to the force of the tradition
which limited the number of strings to seven.




Sec. 18. _The Perfect System._

The term 'Perfect System' ([Greek: systema teleion]) is applied by
the technical writers to a scale which is evidently formed by
successive additions to the heptachord and octachord scales explained
in the preceding chapter. It may be described as a combination of two
scales, called the Greater and Lesser Perfect System.

The Greater Perfect System ([Greek: systema teleion meizon]) consists
of two octaves formed from the primitive octachord System by adding a
tetrachord at each end of the scale. The new notes are named like
those of the adjoining tetrachord of the original octave, but with
the name of the tetrachord added by way of distinction. Thus below
the original Hypate we have a new tetrachord Hypaton ([Greek:
tetrachordon hypaton]), the notes of which are accordingly called
Hypate Hypaton, Parhypate Hypaton, and Lichanos Hypaton: and
similarly above Nete we have a tetrachord Hyperbolaion. Finally the
octave downwards from Mese is completed by the addition of a note
appropriately called Proslambanomenos.

The Lesser Perfect System ([Greek: systema teleion elasson]) is
apparently based upon the ancient heptachord which consisted of two
'conjunct' tetrachords meeting in the Mese. This scale was extended
downwards in the same way as the Greater System, and thus became a
scale of three tetrachords and a tone.

These two Systems together constitute the Perfect and 'unmodulating'
System ([Greek: systema teleion ametabolon]), which may be
represented in modern notation[1] as follows:


      a  Nete Hyperbolaion     \  Tetrachord
      g  Paranete Hyperbolaion  } Hyperbolaion
      f  Trite Hyperbolaion    /
      e  Nete Diezeugmenon
      d  Paranete Diezeugmenon \  Tetrachord
      c  Trite Diezeugmenon     } Diezeugmenon
      b  Paramese              /
            d  Nete Synemmenon       \ Tetrachord
            c  Paranete Synemmenon    } Synemmenon
            b flat   Trite Synemmenon/
      a  Mese            \
      g  Lichanos Meson   } Tetrachord
      f  Parhypate Meson  } Meson
      e  Hypate Meson    /
      d  Lichanos Hypaton  \ Tetrachord
      c  Parhypate Hypaton  }  Hypaton
      b  Hypate Hypaton    /
      a  Proslambanomenos


[Footnote 1: The correspondence between ancient and modern musical
notation was first determined in a satisfactory way by Bellermann
(_Die Tonleitern und Musiknoten der Griechen_), and Fortlage (_Das
musicalische System der Griechen_).]

No account of the Perfect System is given by Aristoxenus, and there
is no trace in his writings of an extension of the standard scale
beyond the limits of the original octave. In one place indeed
(_Harm._ p. 8, 12 Meib.) Aristoxenus promises to treat of Systems,
'and among them of the perfect System' ([Greek: peri te ton allon kai
tou teleiou]). But we cannot assume that the phrase here had the
technical sense which it bore in later writers. More probably it
meant simply the octave scale, in contrast to the tetrachord and
pentachord--a sense in which it is used by Aristides Quintilianus, p.
11 Meib. [Greek: synemmenon de eklethe to holon systema hoti to
prokeimeno teleio to mechri meses syneptai], 'the whole scale was
called conjunct because it is conjoined to the complete scale that
reaches up to Mese' (_i.e._ the octave extending from
Proslambanomenos to Mese). So p. 16 [Greek: kai ha men auton esti
teleia, ha d' ou, atele men tetrachordon, pentachordon, teleion de
oktachordon.] This is a use of [Greek: teleios] which is likely
enough to have come from Aristoxenus. The word was doubtless applied
in each period to the most complete scale which musical theory had
then recognised.

Little is known of the steps by which this enlargement of the Greek
scale was brought about. We shall not be wrong in conjecturing that
it was connected with the advance made from time to time in the form
and compass of musical instruments[1]. Along with the lyre, which
kept its primitive simplicity as the instrument of education and
everyday use, the Greeks had the cithara ([Greek: kithara]), an
enlarged and improved lyre, which, to judge from the representations
on ancient monuments, was generally seen in the hands of professional
players ([Greek: kitharodoi]). The development of the cithara showed
itself in the increase, of which we have good evidence even before
the time of Plato, in the number of the strings.

[Footnote 1: This observation was made by ancient writers, _e.g._ by
Adrastus (Peripatetic philosopher of the second cent. A.D.): [Greek:
epeuxemenes de tes mousikes kai polychordon kai polyphthongon
gegonoton organon to proslephthenai kai epi to bary kai epi to oxy
tois pro[:y]parchousin okto phthongois allous pleionas, <DW25>s k.t.l.
(Theon Smyrn. c. 6).]

The poet Ion, the contemporary of Sophocles, was the author of an
epigram on a certain ten-stringed lyre, which seems to have had a
scale closely approaching that of the Lesser Perfect System[1]. A
little later we hear of the comic poet Pherecrates attacking the
musician Timotheus for various innovations tending to the loss of
primitive simplicity, in particular the use of twelve strings[2].
According to a tradition mentioned by Pausanias, the Spartans
condemned Timotheus because in his cithara he had added four strings
to the ancient seven. The offending instrument was hung up in the
Scias (the place of meeting of the Spartan assembly), and apparently
was seen there by Pausanias himself (Paus. iii. 12, 8).

[Footnote 1: The epigram is quoted in the pseudo-Euclidean
_Introductio_, p. 19 (Meib.): [Greek: ho de] (sc. [Greek: Ion])
[Greek: en dekachordo lyra] (_i.e._ in a poem on the subject of the
ten-stringed lyre):--

              [Greek: ten dekabamona taxin echousa
      tas symphonousas harmonias triodous;
    prin men s' heptatonon psallon dia tessara pantes
      Hellenes, spanian mousan aeiramenoi.]

'The triple ways of music that are in concord' must be the three
conjunct tetrachords that can be formed with ten notes (_b c d e f g
a b-flat c d_). This is the scale of the Lesser Perfect System before
the addition of the Proslambanomenos.]

[Footnote 2: Pherecrates [Greek: cheiron] fr. 1 (quoted by Plut. _de
Mus._ c. 30). It is needless to refer to the other traditions on the
subject, such as we find in Nicomachus (_Harm._ p. 35) and Boethius.]

A similar or still more rapid development took place in the flute
([Greek: aulos]). The flute-player Pronomus of Thebes, who was said
to have been one of the instructors of Alcibiades, invented a flute
on which it was possible to play in all the modes. 'Up to his time,'
says Pausanias (ix. 12, 5), 'flute-players had three forms of flute:
with one they played Dorian music; a different set of flutes served
for the Phrygian mode ([Greek: harmonia]); and the so-called Lydian
was played on another kind again. Pronomus was the first who devised
flutes fitted for every sort of mode, and played melodies different
in mode on the same flute.' The use of the new invention soon became
general, since in Plato's time the flute was the instrument most
distinguished by the multiplicity of its notes: cp. Rep. p. 399
[Greek: ti de? aulopoious e auletas paradexei eis ten polin? e ou
touto polychordotaton?] Plato may have had the invention of Pronomus
in mind when he wrote these words.

With regard to the order in which the new notes obtained a place in
the schemes of theoretical musicians we have no trustworthy
information. The name [Greek: proslambanomenos], applied to the
lowest note of the Perfect System, points to a time when it was the
last new addition to the scale. Plutarch in his work on the _Timaeus_
of Plato ([Greek: peri tes en Timaio psychogonias]) speaks of the
Proslambanomenos as having been added in comparatively recent times
(p. 1029 _c_ [Greek: hoi de neoteroi ton proslambanomenon tono
diapheronta tes hypates epi to bary taxantes to men holon diastema
dis dia pason epoiesan]). The rest of the Perfect System he ascribes
to 'the ancients' ([Greek: tous palaious ismen hypatas men dyo, treis
de netas, mian de mesen kai mian paramesen tithemenous]). An earlier
addition--perhaps the first made to the primitive octave--was a note
called Hyperhypate, which was a tone below the old Hypate, in the
place afterwards occupied on the Diatonic scale by Lichanos Hypaton.
It naturally disappeared when the tetrachord Hypaton came into use.
It is only mentioned by one author, Thrasyllus (quoted by Theon
Smyrnaeus, cc. 35-36[1]).

[Footnote 1: The term [Greek: hyperypate] had all but disappeared
from the text of Theon Smyrnaeus in the edition of Bullialdus (Paris,
1644), having been corrupted into [Greek: hypate] or [Greek:
parypate] in every place except one (p. 141, 3). It has been restored
from MSS. in the edition of Hiller (Teubner, Leipzig, 1878). The word
occurs also in Aristides Quintilianus (p. 10 Meib.), where the plural
[Greek: hyperypatai] is used for the notes below Hypate, and in
Boethius (_Mus._ i. 20).

It may be worth noticing also that Thrasyllus uses the words [Greek:
diezeugmene] and [Greek: hyperbolaia] in the sense of [Greek: nete
diezeugmenon] and [Greek: nete hyperbolaion] (Theon Smyrn. _l. c._).]

The notes of the Perfect System, with the intervals of the scale
which they formed, are fully set out in the two treatises that pass
under the name of the geometer Euclid, viz. the _Introductio
Harmonica_ and the _Sectio Canonis_. Unfortunately the authorship of
both these works is doubtful[1]. All that we can say is that if the
Perfect System was elaborated in the brief interval between the time
of Aristotle and that of Euclid, the materials for it must have
already existed in musical practice.

[Footnote 1: _The Introduction to Harmonics_ ([Greek: eisagoge
harmonike]) which bears the name of Euclid in modern editions
(beginning with J. Pena, Paris, 1557) cannot be his work. In some
MSS. it is ascribed to Cleonides, in others to Pappus, who was
probably of the fourth century A.D. The author is one of the [Greek:
harmonikoi] or Aristoxeneans, who adopt the method of equal
temperament. He may perhaps be assigned to a comparatively early
period on the ground that he recognises only the thirteen keys
ascribed to Aristoxenus--not the fifteen keys given by most later
writers (Aristides Quint., p. 22 Meib.). For some curious evidence
connecting it with the name of the otherwise unknown writer
Cleonides, see K. von Jan, _Die Harmonik des Aristoxenianers
Kleonides_ (Landsberg, 1870). The _Section of the Canon_ ([Greek:
kanonos katatome]) belongs to the mathematical or Pythagorean school,
dividing the tetrachord into two major tones and a [Greek: leimma]
which is somewhat less than a semitone. In point of form it is
decidedly Euclidean: but we do not find it referred to by any writer
before the third century A.D.--the earliest testimony being that of
Porphyry (pp. 272-276 in Wallis' edition).]




Sec. 19. _Relation of System and Key._

Let us now consider the relation between this fixed or standard scale
and the varieties denoted by the terms [Greek: harmonia] and [Greek:
tonos].

With regard to the [Greek: tonoi] or Keys of Aristoxenus we are not
left in doubt. A system, as we have seen, is a series of notes whose
_relative_ pitch is fixed. The key in which the System is taken fixes
the absolute pitch of the series. As Aristoxenus expresses it, the
Systems are melodies set at the pitch of the different keys ([Greek:
tous tonous, eph' hon tithemena ta systemata melodeitai]). If then we
speak of Hypate or Mese (just as when we speak of a moveable Do), we
mean as many different notes as there are keys: but the Dorian Hypate
or the Lydian Mese has an ascertained pitch. The Keys of Aristoxenus,
in short, are so many transpositions of the scale called the Perfect
System.

Such being the relation of the standard System to the key, can we
suppose any different relation to have subsisted between the standard
System and the ancient 'modes' known to Plato and Aristotle under the
name of [Greek: harmoniai]?

It appears from the language used by Plato in the _Republic_ that
Greek musical instruments differed very much in the variety of modes
or [Greek: harmoniai] of which they were susceptible. After Socrates
has determined, in the passage quoted above (p. 7), that he will
admit only two modes, the Dorian and Phrygian, he goes on to observe
that the music of his state will not need a multitude of strings, or
an instrument of all the modes ([Greek: panarmonion])[1]. 'There will
be no custom therefore for craftsmen who make triangles and harps and
other instruments of many notes and many modes. How then about makers
of the flute ([Greek: aulos]) and players on the flute? Has not the
flute the greatest number of notes, and are not the scales which
admit all the modes simply imitations of the flute? There remain then
the lyre and the cithara for use in our city; and for shepherds in
the country a syrinx (pan's pipes).' The lyre, it is plain, did not
admit of changes of mode. The seven or eight strings were tuned to
furnish the scale of one mode, not of more. What then is the relation
between the mode or [Greek: harmonia] of a lyre and the standard
scale or [Greek: systema] which (as we have seen) was based upon the
lyre and its primitive gamut?

[Footnote 1: Plato, Rep. p. 399: [Greek: ouk ara, en d' ego,
polychordias ge oude panarmoniou hemin deesei en tais odais te kai
melesin. Ou moi, ephe, phainetai. Trigonon ara kai pektidon kai
panton organon hosa polychorda kai polyarmonia demiourgous ou
threpsomen. Ou phainometha. Ti de? aulopoious e auletas paradexei eis
ten polin? e ou touto polychordotaton, kai auta ta panarmonia aulou
tynchanei onta mimema? Dela de, e d' hos. Lyra de soi, en d' ego, kai
kithara leipetai, kai kata polin chresima; kai au kat' agrous tois
nomeusi syrinx an tis eie.]

The [Greek: aulos] was not exactly a flute. It had a mouthpiece which
gave it the character rather of the modern oboe or clarinet: see the
_Dictionary of Antiquities_, S. V. TIBIA. The [Greek: panarmonion] is
not otherwise known, and the passage in Plato does not enable us to
decide whether it was a real instrument or only a scale or
arrangement of notes.]

If [Greek: harmonia] means 'key,' there is no difficulty. The scale
of a lyre was usually the standard octave from Hypate to Nete: and
that octave might be in any one key. But if a mode is somehow
characterised by a particular succession of intervals, what becomes
of the standard octave? No one succession of intervals can then be
singled out. It may be said that the standard octave is in fact the
scale of a particular mode, which had come to be regarded as the
type, viz. the Dorian. But there is no trace of any such prominence
of the Dorian mode as this would necessitate. The philosophers who
recognise its elevation and Hellenic purity are very far from
implying that it had the chief place in popular regard. Indeed the
contrary was evidently the case[1].

[Footnote 1: The passage quoted above from the _Knights_ of
Aristophanes (p. 7) is sufficient to show that a marked preference
for the Dorian mode would be a matter for jest.]




Sec. 20. _Tonality of the Greek musical scale._

It may be said here that the value of a series of notes as the basis
of a distinct mode--in the modern sense of the word--depends
essentially upon the _tonality_. A single scale might yield music of
different modes if the key-note were different. It is necessary
therefore to collect the scanty notices which we possess bearing upon
the tonality of Greek music. The chief evidence on the subject is a
passage of the _Problems_, the importance of which was first pointed
out by Helmholtz[1]. It is as follows:


     Arist. _Probl._ xix. 20: [Greek: Dia ti ean men tis ten mesen
     kinese hemon, harmosas tas allas chordas, kai chretai to
     organo, ou monon hotan kata ton tes meses genetai phthongon
     lypei kai phainetai anarmoston, alla kai kata ten allen
     melodian, ean de ten lichanon e tina allon phthongon, tote
     phainetai diapherein monon hotan kakeine tis chretai? e
     eulogos touto symbainei? panta gar ta chresta mele pollakis te
     mese chretai, kai pantes hoi agathoi poietai pykna pros ten
     mesen apantosi, kan apelthosi tachy epanerchontai, pros de
     allen houtos oudemian. kathaper ek ton logon enion
     exairethenton syndesmon ouk estin ho logos Hellenikos, hoion
     to te kai to kai, enioi de outhen lypousi, dia to tois men
     anankaion einai chresthai pollakis, ei estai logos, tois de
     me, houto kai ton phthongon he mese hosper syndesmos esti, kai
     malista ton kalon, dia to pleistakis enyparchein ton phthongon
     autes.]

     'Why is it that if the Mese is altered, after the other
     strings have been tuned, the instrument is felt to be out of
     tune, not only when the Mese is sounded, but through the whole
     of the music,--whereas if the Lichanos or any other note is
     out of tune, it seems to be perceived only when that note is
     struck? Is it to be explained on the ground that all good
     melodies often use the Mese, and all good composers resort to
     it frequently, and if they leave it soon return again, but do
     not make the same use of any other note? just as language
     cannot be Greek if certain conjunctions are omitted, such as
     [Greek: te] and [Greek: kai], while others may be dispensed
     with, because the one class is necessary for language, but not
     the other: so with musical sounds the Mese is a kind of
     'conjunction,' especially of beautiful sounds, since it is
     most often heard among these.'


[Footnote 1: _Die Lehre von den Tonempfindungen_, p. 367, ed. 1863.]

In another place (xix. 36) the question is answered by saying that
the notes of a scale stand in a certain relation to the Mese, which
determines them with reference to it ([Greek: he taxis he hekastes
ede di' ekeinen]): so that the loss of the Mese means the loss of the
ground and unifying element of the scale ([Greek: arthentos tou
aitiou tou hermosthai kai tou synechontos])[1].

These passages imply that in the scale known to Aristotle, viz. the
octave _e - e_, the Mese _a_ had the character of a Tonic or
key-note. This must have been true _a fortiori_ of the older
seven-stringed scale, in which the Mese united the two conjunct
tetrachords. It was quite in accordance with this state of things
that the later enlargement completed the octaves from Mese downwards
and upwards, so that the scale consisted of two octaves of the form
_a-a_. As to the question how the Tonic character of the Mese was
shown, in what parts of the melody it was necessarily heard, and the
like, we can but guess. The statement of the _Problems_ is not
repeated by any technical writer, and accordingly it does not appear
that any rules on the subject had been arrived at. It is significant,
perhaps, that the frequent use of the Mese is spoken of as
characteristic of _good_ melody ([Greek: panta ta chresta mele
pollakis te mese chretai]), as though tonality were a merit rather
than a necessity.

Another passage of the _Problems_ has been thought to show that in
Greek music the melody ended on the Hypate. The words are these
(_Probl._ xix. 33):


  [Greek: Dia ti euarmostoteron apo tou oxeos epi to bary e apo
  tou]


[Footnote 1: So in the Euclidean _Sectio Canonis_ the propositions
which deal with the 'movable' notes, viz. Paranete and Lichanos
(Theor. xvii) and Parhypate and Trite (Theor. xviii), begin by
postulating the Mese ([Greek: esto gar mese ho B k.t.l.]).]


     [Greek: bareos epi to oxy; poteron hoti to apo tes arches
     ginetai archesthai? he gar mese kai hegemon oxytate tou
     tetrachordou; to de ouk ap' arches all' apo teleutes.]

     'Why is a descending scale more musical than an ascending one?
     Is it that in this order we begin with the beginning,--since
     the Mese or leading note[1] is the highest of the
     tetrachord,--but with the reverse order we begin with the
     end?'


There is here no explicit statement that the melody ended on the
Hypate, or even that it began with the Mese. In what sense, then, was
the Mese a 'beginning' ([Greek: arche]), and the Hypate an 'end'? In
Aristotelian language the word [Greek: arche] has various senses. It
might be used to express the relation of the Mese to the other notes
as the basis or ground-work of the scale. Other passages, however,
point to a simpler explanation, viz. that the order in question was
merely conventional. In _Probl._ xix. 44 it is said that the Mese is
the beginning ([Greek: arche]) of one of the two tetrachords which
form the ordinary octave scale (viz. the tetrachord Meson); and again
in _Probl._ xix. 47 that in the old heptachord which consisted of two
conjunct tetrachords (_e-a-d_) the Mese (_a_) was the end of the
upper tetrachord and the beginning of the lower one ([Greek: hoti en
tou men ano tetrachordou teleute, tou de kato arche]). In this last
passage it is evident that there is no reference to the beginning or
end of the melody.

[Footnote 1: The term [Greek: hegemon] or 'leading note' of the
tetrachord Meson, here applied to the Mese, is found in the same
sense in Plutarch, _De Mus._ c. 11, where [Greek: ho peri ton
hegemona keimenos tonos] means the disjunctive tone. Similarly
Ptolemy (_Harm._ i. 16) speaks of the tones in a diatonic scale as
being [Greek: en tois hegoumenois topois], the semitones [Greek: en
tois hepomenois] (sc. of the tetrachord): and again of the ratio 5:4
(the major Third) as the 'leading' one of an Enharmonic tetrachord
([Greek: ton epitetarton hos estin hegoumenos tou enarmoniou
genous]).]

Another instance of the use of [Greek: arche] in connexion with the
musical scale is to be found in the _Metaphysics_ (iv. 11, p. 1018
_b_ 26), where Aristotle is speaking of the different senses in which
things may be prior and posterior:


     [Greek: Ta de kata taxin; tauta d' estin hosa pros ti hen
     horismenon diesteke kata ton logon, hoion parastates
     tritostatou proteron, kai paranete netes; entha men gar ho
     koryphaios, entha de he mese arche.]

     'Other things [are prior and posterior] in _order_: viz. those
     which are at a varying interval from some one definite thing;
     as the second man in the rank is prior to the third man, and
     the Paranete to the Nete: for in the one case the coryphaeus
     is the starting-point, in the other the Mese.'


Here the Mese is again the [Greek: arche] or beginning, but the order
is the ascending one, and consequently the Nete is the end. The
passage confirms what we have learned of the relative importance of
the Mese: but it certainly negatives any inference regarding the note
on which the melody ended.

It appears, then, that the Mese of the Greek standard System had the
functions of a key-note in that System. In other words, the music was
in the _mode_ (using that term in the modern sense) represented by
the octave _a-a_ of the natural key--the Hypo-dorian or Common
Species. We do not indeed know how the predominant character of the
Mese was shown--whether, for example, the melody ended on the Mese.
The supposed evidence for an ending on the Hypate has been shown to
be insufficient. But we may at least hold that as far as the Mese was
a key-note, so far the Greek scale was that of the modern Minor mode
(descending). The only way of escape from this conclusion is to deny
that the Mese of _Probl._ xix. 20 was the note which we have
understood by the term--the Mese of the standard System. This, as we
shall presently see, is the plea to which Westphal has recourse.




Sec. 21. _The Species of a Scale._

The object of the preceding discussion has been to make it clear that
the theory of a system of modes--in the modern sense of the
word--finds no support from the earlier authorities on Greek music.
There is, however, evidence to show that Aristoxenus, and perhaps
other writers of the time, gave much thought to the varieties to be
obtained by taking the intervals of a scale in different order. These
varieties they spoke of as the _forms_ or _species_ ([Greek:
schemata, eide]) of the interval which measured the compass of the
scale in question. Thus, the interval of the Octave ([Greek: dia
pason]) is divided into seven intervals, and these are, in the
Diatonic genus, five tones and two semitones, in the Enharmonic two
ditones, four quarter-tones, and a tone. As we shall presently see in
detail, there are seven species of the Octave in each genus. That is
to say, there are seven admissible octachord scales ([Greek:
systemata emmele]), differing only in the succession of the intervals
which compose them.

Further, there is evidence which goes to connect the seven species of
the Octave with the Modes or [Greek: harmoniai]. In some writers
these species are described under names which are familiar to us in
their application to the modes. A certain succession of intervals is
called the Dorian species of the Octave, another succession is called
the Phrygian species, and so on for the Lydian, Mixo-lydian,
Hypo-dorian, Hypo-phrygian, and Hypo-lydian. It seems natural to
conclude that the species or successions of intervals so named were
characteristic in some way of the modes which bore the same names,
consequently that the modes were not keys, but modes in the modern
sense of the term.

In order to estimate the value of this argument, it is necessary to
ask, (1) how far back we can date the use of these names for the
species of the Octave, and (2) in what degree the species of the
Octave can be shown to have entered into the practice of music at any
period. The answer to these questions must be gathered from a careful
examination of all that Aristoxenus and other early writers say of
the different musical scales in reference to the order of their
intervals.




Sec. 22. _The Scales as treated by Aristoxenus._

The subject of the musical scales ([Greek: systemata]) is treated by
Aristoxenus as a general problem, without reference to the scales in
actual use. He complains that his predecessors dealt only with the
octave scale, and only with the Enharmonic genus, and did not address
themselves to the real question of the melodious sequence of
intervals. Accordingly, instead of beginning with a particular scale,
such as the octave, he supposes a scale of indefinite compass,--just
as a mathematician postulates lines and surfaces of unlimited
magnitude. His problem virtually is, given any interval known to the
particular genus supposed, to determine what intervals can follow it
on a musical scale, either ascending or descending. In the Diatonic
genus, for example, a semitone must be followed by two tones, so as
to make up the interval of a Fourth. In the Enharmonic genus the
dieses or quarter-tones can only occur two together, and every such
pair of dieses ([Greek: pyknon]) must be followed in the ascending
order by a ditone, in the descending order by a ditone or a tone. By
these and similar rules, which he deduces mathematically from one or
two general principles of melody, Aristoxenus in effect determines
all the possible scales of each genus, without restriction of compass
or pitch[1]. But whenever he refers for the purpose of illustration
to a scale in actual use, it is always the standard octave already
described (from Hypate to Nete), or a part of it. Thus nothing can be
clearer than the distinction which he makes between the theoretically
infinite scale, subject only to certain principles or laws
determining the succession of intervals, and the eight notes, of
fixed relative pitch, which constituted the gamut of practical music.

The passages in which Aristoxenus dwells upon the advance which he
has made upon the methods of his predecessors are of considerable
importance for the whole question of the species of the Octave. There
are three or four places which it will be worth while to quote.


     1. Aristoxenus, _Harm._ p. 2, 15 Meib.: [Greek: ta gar
     diagrammata autois ton enarmonion] ([Greek: harmonion] MSS.)
     [Greek: ekkeitai monon systematon, diatonon d' e chromatikon
     oudeis popoth' heoraken; kaitoi ta diagrammata g' auton edelou
     ten pasan tes melodias taxin, en hois peri systematon
     oktachordon enarmonion] ([Greek: harmonion] MSS.) [Greek:
     monon elegon, peri de ton allon genon te kai schematon en auto
     te to genei tonto kai tois loipois oud' epecheirei oudeis
     katamanthanein.]


[Footnote 1: The investigation occupies a considerable space in his
_Harmonics_, viz. pp. 27-29 Meib. (from the words [Greek: peri de
synecheias kai tou hexes]), and again pp. 58-72 Meib.]


     'The diagrams of the earlier writers set forth Systems in the
     Enharmonic genus only, never in the Diatonic or Chromatic: and
     yet these diagrams professed to give the whole scheme of their
     music, and in them they treated of Enharmonic octave Systems
     only; of other genera and other forms of this or any genus no
     one attempted to discover anything.'

     2. Ibid. p. 6, 20 Meib.: [Greek: ton d' allon katholou men
     kathaper emprosthen eipomen oudeis heptai, henos de systematos
     Eratokles epecheirese kath' hen genos exarithmesai ta schemata
     tou dia pason apodeiktikos te periphora ton diastematon
     deiknys; ou katamathon hoti, me prosapodeichthenton] (qu.
     [Greek: proapod.]) [Greek: ton de tou dia pente schematon kai
     ton tou dia tessaron pros de toutois kai tes syntheseos auton
     tis pot' esti kath' hen emmelos syntithentai, pollaplasia ton
     hepta symbainein gignesthai deiknytai.]

     'The other Systems no one has dealt with by a general method:
     but Eratocles has attempted in the case of one System, in one
     genus, to enumerate the forms or _species_ of the Octave, and
     to determine them mathematically by the periodic recurrence of
     the intervals: not perceiving that unless we have first
     demonstrated the forms of the Fifth and the Fourth, and the
     manner of their melodious combination, the forms of the Octave
     will come to be many more than seven.'


The 'periodic recurrence of intervals' here spoken of may be
illustrated on the key-board of a piano. If we take successive
octaves of white notes, _a-a_, _b-b_, and so on, we obtain each time
a different order of intervals (_i.e._ the semitones occur in
different places), until we reach _a-a_ again, when the series begins
afresh. In this way it is shown that only seven species of the Octave
can be found on any particular scale. Aristoxenus shows how to prove
this from first principles, viz. by analysing the Octave as the
combination of a Fifth with a Fourth.

3. Ibid. p. 36, 29 Meib.: [Greek: ton de systematon tas diaphoras hoi
men holos ouk epecheiroun exarithmein, alla peri auton monon ton
heptachordon ha ekaloun harmonias ten episkepsin epoiounto, hoi de
epicheiresantes oudena tropon exerithmounto.]

For [Greek: heptachordon] Meibomius and other editors read [Greek:
hepta oktachordon]--a correction strongly suggested by the parallel
words [Greek: systematon oktachordon] in the first passage quoted.

'Some did not attempt to enumerate the differences of the Systems,
but confined their view to the seven octachord Systems which they
called [Greek: harmoniai]; others who did make the attempt did not
succeed.'

It appears from these passages that before the time of Aristoxenus
musicians had framed diagrams or tables showing the division of the
octave scale according to the Enharmonic genus: and that a certain
Eratocles--of whom nothing else is known--had recognised seven forms
or species of the octachord scale, and had shown how the order of the
intervals in the several species passes through a sort of cycle.
Finally, if the correction proposed in the third passage is right,
the seven species of the Octave were somehow shown in the diagrams of
which the first passage speaks. In what respect Eratocles failed in
his treatment of the seven species can hardly be conjectured.

Elsewhere the diagrams are described by Aristoxenus somewhat
differently, as though they exhibited a division into Enharmonic
dieses or quarter-tones, without reference to the melodious character
of the scale. Thus we find him saying--. _Harm._ p. 28 Meib.: [Greek:
zeteteon de to syneches ouch hos hoi harmonikoi en tais ton
diagrammaton katapyknosesin apodidonai peirontai, toutous
apophainontes ton phthongon hexes allelon keisthai hois symbebeke to
elachiston diastema diechein aph' hauton. ou gar to me dynasthai
dieseis okto kai eikosin hexes melodeisthai tes phones estin, alla
ten triten diesin panta poiousa ouch hoia t' esti prostithenai.]

'We must seek continuity of succession, not as theoretical musicians
do in filling up their diagrams with small intervals, making those
notes successive which are separated from each other by the least
interval. For it is not merely that the voice cannot sing
twenty-eight successive dieses: with all its efforts it cannot sing a
third diesis[1].'

[Footnote 1: This point is one which Aristoxenus is fond of insisting
upon: cp. p. 10, 16 [Greek: ou pros ten katapyknosin blepontas hosper
hoi harmonikoi]: p. 38, 3 [Greek: hoti de estin he katapyknosis
ekmeles kai panta tropon achrestos phaneron]: p. 53, 3 [Greek: kata
ten tou melous physin zeteteon to hexes kai ouch hos hoi eis ten
katapyknosin blepontes eiothasin apodidonai to hexes].

The statement that the ancient diagrams gave a series of twenty-eight
successive dieses or quarter-tones has not been explained. The number
of quarter-tones in an octave is only twenty-four. Possibly it is a
mere error of transcription ([Greek: [=ke]] for [Greek: [=kd]]). If
not, we may perhaps connect it with the seven intervals of the
ordinary octave scale, and the simple method by which the enharmonic
intervals were expressed in the instrumental notation. It has been
explained that raising a note a quarter of a tone was shown by
turning it through a quarter of a circle. Thus, our _c_ being denoted
by [Symbols: E], _c_* was [Symbols: w], and _c_[Symbols: c] was
[Symbols: 3]. Now the ancient diagrams, which divided every tone into
four parts, must have had a character for _c_[Symbols: S]*, or the
note three-quarters of a tone above _c_. Naturally this would be the
remaining position of [Symbols: E], namely [Symbols: m]. Again, we
have seen that when the interval between two notes on the diatonic
scale is only a semitone, the result of the notation is to produce a
certain number of duplicates, so to speak. Thus: [Symbols: K] stands
for _b_, and therefore [Symbols:)1] for _c_: but _c_ is a note of the
original scale, and as such is written [Symbols: q]. It may be that
the diagrams to which Aristoxenus refers made use of these
duplicates: that is to say, they may have made use of all four
positions of a character (such as [Symbols: K 7g]) whether the
interval to be filled was a tone or a semitone. If so, the seven
intervals would give twenty-eight characters (besides the upper
octave-note), and apparently therefore twenty-eight dieses. Some
traces of this use of characters in four positions have been noticed
by Bellermann (_Tonleitern_, p. 65).]

This representation of the musical diagrams is borne out by the
passage in the _Republic_ in which Plato derides the experimental
study of music:

_Rep._ p. 531 a [Greek: tas gar akouomenas au symphonias kai
phthongous allelois anametrountes anenyta, hosper hoi astronomoi,
ponousin. Ne tous theous, ephe, kai geloios ge, pyknomat' atta
onomazontes kai paraballontes ta ota, hoion ek geitonon phonen
thereuomenoi, hoi men phasin eti katakouein en meso tina echen kai
smikrotaton einai touto diastema, ho metreteon, hoi de k.t.l.]

Here Socrates is insisting that the theory of music should be studied
as a branch of mathematics, not by observation of the sounds and
concords actually heard, about which musicians spend toil in vain.
'Yes,' says Glaucon, 'they talk of the close-fitting of intervals,
and put their ears down to listen for the smallest possible interval,
which is then to be the measure.' The smallest interval was of course
the Enharmonic diesis or quarter of a tone, and this accordingly was
the measure or unit into which the scale was divided. A group of
notes separated by a diesis was called 'close' ([Greek: pyknon], or a
[Greek: pyknoma]), and the filling up of the scale in that way was
therefore a [Greek: katapyknosis tou diagrammatos]--a filling up with
'close-set' notes, by the division of every tone into four equal
parts.

An example of a diagram of this kind has perhaps survived in a
comparatively late writer, viz. Aristides Quintilianus, who gives a
scale of two octaves, one divided into twenty-four dieses, the next
into twelve semitones (_De Mus._ p. 15 Meib.). The characters used
are not otherwise known, being quite different from the ordinary
notation: but the nature of the diagram is plain from the
accompanying words: [Greek: haute estin he para tois archaiois kata
dieseis harmonia, heos [=kd] dieseon to proteron diagousa dia pason,
to deuteron dia ton hemitonion auxesasa]: 'this is the [Greek:
harmonia] (division of the scale) according to dieses in use among
the ancients, carried in the case of the first octave as far as
twenty-four dieses, and dividing the second into semitones[1].'

The phrase [Greek: he kata dieseis harmonia], used for the division
of an octave scale into quarter-tones, serves to explain the
statement of Aristoxenus (in the third of the passages above quoted)
that the writers who treated of octave Systems called them
'harmonies' ([Greek: ha ekaloun harmonias]). That statement has
usually been taken to refer to the ancient Modes called [Greek:
harmoniai] by Plato and Aristotle, and has been used accordingly as
proof that the scales of these Modes were based upon the different
species ([Greek: eide]) of the Octave. But the form of the
reference--'which _they called_ [Greek: harmoniai]'--implies some
forgotten or at least unfamiliar use of the word by the older
technical writers. It is very much more probable that the [Greek:
harmoniai] in question are divisions of the octave scale, as shown in
theoretical diagrams, and had no necessary connexion with the Modes.
Apparently some at least of these diagrams were not musical scales,
but tables of all the notes in the compass of an octave; and the
Enharmonic diesis was used, not merely on account of the importance
of that genus, but because it was the smallest interval, and
therefore the natural unit of measurement[2].

[Footnote 1: The fullest account of this curious fragment of notation
is that given by Bellermann in his admirable book, _Die Tonleitern
und Musiknoten der Griechen_, pp. 61-65. His conjectures as to its
origin do not claim a high degree of probability. See the remarks on
pp. 97-99.]

[Footnote 2: Cp. Plato, _Rep._ p. 531: [Greek: kai smikrotaton einai
touto diastema, ho metreteon.] It may even be that this sense of
[Greek: harmonia] was connected with the use for the Enharmonic
genus. It is at least worth notice that the phrase [Greek: ha ekaloun
harmonias] in this passage answers to the adjective [Greek:
enarmonion] in the passage first quoted (compare the words [Greek:
peri auton monon ton hepta oktachordon ha ekaloun harmonias] with
[Greek: peri systematon oktachordon enarmonion monon]).]

The use of [Greek: harmonia] as an equivalent for 'System' or
'division of the scale' appears in an important passage in Plato's
_Philebus_ (p. 17): [Greek: all', o phile, epeidan labes ta
diastemata hoposa esti ton arithmon tes phones oxytetos te peri kai
barytetos, kai hopoia, kai tous horous ton diastematon, kai ta ek
touton hosa systemata gegonen, ha katidontes hoi prosthen paredosan
hemin tois hepomenois ekeinois kalein auta harmonias, k.t.l.] In this
passage,--which has an air of technical accuracy not usual in Plato's
references to music (though perhaps characteristic of the
_Philebus_),--there is a close agreement with the technical writers,
especially Aristoxenus. The main thought is the application of limit
or measure to matter which is given as unlimited or indefinite--the
distinction drawn out by Aristoxenus in a passage quoted below (p.
81). The treatment of the term 'System' is notably Aristoxenean (cp.
_Harm._ p. 36 [Greek: ta systemata theoresai posa te esti kai poia
atta, kai pos ek te ton diastematon kai phthongon synestekota]).
Further, the use of [Greek: harmonia] for [Greek: systema], or rather
of the plural [Greek: harmoniai] for the [Greek: systemata] observed
by the older musical theorists, is exactly what is noticed by
Aristoxenus as if it were more or less antiquated. Even in the time
of Plato it appears as a word of traditional character ([Greek: hoi
prosthen paredosan]), his own word being [Greek: systema]. It need
not be said that there is no such hesitation, either in Plato or in
Aristotle, about the use of [Greek: harmoniai] for the modes.

The same use of [Greek: harmonia] is found in the Aristotelian
_Problems_ (xix. 26), where the question is asked, [Greek: dia ti
mese kaleitai en tais harmoniais, ton de okto ouk esti meson], _i.e._
how can we speak of the Mese or 'middle note' of a scale of eight
notes?

We have now reviewed all the passages in Aristoxenus which can be
thought to bear upon the question whether the [Greek: harmoniai] or
Modes of early Greek music are the same as the [Greek: tonoi] or Keys
discussed by Aristoxenus himself. The result seems to be that we have
found nothing to set against the positive arguments for the
identification already urged. It may be thought, perhaps, that the
variety of senses ascribed to the word [Greek: harmonia] goes beyond
what is probable. In itself however the word meant simply 'musical
scale[1].' The Pythagorean use of it in the sense of 'octave scale,'
and the very similar use in reference to diagrams which represented
the division of that scale, were antiquated in the time of
Aristoxenus. The sense of 'key' was doubtless limited in the first
instance to the use in conjunction with the names Dorian, &c., which
suggested a distinction of pitch. From the meaning 'Dorian scale' to
'Dorian key' is an easy step. Finally, in reference to genus [Greek:
harmonia] meant the Enharmonic scale. It is not surprising that a
word with so many meanings did not keep its place in technical
language, but was replaced by unambiguous words, viz. [Greek: tonos]
in one sense, [Greek: systema] in another, [Greek: genos enarmonion]
in a third. Naturally, too, the more precise terms would be first
employed by technical writers.

[Footnote 1: So in Plato, _Leg._ p. 665 a: [Greek: te de tes kineseos
taxei rhythmos onoma eie, te d' au tes phones, tou te oxeos hama kai
bareos synkerannymenon, harmonia onoma prosagoreuoito.]]




Sec. 23. _The Seven Species._

(See the Appendix, Table I.)

In the _Harmonics_ of Aristoxenus an account of the seven species of
the Octave followed the elaborate theory of Systems already referred
to (p. 48), and doubtless exhibited the application of that general
theory to the particular cases of the Fourth, Fifth, and Octave.
Unfortunately the existing manuscripts have only preserved the first
few lines of this chapter of the Aristoxenean work (p. 74, ll. 10-24
Meib.).

The next source from which we learn anything of this part of the
subject is the pseudo-Euclidean _Introductio Harmonica_. The writer
enumerates the species of the Fourth, the Fifth, and the Octave,
first in the Enharmonic and then in the Diatonic genus. He shows that
if we take Fourths on a Diatonic scale, beginning with Hypate Hypaton
(our _b_), we get successively _b c d e_ (a scale with the intervals
1/2 1 1), _c d e f_ (1 1 1/2) and _d e f g_ (1 1/2 1). Similarly on
the Enharmonic scale we get--


    Hypate Hypaton to Hypate Meson    _b  b* c  e_  (1/4  1/4  2  )
    Parhypate  "    " Parhypate "     _b* c  e  e*_ (1/4  2    1/4)
    Lichanos   "    " Lichanos  "     _c  e  e* f_  (2    1/4  1/4)


In the case of the Octave the species is distinguished on the
Enharmonic scale by the place of the tone which separates the
tetrachords, the so-called Disjunctive Tone ([Greek: tonos
diazeuktikos]). Thus in the octave from Hypate Hypaton to Paramese
(_b-b_) this tone (_a-b_) is the highest interval; in the next
octave, from Parhypate Hypaton to Trite Diezeugmenon (_c-c_), it is
the second highest; and so on. These octaves, or species of the
Octave, the writer goes on to tell us, were anciently called by the
same names as the seven oldest Keys, as follows:


    Mixo-lydian      _b - b_      1/4  1/4  2    1/4  1/4  2    1
    Lydian           _b*- b*_     1/4  2    1/4  1/4  2    1    1/4
    Phrygian         _c - c_      2    1/4  1/4  2    1    1/4  1/4
    Dorian           _e - e_      1/4  1/4  2    1    1/4  1/4  2
    Hypo-lydian      _e*- e*_     1/4  2    1    1/4  1/4  2    1/4
    Hypo-phrygian    _f - f_      2    1    1/4  1/4  2    1/4  1/4
    Hypo-dorian      _a - a_      1    1/4  1/4  2    1/4  1/4  2


On the Diatonic scale, according to the same writer, the species of
an Octave is distinguished by the places of the two semitones. Thus
in the first species, _b-b_, the semitones are the first and fourth
intervals (_b-c_ and _e-f_): in the second, _c-c_, they are the third
and the seventh, and so on. He does not however say, as he does in
the case of the Enharmonic scale, that these species were known by
the names of the Keys. This statement is first made by Gaudentius (p.
20 Meib.), a writer of unknown date. If we adopt it provisionally,
the species of the Diatonic octave will be as follows:


    [Mixo-lydian]      _b - b_    1/2  1    1    1/2  1    1    1
    [Lydian]           _c - c_    1    1    1/2  1    1    1    1/2
    [Phrygian]         _d - d_    1    1/2  1    1    1    1/2  1
    [Dorian]           _e - e_    1/2  1    1    1    1/2  1    1
    [Hypo-lydian]      _f - f_    1    1    1    1/2  1    1    1/2
    [Hypo-phrygian]    _g - g_    1    1    1/2  1    1    1/2  1
    [Hypo-dorian]      _a - a_    1    1/2  1    1    1/2  1    1




Sec. 24. _Relation of the Species to the Keys._

Looking at the octaves which on our key-board, as on the Greek scale,
exhibit the several species, we cannot but be struck with the
peculiar relation in which they stand to the Keys. In the tables
given above the keys stand in the order of their pitch, from the
Mixo-lydian down to the Hypo-dorian: the species of the same names
follow the reverse order, from _b-b_ upwards to _a-a_. This, it is
obvious, cannot be an accidental coincidence. The two uses of this
famous series of names cannot have originated independently. Either
the naming of the species was founded on that of the keys, or the
converse relation obtained between them. Which of these two uses,
then, was the original and which the derived one? Those who hold that
the species were the basis of the ancient Modes or [Greek: harmoniai]
must regard the keys as derivative. Now Aristoxenus tells us, in one
of the passages just quoted, that the seven species had long been
recognised by theorists. If the scheme of keys was founded upon the
seven species, it would at once have been complete, both in the
number of the keys and in the determination of the intervals between
them. But Aristoxenus also tells us that down to his time there were
only six keys,--one of them not yet generally recognised,--and that
their relative pitch was not settled. Evidently then the keys, which
were scales in practical use, were still incomplete when the species
of the Octave had been worked out in the theory of music.

If on the other hand we regard the names Dorian, &c. as originally
applied to keys, we have only to suppose that these names were
extended to the species after the number of seven keys had been
completed. This supposition is borne out by the fact that
Aristoxenus, who mentions the seven species as well known, does not
give them names, or connect them with the keys. This step was
apparently taken by some follower of Aristoxenus, who wished to
connect the species of the older theorists with the system of keys
which Aristoxenus had perfected.

The view now taken of the seven species is supported by the whole
treatment of musical scales ([Greek: systemata]) as we find it in
Aristoxenus. That treatment from first to last is purely abstract and
theoretical. The rules which Aristoxenus lays down serve to determine
the sequence of intervals, but are not confined to scales of any
particular compass. His Systems, accordingly, are not scales in
practical use: they are parts taken anywhere on an ideal unlimited
scale. And the seven species of the Octave are regarded by
Aristoxenus as a scheme of the same abstract order. They represent
the earlier teaching on which he had improved. He condemned that
teaching for its want of generality, because it was confined to the
compass of the Octave and to the Enharmonic genus, and also because
it rested on no principles that would necessarily limit the species
of the Octave to seven. On the other hand the diagrams of the earlier
musicians were unscientific, in the opinion of Aristoxenus, on the
ground that they divided the scale into a succession of
quarter-tones. Such a division, he urged, is impossible in practice
and musically wrong ([Greek: ekmeles]). All this goes to show that
the earlier treatment of Systems, including the seven Species, had
the same theoretical character as his own exposition. The only System
which he recognises for practical purposes is the old standard
octave, from Hypate to Nete: and that System, with the enlargements
which turned it into the Perfect System, kept its ground with all
writers of the Aristoxenean school.

Even in the accounts of the pseudo-Euclid and the later writers, who
treat of the Species of the Octave under the names of the Keys, there
is much to show that the species existed chiefly or wholly in musical
theory. The seven species of the Octave are given along with the
three species of the Fourth and the four species of the Fifth,
neither of which appear to have had any practical application.
Another indication of this may be seen in the seventh or Hypo-dorian
species, which was also called Locrian and Common (ps. Eucl. p. 16
Meib.). Why should this species have more than one name? In the
Perfect System it is singular in being exemplified by two different
octaves, viz. that from Proslambanomenos to Mese, and that from Mese
to Nete Hyperbolaion. Now we have seen that the higher the octave
which represents a species, the lower the key of the same name. In
this case, then, the upper of the two octaves answers to the
Hypo-dorian key, and the lower to the Locrian. But if the species has
its two names from these two keys, it follows that the names of the
species are derived from the keys. The fact that the Hypo-dorian or
Locrian species was also called Common is a further argument to the
same purpose. It was doubtless 'common' in the sense that it
characterised the two octaves which made up the Perfect System. Thus
the Perfect System was recognised as the really important scale.

Another consideration, which has been overlooked by Westphal and
those who follow him, is the difference between the species of the
Octave in the several genera, especially the difference between the
Diatonic and the Enharmonic. This is not felt as a difficulty with
all the species. Thus the so-called Dorian octave _e - e_ is in the
Enharmonic genus _e e* f a b b* c e_, a scale which may be regarded
as the Diatonic with _g_ and _d_ omitted, and the semitones divided.
But the Phrygian _d-d_ cannot pass in any such way into the
Enharmonic Phrygian _c e e* f a b b* c_, which answers rather to the
Diatonic scale of the species _c-c_ (the Lydian). The scholars who
connect the ancient Modes with the species generally confine
themselves to octaves of the Diatonic genus. In this they are
supported by later Greek writers--notably, as we shall see, by
Ptolemy--and by the analogy of the mediaeval Modes or Tones. But on
the other side we have the repeated complaints of Aristoxenus that
the earlier theorists confined themselves to Enharmonic octave
scales. We have also the circumstance that the writer or compiler of
the pseudo-Euclidean treatise, who is our earliest authority for the
names of the species, gives these names for the Enharmonic genus
only. Here, once more, we feel the difference between theory and
practice. To a theorist there is no great difficulty in the terms
Diatonic Phrygian and Enharmonic Phrygian meaning essentially
different things. But the 'Phrygian Mode' in practical music must
have been a tolerably definite musical form.




Sec. 25. _The Ethos of Music._

From Plato and Aristotle we have learned some elements of what may be
called the gamut of sensibility. Between the higher keys which in
Greece, as in Oriental countries generally, were the familiar vehicle
of passion, especially of the passion of grief, and the lower keys
which were regarded, by Plato at least, as the natural language of
ease and license, there were keys expressive of calm and balanced
states of mind, free from the violent extremes of pain and pleasure.
In some later writers on music we find this classification reduced to
a more regular form, and clothed in technical language. We find also,
what is still more to our purpose, an attempt to define more
precisely the musical forms which answered to the several states of
temper or emotion.

Among the writers in question the most instructive is Aristides
Quintilianus. He discusses the subject of musical ethos under the
first of the usual seven heads, that which deals with sounds or notes
([Greek: peri phthongon]). Among the distinctions to be drawn in
regard to notes he reckons that of ethos: the ethos of notes, he
says, is different as they are higher or lower, and also as they are
in the place of a Parhypate or in the place of a Lichanos (p. 13
Meib. [Greek: hetera gar ethe tois oxyterois, hetera tois baryterois
epitrechei, kai hetera men parypatoeidesin, hetera de
lichanoeidesin]). Again, under the seventh head, that of [Greek:
melopoiia] or composition, he treats of the 'regions of the voice'
([Greek: topoi tes phones]). There are three kinds of composition, he
tells us (p. 28), viz. that which is akin to Hypate ([Greek:
hypatoeides]), that which is akin to Mese ([Greek: mesoeides]), and
that which is akin to Nete ([Greek: netoeides]). The first part of
the art of composition is the choice ([Greek: lepsis]) which the
musician is able to make of the region of the voice to be employed
([Greek: lepsis men di' hes heuriskein to mousiko perigignetai apo
poiou tes phones to systema topou poieteon, poteron hypatoeidous e
ton loipon tinos]). He then proceeds to connect these regions, or
different parts of the musical scale, with different branches of
lyrical poetry. 'There are three styles of musical composition
([Greek: tropoi tes melopoiias]), viz. the Nomic, the Dithyrambic,
and the Tragic; and of these the Nomic is netoid, the Dithyrambic is
mesoid, and the Tragic is hypatoid.... They are called styles
([Greek: tropoi]) because according to the melody adopted they
express the ethos of the mind. Thus it happens that composition
([Greek: melopoiia]) may differ in _genus_, as Enharmonic, Chromatic:
in _System_, as Hypatoid, Mesoid, Netoid: in _key_, as Dorian,
Phrygian: in _style_, as Nomic, Dithyrambic: in _ethos_, as we call
one kind of composition "contracting" ([Greek: systaltike]), viz.
that by which we move painful feelings; another "expanding" ([Greek:
diastaltike]), that by which we arouse the spirit ([Greek: thymos]);
and another "middle" ([Greek: mese]), that by which we bring round
the soul to calmness.'

This passage does not quite explicitly connect the three kinds of
ethos--the diastaltic, the systaltic, the intermediate--with the
three regions of the voice; but the connexion was evidently implied,
and is laid down in express terms in the pseudo-Euclidean
_Introductio_ (p. 21 Meib.). According to this Aristoxenean writer,
'the diastaltic ethos of musical composition is that which expresses
grandeur and manly elevation of soul ([Greek: megaloprepeia kai
diarma psyches androdes]), and heroic actions; and these are employed
by tragedy and all poetry that approaches the tragic type. The
systaltic ethos is that by which the soul is brought down into a
humble and unmanly frame; and such a disposition will be fitting for
amatory effusions and dirges and lamentations and the like. And the
hesychastic or tranquilly disposed ethos ([Greek: hesychastikon
ethos]) of musical composition is that which is followed by calmness
of soul and a liberal and peaceful disposition: and this temper will
fit hymns, paeans, laudations, didactic poetry and the like.' It
appears then that difference in the 'place' ([Greek: topos]) of the
notes employed in a composition--difference, that is to say, of
pitch--was the element which chiefly determined its ethos, and (by
consequence) which distinguished the music appropriate to the several
kinds of lyrical poetry.

A slightly different version of this piece of theory is preserved in
the anonymous treatise edited by Bellermann (Secs. 63, 64), where the
'regions of the voice' are said to be four in number, viz. the three
already mentioned, and a fourth which takes its name from the
tetrachord Hyperbolaion ([Greek: topos hyperboloeides]). In the same
passage the boundaries of the several regions are laid down by
reference to the keys. 'The lowest or hypatoid region reaches from
the Hypo-dorian Hypate Meson to the Dorian Mese; the intermediate or
mesoid region from the Phrygian Hypate Meson to the Lydian Mese; the
netoid region from the Lydian Mese to the Nete Synemmenon; the
hyperboloid region embracing all above the last point.' The text of
this passage is uncertain; but the general character of the [Greek:
topoi] or regions of the voice is clearly enough indicated.

The three regions are mentioned in the catechism of Bacchius (p. 11
Meib.): [Greek: topous] (MSS. [Greek: tropous]) [Greek: de tes phones
posous legomen einai? treis. tinas? toutous; oxyn, meson, baryn.] The
varieties of ethos also appear (p. 14 Meib.): [Greek: he de metabole
kata ethos? hotan ek tapeinou eis megaloprepes; e ex hesychou kai
synnou eis parakekinekos.] 'What is change of ethos? when a change is
made from the humble to the magnificent; or from the tranquil and
sober to violent emotion.'

When we compare the doctrine of musical ethos as we find it in these
later writers with the indications to be gathered from Plato and
Aristotle, the chief difference appears to be that we no longer hear
of the ethos of particular modes, but only of that of three or (at
the most) four portions of the scale. The principle of the division,
it is evident, is simply difference of pitch. But if that was the
basis of the ethical effect of music in later times, the circumstance
goes far to confirm us in the conclusion that it was the pitch of the
music, rather than any difference in the succession of the intervals,
that principally determined the ethical character of the older modes.




Sec. 26. _The Ethos of the Genera and Species._

Although the pitch of a musical composition--as these passages
confirm us in believing--was the chief ground of its ethical
character, it cannot be said that no other element entered into the
case.

In the passage quoted above from Aristides Quintilianus (p. 13 Meib.)
it is said that ethos depends first on pitch ([Greek: hetera ethe
tois oxyterois, hetera tois baryterois]), and secondly on the
moveable notes, that is to say, on the _genus_. For that is evidently
involved in the words that follow: [Greek: kai hetera men
parypatoeidesin, hetera de lichanoeidesin.] By [Greek:
parypatoeideis] and [Greek: lichanoeideis] he means all the moveable
notes ([Greek: phthongoi pheromenoi]): the first are those which hold
the place of Parhypate in their tetrachord, viz. the notes called
Parhypate or Trite: the second are similarly the notes called
Lichanos or Paranete. These moveable notes, then, give an ethos to
the music because they determine the genus of the scale. Regarding
the particular ethos belonging to the different genera, there is a
statement of the same author (p. 111) to the effect that the Diatonic
is masculine and austere ([Greek: arrhenopon d' esti kai
austeroteron]), the Chromatic sweet and plaintive ([Greek: hediston
te kai goeron]), the Enharmonic stirring and pleasing ([Greek:
diegertikon d' esti touto kai epion]). The criticism doubtless came
from some earlier source.

Do we ever find ethos attributed to this or that _species_ of the
Octave? I can find no passage in which this source of ethos is
indicated. Even Ptolemy, who is the chief authority (as we shall see)
for the value of the species, and who makes least of mere difference
of pitch, recognises only two forms of modulation in the course of a
melody, viz. change of genus and change of pitch[1].




Sec. 27. _The Musical Notation._

As the preceding argument turns very much upon the practical
importance of the scale which we have been discussing, first as the
single octave from the original Hypate to Nete, then in its enlarged
form as the Perfect System, it may be worth while to show that some
such scale is implied in the history of the Greek musical notation.

The use of written characters ([Greek: semeia]) to represent the
sounds of music appears to date from a comparatively early period in
Greece. In the time of Aristoxenus the art of writing down a melody
([Greek: parasemantike]) had come to be considered by some persons
identical with the science of music ([Greek: harmonike]),--an error
which Aristoxenus is at some pains to refute. It is true that the
authorities from whom we derive our knowledge of the Greek notation
are post-classical. But the characters themselves, as we shall
presently see, furnish sufficient evidence of their antiquity.

[Footnote 1: Ptol. _Harm._ ii. 6. After drawing a distinction between
difference of key as affecting the whole of a melody or piece of
music and as a means of change in the course of it--the distinction,
in short, between transposition and modulation proper--he says of the
latter: [Greek: haute de hosper ekpiptein auten] (sc. [Greek: ten
aisthesin]) [Greek: poiei tou synethous kai prosdokomenou melous,
hotan epi pleon men syneiretai to akolouthon, metabaine de pe pros
heteron eidos, etoi kata to genos e kata ten tasin.] That is to say,
the sense of change is produced by a change of genus or of pitch. A
change of _species_ is not suggested. So Dionys. Hal. _De Comp.
Verb._ c. 19 [Greek: hoi de ge dithyrambopoioi kai tous tropous]
(keys) [Greek: meteballon, Dorikous te kai Phrygious kai Lydious en
to auto asmati poiountes; kai tas melodias exellatton, tote men
enarmonious poiountes, k.t.l.]]

The Greek musical notation is curiously complicated. There is a
double set of characters, one for the note assigned to the singer,
the other for those of the lyre or other instrument. The notes for
the voice are obviously derived from the letters of the ordinary
Ionic alphabet, multiplied by the use of accents and other
diacritical marks. The instrumental notes were first explained less
than thirty years ago by Westphal. In his work _Harmonik und Melopoeie
der Griechen_ (c. viii _Die Semantik_) he showed, in a manner as
conclusive as it is ingenious, that they were originally taken from
the first fourteen letters of an alphabet of archaic type, akin to
the alphabets found in certain parts of Peloponnesus. Among the
letters which he traces, and which point to this conclusion, the
most-significant are the digamma, the primitive crooked iota
[Symbols: Li], and two forms of lambda, [Symbols: <] and [Symbols:
F], the latter of which is peculiar to the alphabet of Argos. Of the
other characters [Symbols: M], which stands for alpha, is best
derived from the archaic form [Symbols: NJ]. For beta we find
[Symbols: c], which may come from an archaic form of the letter[1].
The character [Symbols: El], as Westphal shows, is for [Symbols:7],
or delta with part of one side left out. Similarly the ancient
[Symbols: O], when the circle was incomplete, yielded the character
[Symbols: C]. The crooked iota ([Symbols:'-i]) appears as
[Symbols:h]. The two forms of lambda serve for different notes, thus
bringing the number of symbols up to fifteen. Besides these there are
two characters, [Symbols: O] and [Symbols: 6], which cannot be
derived in the same way from any alphabet. As they stand for the
lowest notes of the scale, they are probably an addition, later than
the rest of the system. At the upper end, again, the scale is
extended by the simple device of using the same characters for notes
an octave higher, distinguishing them in this use by an accent. The
original fifteen characters, with the letters from which they are
derived, and the corresponding notes in the modern musical scale, are
as follows:


    [Symbols: H h E  r P F C K r l < E N Z M]
    [Greek: e i e l^1 g m [digamma] th k d l^2 b n z a]
    _a b c d e f g a b c d e f g a_


[Footnote 1: Since this was written I have learned from Mr. H. S.
Jones that the form [Symbols:E] for beta occurs on an inscription
dated about 500 B.C., viz. Count Tyszkiewicz's bronze plate,
published simultaneously by Robert in the _Monumenti Antichi
pubblicati per cura della reale Accademia dei Lincei_, i. pp. 593
(with plate), and Froehner in the _Revue Archeologique_, 1891
July-August, pp. 51 ff. Pl. xix. Mr. Jones points out that this
[Symbols:E] connects the crescent beta ([Symbols: C]) of Naxos,
Delos, &c. with the common form, and is evidently therefore an early
form of the letter.

I take this opportunity of thanking Mr. Jones for other help,
especially in regard to the subject of this section.]

These notes, it will be seen, compose two octaves of the Diatonic
scale, identical with the two octaves of the Greater Perfect System.
They may be regarded as answering to the white notes of the modern
keyboard,--those which form the complete scale in the so-called
'natural' key.

The other notes, viz. those which are required not only in different
keys of the Diatonic scale, but also in all Enharmonic and Chromatic
scales, are represented by the same characters modified in some
simple way. Usually a character is turned half round backwards to
raise it by one small interval (as from Hypate to Parhypate), and
reversed to raise it by both (Hypate to Lichanos). Thus the letter
epsilon, [Symbols: E], stands for our _c_: and accordingly [Symbols:
W] ([Symbols: E] [Greek: anestrammenon] or [Greek: hyption]) stands
for _c*_, and [Symbols: 3] ([Symbols: E] [Greek: apestrammenon]) for
_c[Symbols: #]_. The Enharmonic scale _c-c*-c[Symbols: #]-f_ is
therefore written [Symbols: E W 3 f'], the two modifications of the
letter [Symbols: E] representing the two 'moveable' notes of the
tetrachord. Similarly we have the triads [Symbols: h I rl, F "q, Cup,
KY>1, <V>, CUm]. As some letters do not admit of this kind of
differentiation, other methods are employed. Thus [Symbols: D] is
made to yield the forms [Symbols: ri] (for [Symbols: 7]) [Symbols: L
A]: from [Symbols: H] (or [Symbols: B]) are obtained the forms
[Symbols: Li] and [Symbols: R]: and from [Symbols: Z] (or [Symbols:
i]) the forms [Symbols: A] and [Symbols: A]. The modifications of
[Symbols: N] are [Symbols: /] and [Symbols: \]: those of [Symbols:
'I] are [Symbols: A] and [Symbols: N].

The method of writing a Chromatic tetrachord is the same, except that
the higher of the two moveable notes is marked by a bar or accent.
Thus the tetrachord _c c[Symbols: #] d f_ is written [Symbols: E W 3'
/`'].

In the Diatonic genus we should have expected that the original
characters would have been used for the tetrachords _b c d e_ and _e
f g a_; and that in other tetrachords the second note, being a
semitone above the first, would have been represented by a reversed
letter ([Greek: gramma apestrammenon]). In fact, however, the
Diatonic Parhypate and Trite are written with the same character as
the Enharmonic. That is to say, the tetrachord _b c d e_ is not
written [Symbols: h E H r], but [Symbols: Fix I-r]: and _d e[Symbols:
b] f g_ is not [Symbols: I], but [Symbols: I-tl F].

Let us now consider how this scheme of symbols is related to the
Systems already described and the Keys in which those Systems may be
set ([Greek: tonoi eph' hon tithemena ta systemata melodeitai]).

The fifteen characters, it has been noticed, form two diatonic
octaves. It will appear on a little further examination that the
scheme must have been constructed with a view to these two octaves.
The successive notes are not expressed by the letters of the alphabet
in their usual order (as is done in the case of the vocal notes). The
highest note is represented by the first letter, [Greek: A]: and then
the remaining fourteen notes are taken in pairs, each with its
octave: and each of the pairs of notes is represented by two
successive letters--the two forms of lambda counting as one such pair
of letters. Thus:


  The higher and lower _e_ are denoted by [Greek: b]  and  [Greek: g]
      "     "     "    _c_     "     "    [Greek: d]   "   [Greek: e]
      "     "     "    _g_     "     "    [Symbol: digamma] "  [Greek: z]
      "     "     "    _a_     "     "    [Greek: e]   "   [Greek: th]
      "     "     "    _b_     "     "    [Greek: i]   "   [Greek: k]
      "     "     "    _d_     "     "    [Greek: l^1] "   [Greek: l^2]
      "     "     "    _f_     "     "    [Greek: m]   "   [Greek: n]


On this plan the alphabetical order of the letters serves as a series
of links connecting the highest and lowest notes of every one of the
seven octaves that can be taken on the scale. It is evident that the
scheme cannot have grown up by degrees, but is the work of an
inventor who contrived it for the practical requirements of the music
of his time.

Two questions now arise, which it is impossible to separate. What is
the scale or System for which the notation was originally devised?
And how and when was the notation adapted to exhibit the several keys
in which any such System might be set?

The enquiry must start from the remarkable fact that the two octaves
represented by the fifteen original letters are in the _Hypo-lydian_
key--the key which down to the time of Aristoxenus was called the
Hypo-dorian. Are we to suppose that the scheme was devised in the
first instance for that key only? This assumption forms the basis of
the ingenious and elaborate theory by which M. Gevaert explains the
development of the notation (_Musique de l'Antiquite_, t. I. pp. 244
ff.). It is open to the obvious objection that the Hypo-lydian (or
Hypo-dorian) cannot have been the oldest key. M. Gevaert meets this
difficulty by supposing that the original scale was in the Dorian
key, and that subsequently, from some cause the nature of which we
cannot guess, a change of pitch took place by which the Dorian scale
became a semitone higher. It is perhaps simpler to conjecture that
the original Dorian became split up, so to speak, into two keys by
difference of local usage, and that the lower of the two came to be
called Hypo-dorian, but kept the original notation. A more serious
difficulty is raised by the high antiquity which M. Gevaert assigns
to the Perfect System. He supposes that the inventor of the notation
made use of an instrument (the _magadis_) which 'magadised' or
repeated the notes an octave higher. But this would give us a
repetition of the primitive octave _e - e_, rather than an
enlargement by the addition of tetrachords at both ends.

M. Gevaert regards the adaptation of the scheme to the other keys as
the result of a gradual process of extension. Here we may distinguish
between the recourse to the modified characters--which served
essentially the same purpose as the 'sharps' and 'flats' in the
signature of a modern key--and the additional notes obtained either
by means of new characters ([Symbols: a] and [Symbols: e]), or by the
use of accents ([Symbols:?'], &c.). The Hypo-dorian and
Hypo-phrygian, which employ the new characters [Symbols: a] and
[Symbols: e], are known to be comparatively recent. The Phrygian and
Lydian, it is true, employ the accented notes; but they do so only in
the highest tetrachord (Hyperbolaion), which may not have been
originally used in these high keys. The modified characters doubtless
belong to an earlier period. They are needed for the three oldest
keys--Dorian, Phrygian, Lydian--and also for the Enharmonic and
Chromatic genera. If they are not part of the original scheme, the
musician who devised them may fairly be counted as the second
inventor of the instrumental notation.

In setting out the scales of the several keys it will be unnecessary
to give more than the standing notes ([Greek: phthongoi hestotes]),
which are nearly all represented by original or unmodified
letters--the moveable notes being represented by the modified forms
described above. The following list includes the standing notes, viz.
Proslambanomenos, Hypate Hypaton, Hypate Meson, Mese, Paramese, Nete
Diezeugmenon and Nete Hyperbolaion in the seven oldest keys: the two
lowest are marked as doubtful:--


    TABLE LEGEND:
    Column A = Prosl.
    Column B = Hyp. Hypaton.
    Column C = Hyp. Meson.
    Column D = Mese.
    Column E = Par.
    Column F = Nete Diez.
    Column G = Nete Hyperb.

                             A    B   C   D   E   F   G

    Mixo-lydian    [Symbols] 4    id  D   >   N   \       = _e[Symbol: b] - e[Symbol: b]_
    Lydian         [Symbols] I-   r   c   <   c   m       = _d - d_
    Phrygian       [Symbols] E    I-  F   11  <   Z       = _c - c_
    Dorian         [Symbols] R    E   I'  D   ri  N   \   = _b[Symbol: b] - b[Symbol: b]_
    Hypo-lydian    [Symbols] H    h   r   C   I<  c   M   = _a - a_
    [Hypo-phrygian [Symbols]      H   I-  F   C   <   Z   = _g - g_
    [Hypo-dorian   [Symbols]          E  /4   F   11  N   = _f - f_


It will be evident that this scheme of notation tallies fairly well
with what we know of the compass of Greek instruments about the end
of the fifth century, and also with the account which Aristoxenus
gives of the keys in use up to his time. We need only refer to what
has been said above on p. 17 and p. 37.

It would be beyond the scope of this essay to discuss the date of the
Greek musical notation. A few remarks, however, may be made,
especially with reference to the high antiquity assigned to it by
Westphal.

The alphabet from which it was derived was certainly an archaic one.
It contained several characters, in particular [Symbols: F] for
digamma, [Symbols: LI] for iota, and [Symbols: I-] for lambda, which
belong to the period before the introduction of the Ionian alphabet.
Indeed if we were to judge from these letters alone we should be led
to assign the instrumental notation (as Westphal does) to the time of
Solon. The three-stroke iota ([Symbols: I]), in particular, does not
occur in any alphabet later than the sixth century B.C. On the other
hand, when we find that the notation implies the use of a musical
System in advance of any scale recognised in Aristotle, or even in
Aristoxenus, such a date becomes incredible. We can only suppose
either (1) that the use of [Symbols: Li] in the fifth century was
confined to localities of which we have no complete epigraphic
record, or (2) that [Symbols: i] as a form of iota was still
known--as archaic forms must have been--from the older public
inscriptions, and was adopted by the inventor of the notation as
being better suited to his purpose than [Symbols: 1].

With regard to the place of origin of the notation the chief fact
which we have to deal with is the use of the character [Symbols: I-]
for lambda, which is distinctive of the alphabet of Argos, along with
the commoner form [Symbols: <]. Westphal indeed asserts that both
these forms are found in the Argive alphabet. But the inscription (C.
I. 1) which he quotes[1] for [Symbols: <] really contains only
[Symbols: t-] in a slightly different form. We cannot therefore say
that the inventor of the notation derived it entirely from the
alphabet of Argos, but only that he shows an acquaintance with that
alphabet. This is confirmed by the fact that the form [Symbols: Li]
for iota is not found at Argos. Probably therefore the inventor drew
upon more than one alphabet for his purpose, the Argive alphabet
being one.

[Footnote 1: _Harmonik und Melopoeie_, p. 286 (ed. 1863). The true
form of the letter is given by Mr. Roberts, _Greek Epigraphy_, p.
109.]

The special fitness of the notation for the scales of the Enharmonic
genus may be regarded as a further indication of its date. We shall
see presently that that genus held a peculiar predominance in the
earliest period of musical theory--that, namely, which was brought to
an end by Aristoxenus.

If the author of the notation--or the second author, inventor of the
modified characters--was one of the musicians whose names have come
down to us, it would be difficult to find a more probable one than
that of Pronomus of Thebes. One of the most striking features of the
notation, at the time when it was framed, must have been the
adjustment of the keys. Even in the time of Aristoxenus, as we know
from the passage so often quoted, that adjustment was not universal.
But it is precisely what Pronomus of Thebes is said to have done for
the music of the flute (_supra_, p. 38). The circumstance that the
system was only used for instrumental music is at least in harmony
with this conjecture. If it is thought that Thebes is too far from
Argos, we may fall back upon the notice that Sacadas of Argos was the
chief composer for the flute before the time of Pronomus[1], and
doubtless Argos was one of the first cities to share in the advance
which Pronomus made in the technique of his art.

[Footnote 1: Pausanias (iv. 27, 4) says of the founding of Messene:
[Greek: eirgazonto de kai hypo mousuies alles men oudemias, aulon de
Boiotion kai Argeion; ta te Sakada kai Pronomou mele tote de
proechthe malista eis hamillan.]]




Sec. 28. _Traces of the Species in the Notation._

Before leaving this part of the subject it will be well to notice the
attempt which Westphal makes to connect the species of the Octave
with the form of the musical notation.

The basis of the notation, as has been explained (p. 69), is formed
by two Diatonic octaves, denoted by the letters of the alphabet from
[Greek: a] to [Greek: n], as follows:


    [Greek: e i e l g m [digamma] th k d l b n z a]
    _     a b c d e f g            a b c d e f g a_

In this scale, as has been pointed out (p. 71), the notes which are
at the distance of an octave from each other are always expressed by
two _successive_ letters of the alphabet. Thus we find--


  [Greek: b - g] is the octave _e - e_, the Dorian species.
  [Greek: d - e]     "    "    _c - c_, the Lydian species.
  [Greek: [digamma] - z]"     "    _g - g_, the Hypo-phrygian species.
  [Greek: e - th]    "    "    _a - a_, the Hypo-dorian species.


Westphal adopts the theory of Boeckh (as to which see p. 11) that the
Hypo-phrygian and Hypo-dorian species answered to the ancient Ionian
and Aeolian modes. On this assumption he argues that the order of the
pairs of letters representing the species agrees with the order of
the Modes in the historical development of Greek music. For the
priority of Dorian, Ionian, and Aeolian he appeals to the authority
of Heraclides Ponticus, quoted above (p. 9). The Lydian, he supposes,
was interposed in the second place on account of its importance in
education,--recognised, as we have seen, by Aristotle in the
_Politics_ (viii. 7 _ad fin._). Hence he regards the notation as
confirming his theory of the nature and history of the Modes.

The weakness of this reasoning is manifold. Granting that the
Hypo-dorian and Hypo-phrygian answer to the old Aeolian and Ionian
respectively, we have to ask what is the nature of the priority which
Heraclides Ponticus claims for his three modes, and what is the value
of his testimony. What he says is, in substance, that these are the
only kinds of music that are truly Hellenic, and worthy of the name
of modes ([Greek: harmoniai]). It can hardly be thought that this is
a criticism likely to have weighed with the inventor of the notation.
But if it did, why did he give an equally prominent place to Lydian,
one of the modes which Heraclides condemned? In fact, the
introduction of Lydian goes far to show that the coincidence--such as
it is--with the views of Heraclides is mere accident. Apart, however,
from these difficulties, there are at least two considerations which
seem fatal to Westphal's theory:

1. The notation, so far as the original two octaves are concerned,
must have been devised and worked out at some one time. No part of
these two octaves can have been completed before the rest. Hence the
order in which the letters are taken for the several notes has no
historical importance.

2. The notation does not represent only the _species_ of a scale,
that is to say, the relative pitch of the notes which compose it, but
it represents also the absolute pitch of each note. Thus the octaves
which are defined by the successive pairs of letters, [Greek:b-g,
d-e], and the rest, are octaves of definite notes. If they were
framed with a view to the ancient modes, as Westphal thinks, they
must be the actual scales employed in these modes. If so, the modes
followed each other, in respect of pitch, in an order exactly the
reverse of the order observed in the keys. It need hardly be said
that this is quite impossible. Sec. 29. _Ptolemy's Scheme of Modes._

The first writer who takes the Species of the Octave as the basis of
the musical scales is the mathematician Claudius Ptolemaeus (fl.
140-160 A.D.). In his _Harmonics_ he virtually sets aside the scheme
of keys elaborated by Aristoxenus and his school, and adopts in their
place a system of scales answering in their main features to the
mediaeval Tones or Modes. The object of difference of key, he says,
is not that the music as a whole may be of a higher or lower pitch,
but that a melody may be brought within a certain compass. For this
purpose it is necessary to vary the succession of intervals (as a
modern musician does by changing the signature of the clef). If, for
example, we take the Perfect System ([Greek: systema ametabolon]) in
the key of _a_ minor--which is its natural key,--and transpose it to
the key of _d_ minor, we do so, according to Ptolemy, not in order to
raise the general pitch of our music by a Fourth, but because we wish
to have a scale with _b_ flat instead of _b_ natural. The flattening
of this note, however, means that the two octaves change their
species. They are now of the species _e - e_. Thus, instead of
transposing the Perfect System into different keys, we arrive more
directly at the desired result by changing the species of its
octaves. And as there are seven possible species of the Octave, we
obtain seven different Systems or scales. From these assumptions it
follows, as Ptolemy shows in some detail, that any greater number of
keys is useless. If a key is an octave higher than another, it is
superfluous because it gives us a mere repetition of the same
intervals[1].

[Footnote 1: _Harm._ ii. 8 [Greek: hoi de hyperekpiptontes tou dia
pason tous ap' autou tou dia pason apotero parelkontos hypotithentai,
tous autous aei ginomenous tois proeilemmenois.]]

If we interpose a key between (_e.g._) the Hypo-dorian and the
Hypo-phrygian, it must give us over again either the Hypo-dorian or
the Hypo-phrygian scale[1]. Thus the fifteen keys of the
Aristoxeneans are reduced to seven, and these seven are not
transpositions of a single scale, but are all of the same pitch. See
the table at the end of the book.

With this scheme of Keys Ptolemy combined a new method of naming the
individual notes. The old method, by which a note was named from its
relative place in the Perfect System, must evidently have become
inconvenient. The Lydian Mese, for example, was two tones higher than
the Dorian Mese, because the Lydian scale as a whole was two tones
higher than the Dorian. But when the two scales were reduced to the
same compass, the old Lydian Mese was no longer in the middle of the
scale, and the name ceased to have a meaning. It is as though the
term 'dominant' when applied to a Minor key were made to mean the
dominant of the relative Major key. On Ptolemy's method the notes of
each scale were named from their places in it. The old names were
used, Proslambanomenos for the lowest, Hypate Hypaton for the next,
and so on, but without regard to the intervals between the notes.
Thus there were two methods of naming, that which had been in use
hitherto, termed 'nomenclature according to _value_' ([Greek:
onomasia kata dynamin]), and the new method of naming from the
various scales, termed 'nomenclature according to _position_'
([Greek: onomasia kata thesin]). The former was in effect a retention
of the Perfect System and the Keys: the latter put in their place a
scheme of seven different standard Systems.

[Footnote 1: _Harm._ ii. 11 [Greek: hoste med' an heteron eti doxai
to eidei ton tonon para ton proteron, all' hypodorion palin, e ton
auton hypophrygion, oxyphonoteron tinos e baryphonoteron monon.]]

In illustration of his theory Ptolemy gives tables showing in numbers
the intervals of the octaves used in the different keys and genera.
He shows two octaves in each key, viz. that from Hypate Meson
([Greek: kata thesin]) to Nete Diezeugmenon (called the octave
[Greek: apo netes]), and that from Proslambanomenos to Mese (the
octave [Greek: apo meses]). As he also gives the divisions of five
different 'colours' or varieties of genus, the whole number of
octaves is no less than seventy.

Ptolemy does not exclude difference of pitch altogether. The whole
instrument, he says, may be tuned higher or lower at pleasure[1].
Thus the pitch is treated by him as modern notation treats the
_tempo_, viz. as something which is not absolutely given, but has to
be supplied by the individual performer.

Although the language of Ptolemy's exposition is studiously
impersonal, it may be gathered that his reduction of the number of
keys from fifteen to seven was an innovation proposed by himself[2].
If this is so, the rest of the scheme,--the elimination of the
element of pitch, and the 'nomenclature by position,'--must also be
due to him. Here, however, we find ourselves at issue with Westphal
and those who agree with him on the main question of the Modes.
According to Westphal the nomenclature by position is mentioned by
Aristoxenus, and is implied in at least one important passage of the
Aristotelian _Problems_. We have now to examine the evidence which he
adduces to support his contention.

[Footnote 1: _Harm._ ii. 7 [Greek: pros ten toiauten diaphoran he ton
organon holon epitasis e palin anesis aparkei.]]

[Footnote 2: This may be traced in the occasionally controversial
tone; as _Harm._ ii. 7 [Greek: hoi men ep' elatton tou dia pason
phthasantes, hoi d' ep' auto monon, hoi de epi to meizon toutou,
prokopen tina schedon toiauten aei ton neoteron para tous
palaioterous theromenon, anoikeion tes peri to hermosmenon physeos te
kai apokatastaseos; he mone perainein anankaion esti ten ton esomenon
akron tonon diastasin]. We may compare c. 11.]




Sec. 30. _Nomenclature by Position._

Two passages of Aristoxenus are quoted by Westphal in support of his
contention. The first (p. 6 Meib.) is one in which Aristoxenus
announces his intention to treat of Systems, their number and nature:
'setting out their differences in respect of compass ([Greek:
megethos]), and for each compass the differences in form and
composition and position ([Greek: tas te kata schema kai kata
synthesin kai kata thesin]), so that no element of melody,--either
compass or form or composition or position,--may be unexplained.' But
the word [Greek: thesis], when applied to Systems, does not mean the
'position' of single notes, but of groups of notes. Elsewhere (p. 54
Meib.) he speaks of the position of tetrachords towards each other
([Greek: tas ton tetrachordon pros allela theseis]), laying it down
that any two tetrachords in the same System must be consonant either
with each other or with some third tetrachord. The other passage
quoted by Westphal (p. 69 Meib.) is also in the discussion of
Systems. Aristoxenus is pointing out the necessity of recognising
that some elements of melodious succession are fixed and limited,
others are unlimited:


     [Greek: kata men oun ta megethe ton diastematon kai tas ton
     phthongon taseis apeira pos phainetai einai ta peri melos,
     kata de tas dynameis kai kata ta eide kai kata tas theseis
     peperasmena te kai tetagmena.]

     'In the size of the intervals and the pitch of the notes the
     elements of melody seem to be infinite; but in respect of the
     values (_i.e._ the relative places of the notes) and in
     respect of the forms (_i.e._ the succession of the intervals)
     and in respect of the positions they are limited and settled.'


Aristoxenus goes on to illustrate this by supposing that we wish to
continue a scale downwards from a [Greek: pyknon] or pair of small
intervals (Chromatic or Enharmonic). In this case, as the [Greek:
pyknon] forms the lower part of a tetrachord, there are two
possibilities. If the next lower tetrachord is disjunct, the next
interval is a tone; if it is conjunct, the next interval is the large
interval of the genus ([Greek: he men gar kata tonon eis diazeuxin
agei to tou systematos eidos, he de kata thateron diastema ho ti
depot' echei megethos eis synaphen]). Thus the succession of
intervals is determined by the relative position of the two
tetrachords, as to which there is a choice between two definite
alternatives. This then is evidently what is meant by the words
[Greek: kata tas theseis][1]. On the other hand the [Greek: thesis]
of Ptolemy's nomenclature is the absolute pitch (_Harm._ ii. 5
[Greek: pote men par' auten ten thesin, to oxyteron haplos e
baryteron, onomazomen]), and this is one of the elements which
according to Aristoxenus are indefinite.

[Footnote 1: So Bacch. p. 19 Meib. [Greek: theseis de tetrachordon
hois to melos horizetai eisin hepta? synaphe, diazeuxis,
hypodiazeuxis, k.t.l.] (see the whole passage).]

Westphal also finds the nomenclature by position implied in the
passage of the Aristotelian _Problems_ (xix. 20) which deals with the
peculiar relation of the Mese to the rest of the musical scale. The
passage has already been quoted and discussed (_supra_, p. 43), and
it has been pointed out that if the Mese of the Perfect System
([Greek: mese kata dynamin]) is the key-note, the scale must have
been an octave of the _a_-species. If octaves of other species were
used, as Westphal maintains, it becomes necessary to take the Mese of
this passage to be the [Greek: mese kata thesin], or Mese by
position. That is, Westphal is obliged by his theory of the Modes to
take the term Mese in a sense of which there is no other trace before
the time of Ptolemy. But--

(1) It is highly improbable that the names of the notes--Mese,
Hypate, Nete and the rest--should have had two distinct meanings.
Such an ambiguity would have been intolerable, and only to be
compared with the similar ambiguity which Westphal's theory implies
in the use of the terms Dorian, &c.

(2) If the different species of the octave were the practically
important scales, as Westphal maintains, the position of the notes in
these scales must have been correspondingly important. Hence the
nomenclature by position must have been the more usual and familiar
one. Yet, as we have shown, it is not found in Aristotle, Aristoxenus
or Euclid--to say nothing of later writers.

(3) The nomenclature by position is an essential part of the scheme
of Keys proposed by Ptolemy. It bears the same relation to Ptolemy's
octaves as the nomenclature by 'value' bears to the old standard
octave and the Perfect System. It was probably therefore devised
about the time of Ptolemy, if not actually by him.




Sec. 31. _Scales of the Lyre and Cithara._

The earliest evidence in practical music of any octaves other than
those of the standard System is to be found in the account given by
Ptolemy of certain scales employed on the lyre and cithara. According
to this account the scales of the lyre (the simpler and commoner
instrument) were of two kinds. One was Diatonic, of the 'colour' or
variety which Ptolemy recognises as the prevailing one, viz. the
'Middle Soft' or 'Tonic' ([Greek: diatonon toniaion])[1].

[Footnote 1: We may think of this as a scale in which the semitones
are considerably smaller, _i.e._ in which _c_ and _f_ are nearly a
quarter of a tone flat.]

The other was a 'mixture' of this Diatonic with the standard
Chromatic ([Greek: chroma suntonon]): that is to say, the octave
consisted of a tetrachord of each genus. These octaves apparently
might be of any _species_, according to the key chosen[1]. On the
cithara,--which was a more elaborate form of lyre, confined in
practice to professional musicians,--six different octave scales were
employed, each of a particular species and key. They are enumerated
and described by Ptolemy in two passages (_Harm._ i. 16 and ii. 16),
which in some points serve to correct each other.[2]

[Footnote 1: Ptol. _Harm._ ii. 16 [Greek: periechetai de ta men en te
lyra kaloumena sterea tonou tinos hypo ton tou toniaiou diatonou
arithmon tou autou tonou, ta de malaka hypo ton en to migmati tou
malakou chromatos apithmon tou autou tonou]. Here [Greek: tonou
tinos] evidently means 'of any given key,' and [Greek: tou autou
tonou] 'of that key.' There is either no restriction, or none that
Ptolemy thought worth mentioning, in the choice of the key and
species.]

[Footnote 2: The two passages enumerate the scales in a slightly
different manner. In i. 16 they are arranged in view of the genus or
colour into--


          Pure Middle Soft Diatonic, viz.--
                   [Greek: sterea], of the lyre.
                   [Greek: tritai]      }  of the cithara.
                   [Greek: hypertropa]  }

          Mixture of Chromatic, viz.--
                   [Greek: malaka], of the lyre.
                   [Greek: tropika], of the cithara.

          Mixture of Soft Diatonic, viz.--
                   [Greek: parypatai], of the cithara.

          Mixture of [Greek: diatonon syntonon], viz.--
                   [Greek: lydia]  }  of the cithara.
                   [Greek: iastia] }


It is added, however, that in their use of this last 'mixture'
musicians are in the habit of tuning the cithara in the Pythagorean
manner, with two Major tones and a [Greek: leimma] (called [Greek:
diatonon ditoniaion]).

In the second passage (ii. 16) the scales of the lyre are given
first, then those of the cithara with the key of each. The order is
the same, except that [Greek: parypatai] comes before [Greek:
tropika] (now called [Greek: tropoi]), and [Greek: lydia] is placed
last. The words [Greek: ta de lydia hoi tou toniaiou diatonou] [sc.
[Greek: arithmoi periechousi]] [Greek: tou doriou] cannot be correct,
not merely because they contradict the statement of the earlier
passage that [Greek: lydia] denoted a mixture with [Greek: diatonon
syntonon] (or in practice [Greek: diatonon ditoniaion]), but also
because the scales that do not admit mixture are placed first in the
list in both passages. Hence we should doubtless read [Greek: ta de
lydia hoi <tou migmatos> tou <di>toniaiou diatonou tou Doriou].]

Of the six scales two are of the Hypo-dorian or Common species
(_a-a_). One of these, called [Greek: tritai], is purely Diatonic of
the Middle Soft variety; the intervals expressed by fractions are as
follows:


      _a_ 9/8 _b_ 28/27 _c_ 8/7 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_


The other, called [Greek: tropoi] or [Greek: tropika], is a mixture,
Middle Soft Diatonic in the upper tetrachord, and Chromatic in the
lower:


_a_ 9/8 _b_ 22/21 _c_ 12/11 _c_[Symbols: sharp] 7/6 _e_ 28/27 _f_ 8/7
_g_ 9/8 _a_


Two scales are of the Dorian or _e_-species, viz. [Greek: parypatai],
a combination of Soft and Middle Soft Diatonic:


      _e_ 21/20 _f_ 10/9 _g_ 8/7 _a_ 9/8 _b_ 28/27 _c_ 8/7 d 9/8 _e_


and [Greek: lydia], in which the upper tetrachord is of the strict or
'highly strung' Diatonic ([Greek: diatonon syntonon]--our 'natural'
temperament):


      _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 16/15 _c_ 9/8 _d_ 10/9 _e_


     Westphal (_Harmonik und Melopoeie_, 1863, p. 255) supposes a
     much deeper corruption. He would restore [Greek: ta de lydia
     [kai iastia hoi tou migmatos tou syntonou diatonou tou ... ta
     de ...] hoi tou toniaiou diatonou tou Doriou]. This introduces
     a serious discrepancy between the two passages, as the number
     of scales in the second list is raised to eight (Westphal
     making [Greek: iastia] and [Greek: iastiaioliaia] distinct
     scales, and furthermore inserting a new scale, of unknown
     name). Moreover the (unknown) scale of unmixed [Greek:
     diatonon toniaion] is out of its place at the end of the list.
     Westphal's objection to [Greek: lydia] as the name of a scale
     of the _Dorian_ species of course only holds good on his
     theory of the Modes.

     The only other differences between the two passages are:

     (1) In the scales of the lyre called [Greek: malaka] the
     admixture, according to i. 16, is one of [Greek: chromatikon
     syntonon], according to ii. 16 of [Greek: chr. malakon]. But,
     as Westphal shows, Soft Chromatic is not admitted by Ptolemy
     as in practical use. It would seem that in the second passage
     the copyist was led astray by the word [Greek: malaka] just
     before.

     (2) The [Greek: iastia] of i. 16 is called [Greek:
     iastiaioliaia] in ii. 16. We need not suppose the text to be
     faulty, since the two forms may have been both in use.

     Another point overlooked in Westphal's treatment is that
     [Greek: diatonon syntonon] and [Greek: d. ditoniaion] are not
     really distinguished by Ptolemy. In one passage (i. 16) he
     gives his [Greek: lydia] and [Greek: iastia] as a mixture with
     [Greek: d. syntonon], adding that in practice it was [Greek:
     d. ditoniaion]. In the other (ii. 16) he speaks at once of
     [Greek: d. ditoniaion]. This consideration brings the two
     places into such close agreement that any hypothesis involving
     discrepancy is most improbable.


In practice it appears that musicians tuned the tetrachord _b-e_ of
this scale with the Pythagorean two Major tones and [Greek: leimma].

Of the remaining scales one, called [Greek: hypertropa], is Phrygian
in species (_d-d_), and of the standard genus:


      _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_ 9/8 _a_ 9/8 _b_ 28/27 _c_ 8/7 _d_


One, called [Greek: iastia], or [Greek: iastiaioliaia], is of the
Hypo-phrygian or _g_-species, the tetrachord _b-e_ being 'highly
strung' Diatonic or (in practice) Pythagorean, viz.:


      _g_ 9/8 _a_ 9/8 _b_ 256/243 _c_ 9/8 _d_ 9/8 _e_ 28/27 _f_ 8/7 _g_


Regarding the tonality of these scales there is not very much to be
said. In the case of the Hypo-dorian and Dorian octaves it will be
generally thought probable that the key-note is _a_ (the [Greek: mese
kata dynamin]). If so, the difference between the two species is not
one of 'mode,'--in the modern sense,--but consists in the fact that
in the Hypo-dorian the compass of the melody is from the key-note
upwards, while in the Dorian it extends a Fourth below the key-note.
It is possible, however, that the lowest note (_e_) of the Dorian
octave was sometimes the key-note: in which case the _mode_ was
properly Dorian. In the Phrygian octave of Ptolemy's description the
key-note cannot be the Fourth or Mese [Greek: kata thesin] (_g_),
since the interval _g-c_ is not consonant (9/8 x 9/8 x 28/27 being
less than 4/3). Possibly the lowest note (_d_) is the key-note; if so
the scale is of the Phrygian mode (in the modern sense). In the
Hypo-phrygian octave there is a similar objection to regarding the
Mese [Greek: kata thesin] (_c_) as the key-note, and some probability
in favour of the lowest note (_g_). If the Pythagorean division of
the tetrachord _g-c_ were replaced by the natural temperament, which
the language used by Ptolemy[1] leads us to regard as the true
division, the scale would exhibit the intervals--


          _g_ 5/4 _b_ 6/5 _d_ 7/6 _f_ 8/7 _g_


which give the natural chord of the Seventh. This however is no more
than a hypothesis.

It evidently follows from all this that Ptolemy's octaves do not
constitute a system of _modes_. They are merely the groups of notes,
of the compass of an octave, which are most likely to be used in the
several keys, and which Ptolemy or some earlier theorist chose to
call by the names of those keys.

[Footnote 1: _Harm._ i. 16 [Greek: plen kathoson adousi men
akolouthos to dedeigmeno syntono diatoniko, kathaper exestai skopein
apo tes ton oikeion autou logon paraboles, harmozontai de heteron ti
genos] (sc. the Pythagorean), [Greek: xynengizon men ekeino, k.t.l.]]




Sec. 32. _Remains of Greek Music._

The extant specimens of Greek music are mostly of the second century
A.D., and therefore nearly contemporary with Ptolemy. The most
considerable are the melodies of three lyrical pieces or hymns, viz.
(1) a hymn to Calliope, (2) a hymn to Apollo (or Helios),--both
ascribed to a certain Dionysius,--and (3) a hymn to Nemesis, ascribed
to Mesomedes[2]. Besides these there are (4) some short instrumental
passages or exercises given by Bellermann's _Anonymus_ (pp. 94-96).
And quite recently the list has been increased by (5) an inscription
discovered by Mr. W. M. Ramsay, which gives a musical setting of four
short gnomic sentences, and (6) a papyrus fragment (now in the
collection of the Arch-duke Rainer) of the music of a chorus in the
_Orestes_ of Euripides. These two last additions to our scanty stock
of Greek music are set out and discussed by Dr. Wessely of Vienna and
M. Ruelle in the _Revue des Etudes Grecques_ (V. 1892, pp. 265-280),
also by Dr. Otto Crusius in the _Philologus_, Vol. LII, pp.
160-200[1].

[Footnote 2: It seems needless to set out these melodies here. The
first satisfactory edition of them is that of Bellermann, _Die Hymnen
des Dionysius und Mesomedes_ (Berlin, 1840). They are given by
Westphal in his _Musik des griechischen Alterthumes_ (1883), and by
Gevaert, _Musique de l'Antiquite_, vol. i. pp. 445 ff.; also in Mr.
W. Chappell's _History of Music_ (London, 1874), where the melodies
of the first and third hymns will be found harmonised by the late Sir
George Macfarren.

The melody published by Kircher (_Musurgia_, i. p. 541) as a fragment
of the first Pythian ode of Pindar has no attestation, and is
generally regarded as a forgery.]

The music of the three hymns is noted in the Lydian key (answering to
the modern scale with one [symbol: flat]). The melody of the second
hymn is of the compass of an octave, the notes being those of the
Perfect System from Parhypate Hypaton to Trite Diezeugmenon (_f - f_
with one [symbol: flat]). The first employs the same octave with a
lower note added, viz. Hypate Hypaton (_e_): the third adds the next
higher note, Paranete Diezeugmenon (_g_). Thus the Lydian key may be
said, in the case of the second hymn, and less exactly in the case of
the two others, to give the Lydian or _c_-species of the octave in
the most convenient part of the scale; just as on Ptolemy's system of
Modes we should expect it to do.

This octave, however, represents merely the _compass_ (_ambitus_ or
_tessitura_) of the melody: it has nothing to do with its _tonality_.
In the first two hymns, as Bellermann pointed out, the key-note is
the Hypate Meson; and the mode--in the modern sense of that word--is
that of the octave _e - e_ (the Dorian mode of Helmholtz's theory).
In the third hymn the key-note appears to be the Lichanos Meson, so
that the mode is that of _g-g_, viz. the Hypo-phrygian.

[Footnote 1: Of the discovery made at Delphi, after most of this book
was in type, I hope to say something in the _Appendix_.]

Of the instrumental passages given by the _Anonymus_ three are
clearly in the Hypo-dorian or common mode, the Mese (_a_) being the
key-note. (See Gevaert, i. p. 141.) A fourth (Sec. 104) also ends on the
Mese, but the key-note appears to be the Parhypate Meson (_f_).
Accordingly Westphal and Gevaert assign it to the Hypo-lydian species
(_f - f_). In Westphal's view the circumstance of the end of the
melody falling, not on the key-note, but on the Third or Mediant of
the octave, was characteristic of the Modes distinguished by the
prefix _syntono-_, and accordingly the passage in question is
pronounced by him to be Syntono-lydian. All those passages, however,
are mere fragments of two or three bars each, and are quoted as
examples of certain peculiarities of rhythm. They can hardly be made
to lend much support to any theory of the Modes.

The music of Mr. Ramsay's inscription labours under the same defect
of excessive shortness. If, however, we regard the four brief
sentences as set to a continuous melody, we obtain a passage
consisting of thirty-six notes in all, with a compass of less than an
octave, and ending on the lowest note of that compass. Unlike the
other extant specimens of Greek music it is written in the Ionian
key--a curious fact which has not been noticed by Dr. Wessely.


INSCRIPTION WITH MUSICAL NOTES.

[Music:

    [Greek: hos-on zes phai-nou.
    me-den hol-os sy ly-pou.
    pros o-li-gon es-ti to zen.
    to te-los ho chro-nos a-pai-tei.]

]

The notes which enter into this melody form the scale _f[Symbols:
sharp]-g-a-b-c[Symbols: sharp]-d-e[-f[Symbols: sharp]]_, which is an
octave of the Dorian species (_e - e_ on the white notes). Hence if
_f_[Symbols: sharp], on which the melody ends, is the key-note, the
_mode_ is the Dorian. On the other hand the predominant notes are
those of the triad _a-c[Symbols: sharp]-e_, which point to the key of
_a_ major, with the difference that the Seventh is flat (_g_ instead
of _g_[Symbols: sharp]). On this view the music would be in the
Hypo-phrygian mode.

However this may be, the most singular feature of this fragment
remains to be mentioned, viz. the agreement between the musical notes
and the _accentuation_ of the words. We know from the grammarians
that an acute accent signified that the vowel was sounded with a rise
in the pitch of the voice, and that a circumflex denoted a rise
followed on the same syllable by a lower note--every such rise and
fall being quite independent both of syllabic quantity and of stress
or _ictus_. Thus in ordinary speech the accents formed a species of
melody,--[Greek: logodes ti melos], as it is called by
Aristoxenus[1]. When words were _sung_ this 'spoken melody' was no
longer heard, being superseded by the melody proper. Dionysius of
Halicarnassus is at pains to explain (_De Comp. Verb._, c. 11), that
the melody to which words are set does not usually follow or resemble
the quasi-melody of the accents, _e.g._ in the following words of a
chorus in the _Orestes_ of Euripides (ll. 140-142):--

    [Greek: siga siga leukon ichnos arbyles
    tithete, me ktypeite;
    apoprobat' ekeis' apopro moi koitas,]

[Footnote 1: _Harm._ p. 18 Meib. [Greek: legetai gar de kai logodes
ti melos, to synkeimenon ek ton prosodion, to en tois onomasi;
physikon gar to epiteinein kai anienai en to dialegesthai].]

he notices that the melody differs in several points from the spoken
accents: (1) the three first words are all on the same note, in spite
of the accents; (2) the last syllable of [Greek: arbyles] is as high
as the second, though that is the only accented syllable: (3) the
first syllable of [Greek: tithete] is lower than the two others,
instead of being higher: (4) the circumflex of [Greek: ktypeite] is
lost ([Greek: ephanistai]), because the word is all on the same
pitch; (5) the fourth syllable of [Greek: apoprobate] is higher in
pitch, instead of the third. In Mr. Ramsay's inscription, however,
the music follows the accents as closely as possible. Every acute
accent coincides with a rise of pitch, except in [Greek: hoson],
which begins the melody, and in [Greek: esti], for which we should
perhaps read the orthotone [Greek: esti]. Of the four instances of
the circumflex accent three exhibit the two notes and the falling
pitch which we expect. The interval is either a major or a minor
Third. In the other case ([Greek: zes) the next note is a Third
lower: but it does not seem to belong to the circumflexed syllable.
All this cannot be accidental. It leads us to the conclusion that the
musical notes represent a kind of recitative, or imitation of spoken
words, rather than a melody in the proper sense of the term.

If any considerable specimen of the music of Euripides had survived,
it might have solved many of the problems with which we have been
dealing. The fragment before us extends over about six lines in
dochmiac metre (_Orestes_ 338-343), with the vocal notation: but no
single line is entire. The key is the Lydian. The genus is either
Enharmonic or Chromatic. Assuming that it is Enharmonic--the
alternative adopted by Dr. Wessely--the characters which are still
legible may be represented in modern notation as follows:

[Music: [_Euripides_, _Orestes 338-344_.

    [Greek: (katolo)phy-ro-mai; ma-te-ros (haima sas ho d' ana)bak-cheu-ei;
    ho me-gas (olbos ou monimo)s en bro-tois;
    a-na (de laiphos hos ti)s a-ka-tou tho-as ti-na(xas daimon)
    kat-e-kly-sen (deinon ponon) hos pon-tou labrois k.t.l.

]

It should be observed that in the fragment the line [Greek:
katolophyromai katolophyromai] comes before 338 ([Greek: materos
k.t.l.]), not after it, as in our texts[1].

[Footnote 1: I need not repeat what is said by Dr. Wessely and M.
Ruelle in defence of the genuineness of our fragment. They justly
point to the remarkable coincidence that the music of this very play
is quoted by Dionysius of Halicarnassus (_l. c._). It would almost
seem as if it was the only well-known specimen of music of the
classical period of tragedy.

The transcription of Dr. Crusius, with his conjectural restorations,
will be found in the _Appendix_. I have only introduced one of his
corrections here, viz. the note on the second syllable of [Greek:
kateklysen].]

The notes employed, according to the interpretation given above, give
the scale _g-a-a*-a#-d-e-e*_. If the genus is Chromatic, as M. Ruelle
is disposed to think, they are _g-a-a#-b-d-e-f_. When these scales
are compared with the Perfect System we find that they do not
entirely agree with it. Whether the genus is Enharmonic or Chromatic
the notes from _a_ to _e*_ (or _f_) answer to those of the Perfect
System (of the same genus) from Hypate Meson to Trite Diezeugmenon.
But in either case the lowest note (_g_) finds no place in the
System, since it can only be the Diatonic Lichanos Hypaton. It is
possible, however, that the scale belongs to the period when the
original octave had been extended by the addition of a tone below the
Hypate--the note, in fact, which we have already met with under the
name of Hyper-hypate (p. 39). Thus the complete scale may have
consisted of the disjunct tetrachords _a-d_ and _e-a_, with the tone
_g-a_. It may be observed here that although the scale in question
does not fit into the Perfect System, it conforms to the general
rules laid down by Aristoxenus for the melodious succession of
intervals. It is unnecessary therefore to suppose (as Dr. Wessely and
M. Ruelle do) that the scale exhibits a _mixture_ of different
genera.

It must be vain to attempt to discover the tonality of a short
fragment which has neither beginning nor end. The only group of notes
which has the character of a cadence is that on the word
[Greek:(olo)phypomai], and again on the words [Greek: en brotois],
viz. the notes _a# a* a_ (if the genus is the Enharmonic). The same
notes occur in reversed order on [Greek: akatou] and [Greek:
(kat)eklusen]. This seems to bear out the common view of the
Enharmonic as produced by the introduction of an 'accidental' or
passing note. It will be seen, in fact, that the Enharmonic notes
(_a*_ and _e*_) only occur before or after the 'standing' notes (_a_
and _e_).

Relying on the fact that the lowest note is _g_, Dr. Wessely and M.
Ruelle pronounce the mode to be the Phrygian (_g-g_ in the key with
one [Symbols: flat], or _d-d_ in the natural key). I have already put
forward a different explanation of this _g_, and will only add here
that it occurs twice in the fragment, both times on a short
syllable[1]. The important notes, so far as the evidence goes, are
_a_, which twice comes at the end of a verse (with a pause in the
sense), and _e_, which once has that position. If _a_ is the
key-note, the mode--in the modern sense--is Dorian (the _e_-species).
If _e_ is the key-note, it is Mixo-lydian (the _b_-species).

[Footnote 1: Dr. Crusius, however, detects a [Symbols: phi]; (the
sign for _g_) over the first syllable of [Greek: kateklusen] and the
second syllable of [Greek: pontou]. There is little trace of them in
his facsimile.]




Sec. 33. _Modes of Aristides Quintilianus._

The most direct testimony in support of the view that the ancient
Modes were differentiated by the succession of their intervals has
still to be considered. It is the account given by Aristides
Quintilianus (p. 21 Meib.) of the six Modes ([Greek: harmoniai]) of
Plato's _Republic_. After describing the genera and their varieties
the 'colours,' he goes on to say that there were other divisions of
the tetrachord ([Greek: tetrachordikai diaireseis]) which the most
ancient musicians used for the [Greek: harmoniai], and that these
were sometimes greater in compass than the octave, sometimes less. He
then gives the intervals of the scale for each of the six Modes
mentioned by Plato, and adds the scales in the ancient notation. They
are of the Enharmonic genus, and may be represented by modern notes
as follows:--


      Mixo-lydian      _b-b*-c-d-e-e*-f-b_
      Syntono-lydian   _e-e*-f-a-c_
      Phrygian         _d-e-e*-f-a-b-b*-c-d_
      Dorian           _d-e-e*-f-a-b-b*-c-e_
      Lydian           _e*-f-a-b-b*-c-e-e*_
      Ionian           _e-e*-f-a-c-d_


Comparing these scales with the Species of the Octave, we find a
certain amount of correspondence. As has been already noticed (p.
22), the names Syntono-lydian and Lydian answer to the ordinary
Lydian and Hypo-lydian respectively. Accordingly the Lydian of
Aristides agrees with the Hypo-lydian species as given in the
pseudo-Euclidean _Introductio_. The Dorian of Aristides is the Dorian
species of the _Introductio_, but with an additional note, a tone
below the Hypate.

The Phrygian of Aristides is not the Enharmonic Phrygian species; but
it is derived from the diatonic Phrygian octave _d-e-f-g-a-b-c-d_ by
inserting the enharmonic notes _e*_ and _b*_, and omitting the
diatonic _g_. By a similar process the Mixo-lydian of Aristides may
be derived from the diatonic octave _b-b_, except that _a_ as well as
_g_ is omitted, and on the other hand _d_ is retained. If the scale
of the Syntono-lydian is completed by the lower _c_ (as analogy would
require), it will answer similarly to the Lydian species (_c-c_).




Sec. 34. _Credibility of Aristides Quintilianus._

But what weight can be given to Aristides as an authority on the
music of the time of Plato? The answer to this question depends upon
several considerations.

1. The date of Aristides is unknown. He is certainly later than
Cicero, since he quotes the _De Republica_ (p. 70 Meib.). From the
circumstance that he makes no reference to the musical innovations of
Ptolemy it has been supposed that he was earlier than that writer.
But, as Aristides usually confines himself to the theory of
Aristoxenus and his school, the argument from silence is not of much
value. On the other hand he gives a scheme of notation containing two
characters, [Symbol: [] and [Symbol: *], which extend the scale two
successive semi-tones beyond the lowest point of the notation given
by Alypius[1]. For this reason it is probable that Aristides is one
of the latest of the writers on ancient music.

[Footnote 1: This argument is used, along with some others not so
cogent, in Mr. W. Chappell's _History of Music_ (p. 130).]

2. The manner in which Aristides introduces his information about the
Platonic Modes is highly suspicious. He has been describing the
various divisions of the tetrachord according to the theory of
Aristoxenus, and adds that there were anciently other divisions in
use. So far Aristides is doubtless right, since Aristoxenus himself
says that the divisions of the tetrachord are theoretically infinite
in number (p. 26 Meib.),--that it is possible, for example, to
combine the Parhypate of the Soft Chromatic with the Lichanos of the
Diatonic (p. 52 Meib.). But all this concerns the genus of the scale,
and has nothing to do with the species of the Octave, with which
Aristides proceeds to connect it. It follows either that there is
some confusion in the text, or that Aristides was compiling from
sources which he did not understand.

3. The Platonic Modes were a subject of interest to the early musical
writers, and were discussed by Aristoxenus himself (Plut. _de Mus._
c. 17). If Aristoxenus had had access to such an account as we have
in Aristides, we must have found some trace of it, either in the
extant _Harmonics_ or in the quotations of Plutarch and other
compilers.

4. Of the four scales which extend to the compass of an octave, only
one, viz. the Dorian, conforms to the rules which are said by
Aristoxenus to have prevailed in early Greek music. The Phrygian
divides the Fourth _a-d_ into four intervals instead of three, by the
sequence _a b b* c d_. As has been observed, it is neither the
Enharmonic Phrygian species (_c e e* f a b b* c_), nor the Diatonic
_d-d_, but a mixture of the two. Similarly the Mixo-lydian divides
the Fourth _b_-_e_ into four intervals (_b b* c d e_), by introducing
the purely Diatonic note _d_. The Lydian is certainly the Lydian
Enharmonic species of the pseudo-Euclid; but we can hardly suppose
that it existed in practical music. Aristoxenus lays it down
emphatically that a quarter-tone is always followed by another: and
we cannot imagine a scale in which the highest and lowest notes are
in no harmonic relation to the rest.

5. Two of the scales are incomplete, viz. the Ionian, which has six
notes and the compass of a Seventh, and the Syntono-lydian, which
consists of five notes, with the compass of a Minor Sixth. We
naturally look for parallels among the defective scales noticed in
the _Problems_ and in Plutarch's dialogues. But we find little that
even illustrates the modes of Aristides. The scales noticed in the
_Problems_ (xix. 7, 32, 47) are hepta-chord, and generally of the
compass of an octave. In one passage of Plutarch (_De Mus._ c. 11)
there is a description--quoted from Aristoxenus--of an older kind of
Enharmonic, in which the semitones had not yet been divided into
quarter-tones. In another chapter (c. 19) he speaks of the omission
of the Trite and also of the Nete as characteristic of a form of
music called the [Greek: spondeiakos tropos]. It may be said that in
the Ionian and Syntono-lydian of Aristides the Enharmonic Trite
(_b*_) and the Nete (_e_) are wanting. But the Paramese (_b_) is also
wanting in both these modes. And the Ionian is open to the
observation already made with regard to the Phrygian, viz. that the
two highest notes (_c d_) involve a mixture of Diatonic with
Enharmonic scale. We may add that Plutarch (who evidently wrote with
Aristoxenus before him) gives no hint that the omission of these
notes was characteristic of any particular modes.

6. It is impossible to decide the question of the modes of Aristides
without some reference to another statement of the same author. In
the chapter which treats of Intervals (pp. 13-15 Meib.) he gives the
ancient division of two octaves, the first into dieses or
quarter-tones, the second into semitones. The former of these
([Greek: he para tois archaiois kata dieseis harmonia]) is as
follows:


                [1] 2  3  4  5  6  7  8  9  10 11 12

      [Symbols:    -o  <  6 1-1 9  L  J  A  V  E  3]
      [Symbols:     o- >  9  n  6  J  r- v  0  3  E]

                13  14  15  16 17 18 19  20  21  22 23  24

      [Symbols: 3..  N 1-1  3  E   , '-  cc   >   <  Y   Y]
      [Symbols: r   a..1-1  E  3   A ,'- 33   <          Y]


After every allowance has been made for the probability that these
signs or some of them have reached us in a corrupt form, it is
impossible to reduce them to the ordinary notation, as Meibomius
sought to do. The scholar who first published them as they stand in
the MSS. (F. L. Perne, see Bellermann, _Tonleitern_, p. 62) regarded
them as a relic of a much older system of notation. This is in
accordance with the language of Aristides, and indeed is the only
view consistent with a belief in their genuineness. They are too like
the ordinary notation to be quite independent, and cannot have been
put forward as an improvement upon it. Are they, then, earlier?
Bellermann has called our attention to a peculiarity which seems
fatal to any such claim. They consist, like the ordinary signs, of
two sets, one written above the other, and in every instance one of
the pair is simply a reversed or inverted form of the other. With the
ordinary signs this is not generally the case, since the two sets,
the vocal and instrumental notes, are originally independent. But it
is the case with the three lowest notes, viz. those which were added
to the series at a later time. When these additional signs were
invented the vocal and instrumental notes had come to be employed
together. The inventor therefore devised a pair of signs in each
case, and not unnaturally made them correspond in form. In the scale
given by Aristides this correspondence runs through the whole series,
which must therefore be of later date. But if this is so, the
characters can hardly represent a genuine system of notation. In
other words, Aristides must have been imposed upon by a species of
forgery.

7. Does the fragment of the _Orestes_ tell for or against the Modes
described by Aristides?

The scale which is formed by the notes of the fragment agrees, so far
as it extends, with two of the scales now in question, viz. the
Phrygian and the Dorian. Taking the view of its tonality expressed in
the last chapter (p. 93), we should describe it as the Dorian scale
of Aristides with the two highest notes omitted. The omission, in so
short a fragment, is of little weight; and the agreement in the use
of an additional lower note (Hyper-hypate) is certainly worth notice.
On the other hand, the Dorian is precisely the mode, of those given
in the list of Aristides, which least needs defence, as it is the
most faithful copy of the Perfect System. Hence the fact that it is
verified by an actual piece of music does not go far in support of
the other scales in the same list.

If our suspicions are well-founded, it is evident that they seriously
affect the genuineness of all the antiquarian learning which
Aristides sets before his readers, and in particular of his account
of the Platonic modes. I venture to think that they go far to deprive
that account of the value which it has been supposed to have for the
history of the earliest Greek music.

For the later period, however, to which Aristides himself belongs,
these apocryphal scales are a document of some importance. The fact
that they do not agree entirely with the species of the Octave as
given by the pseudo-Euclid leads us to think that they may be
influenced by scales used in actual music. This applies especially to
the Phrygian, which (as has been shown) is really diatonic. The
Ionian, again, is perhaps merely an imperfect form of the same scale,
viz. the octave _d-d_ with lower _d_ omitted. And the Syntono-lydian
may be the Lydian diatonic octave _c-c_ with a similar omission of
the lower _c_. Sec. 35. _Evidence for Scales of different species._

The object of the foregoing discussion has been to show, in the first
place, that there was no such distinction in ancient Greek music as
that which scholars have drawn between Modes ([Greek: harmoniai]) and
Keys ([Greek: tonoi] or [Greek: tropoi]): and, in the second place,
that the musical scales denoted by these terms were primarily
distinguished by difference of _pitch_,--that in fact they were so
many keys of the standard scale known in its final form as the
Perfect System. The evidence now brought forward in support of these
two propositions is surely as complete as that which has been allowed
to determine any question of ancient learning.

It does not, however, follow that the Greeks knew of no musical forms
analogous to our Major and Minor modes, or to the mediaeval Tones. On
the contrary, the course of the discussion has led us to recognise
distinctions of this kind in more than one instance. The doctrine
against which the argument has been mainly directed is not that
ancient scales were of more than one species or 'mode' (as it is now
called), but that difference of species was the basis of the ancient
Greek Modes. This will become clear if we bring together all the
indications which we have observed of scales differing from each
other in species, that is, in the _order_ of the intervals in the
octave. In doing so it will be especially important to be guided by
the principle which we laid down at the outset, of arranging our
materials according to chronology, and judging of each piece of
evidence strictly with reference to the period to which it belongs.
It is only thus that we can hope to gain a conception of Greek music
as the living and changing thing that we know it must have been.

1. The principal scale of Greek music is undoubtedly of the
Hypo-dorian or common species. This is sufficiently proved by the
facts (1) that two octaves of this species (_a-a_) constitute the
scale known as the Greater Perfect System, and (2) that the central
_a_ of this system, called the Mese, is said to have been the
key-note, or at least to have had the kind of importance in the scale
which we connect with the key-note (Arist. _Probl._ xix. 20). This
mode, it is obvious, is based on the scale which is the descending
scale of the modern Minor mode. It may therefore be identified with
the Minor, except that it does not admit the leading note.

It should be observed that this mode is to be recognised not merely
in the Perfect System but equally in the primitive octave, of the
form _e - e_, out of which the Perfect System grew. The important
point is the tonic character of the Mese (_a_), and this, as it
happens, rests upon the testimony of an author who knows the
primitive octave only. The fact that that octave is of the so-called
Dorian species does not alter the _mode_ (as we are now using that
term), but only the compass of the notes employed.

The Hypo-dorian octave is seen in two of the scales of the cithara
given by Ptolemy (p. 85), viz. those called [Greek: tritai] and
[Greek: tropoi], and the Dorian octave (_e - e_) in two scales,
[Greek: parupatai] and [Greek: ludia]. It is very possible (as was
observed in commenting on them) that the two latter scales were in
the key of _a_, and therefore Hypo-dorian in respect of mode. The
Hypo-dorian mode is also exemplified by three at least of the
instrumental passages given by the _Anonymus_ (_supra_, p. 89).

2. The earliest trace of a difference of species appears to be found
in the passage on the subject of the Mixo-lydian mode quoted above
(p. 24) from Plutarch's _Dialogue on Music_. In that mode, according
to Plutarch, it was discovered by a certain Lamprocles of Athens that
the Disjunctive Tone was the highest interval, that is to say, that
the octave in reality consisted of two conjunct tetrachords and a
tone:

[Music: Mese Disj. Tone]

As the note which is the meeting-point of the two tetrachords is
doubtless the key-note, we shall not be wrong in making it the Mese,
and thus finding the octave in question in the Perfect System and in
the oldest part of it, viz. the tetrachords Meson and Synemmenon,
with the Nete Diezeugmenon. How then did this octave come to be
recognised by Lamprocles as distinctively Mixo-lydian? We cannot tell
with certainty, because we do not know what the Mixo-lydian scale was
before his treatment of it. Probably, however, the answer is to be
sought in the relation in respect of pitch between the Dorian and
Mixo-lydian keys. These, as we have seen (p. 23), were the keys
chiefly employed in tragedy, and the Mixo-lydian was a Fourth higher
than the other. Now when a scale consisting of white notes is
transposed to a key a Fourth higher, it becomes a scale with one
[Symbol: Flat]. In ancient language, the tetrachord Synemmenon
(_a-b[Symbol: Flat]-c-d_) takes the place of the tetrachord
Diezeugmenon. In some such way as this the octave of this form may
have come to be associated in a special way with the use of the
Mixo-lydian key.

However this may be, the change from the tetrachord Diezeugmenon to
the tetrachord Synemmenon, or the reverse, is a change of mode in the
modern sense, for it is what the ancients classified as a change of
System ([Greek: metabole kata systema])[1]. Nor is it hard to
determine the two 'modes' concerned, if we may trust to the authority
of the Aristotelian _Problems_ (_l. c._) and regard the Mese as
always the key-note. For if _a_ is kept as the key-note, the octave
_a-a_ with one [Symbol: b] is the so-called Dorian (_e - e_ on the
white notes). In this way we arrive at the somewhat confusing result
that the ancient Dorian species (_e - e_ but with _a_ as key-note)
yields the Hypo-dorian or modern Minor mode: while the Dorian mode of
modern scientific theory[2] has its ancient prototype in the
Mixo-lydian species, viz. the octave first brought to light by
Lamprocles. The difficulty of course arises from the species of the
Octave being classified according to their compass, without reference
to the tonic character of the Mese.

The Dorian mode is amply represented in the extant remains of Greek
music. It is the mode of the two compositions of Dionysius, the Hymn
to Calliope and the Hymn to Apollo (p. 88), perhaps also of Mr.
Ramsay's musical inscription (p. 90). It would have been satisfactory
if we could have found it in the much more important fragment of the
_Orestes_. Such indications as that fragment presents seem to me to
point to the Dorian mode (Mixo-lydian of Lamprocles).

3. The scales of the cithara furnish one example of the Phrygian
species (_d-d_), and one of the Hypo-phrygian (_g-g_): but we have no
means of determining which note of the scale is to be treated as the
key-note.

[Footnote 1: Ps. Eucl. _Introd._ p. 20 Meib. [Greek: kata systema de
hotan ek synaphes eis diazeuxin e anapalin metabole ginetai]. Anonym.




Sec. 65 [Greek: systematikai de] (sc. [Greek: metabolai]) [Greek:
hopotan ek diazeuxeos eis synaphen e empalin metelthe to melos].]

[Footnote 2: As represented primarily by the analysis of Helmholtz,
_Die Tonempfindungen_, p. 467, ed. 1863.]

In the Hymn to Nemesis, however, in spite of the incomplete form in
which it has reached us, there is a sufficiently clear example of the
Hypo-phrygian mode. It has been suggested as possible that the melody
of Mr. Ramsay's inscription is also Hypo-phrygian, and if so the
evidence for the mode would be carried back to the first century.

The Hypo-phrygian is the nearest approach made by any specimen of
Greek music to the modern Major mode,--the Lydian or _c_-species not
being found even among the scales of the cithara as given by Ptolemy.
It is therefore of peculiar interest for musical history, and we look
with eagerness for any indication which would allow us to connect it
with the classical period of Greek art. One or two sayings of
Aristotle have been thought to bear upon this issue.

The most interesting is a passage in the _Politics_ (iv. 3, cp. p.
13), where Aristotle is speaking of the multiplicity of forms of
government, and showing how a great number of varieties may
nevertheless be brought under a few classes or types. He illustrates
the point from the musical Modes, observing that all constitutions
may be regarded as either oligarchical (government by a minority) or
democratical (government by the majority), just as in the opinion of
some musicians ([Greek: hos phasi tines]) all modes are essentially
either Dorian or Phrygian. What, then, is the basis of this grouping
of certain modes together as Dorian, while the rest are Phrygian in
character? According to Westphal it is a form of the opposition
between the true Hellenic music, represented by Dorian, and the
foreign music, the Phrygian and Lydian, with their varieties.
Moreover, it is in his view virtually the same distinction as that
which obtains in modern music between the Minor and the Major
scales[1]. This account of the matter, however, is not supported by
the context of the passage. Aristotle draws out the comparison
between forms of government and musical modes in such a way as to
make it plain that in the case of the modes the distinction was one
of pitch ([Greek: tas suntonoteras ... tas d' aneimenas kai
malakas]). The Dorian was the best, because the highest, of the lower
keys,--the others being Hypo-dorian (in the earlier sense,
immediately below Dorian), and Hypo-phrygian--while Phrygian was the
first of the higher series which took in Lydian and Mixo-lydian. The
division would be aided, or may even have been suggested, by the
circumstance that it nearly coincided with the favourite contrast of
Hellenic and 'barbarous' modes[2]. There is another passage, however,
which can hardly be reconciled with a classification according to
pitch alone. In the chapters dealing with the ethical character of
music Aristotle dwells (as will be remembered) upon the exciting and
orgiastic character of the Phrygian mode, and notices its especial
fitness for the dithyramb. This fitness or affinity, he says, was so
marked that a poet who tried to compose a dithyramb in another mode
found himself passing unawares into the Phrygian (_Pol._ viii. 7). It
is natural to understand this of the use of certain sequences of
intervals, or of cadences, such as are characteristic of a 'mode' in
the modern sense of the word, rather than of a change of key. If this
is so we may venture the further hypothesis that the Phrygian music,
in some at least of its forms, was distinguished not only by pitch,
but also by the more or less conscious use of scales which differed
in type from the scale of the Greek standard system.

[Footnote 1: _Harmonik und Melopoeie_, p. 356 (ed. 1863): 'Die aelteste
griechische Tonart ist demnach eine Molltonart.... Aus Kleinasien
wurden zunaechst zwei Durtonarten nach Griechenland eingefuehrt, die
lydische und phrygische.' In the 1886 edition of the same book (p.
189) Westphal discovers a similar classification of modes implied in
the words of Plato, _Rep._ p. 400 a [Greek: tri' atta estin eide ex
hon hai baseis plekontai, hosper en tois phthongois tettara hothen
hai pasai harmoniai]. But Plato is evidently referring to some matter
of common knowledge. The three forms or elements of which all rhythms
are made up are of course the ratios 1: 1, 2: 1 and 3: 2, which yield
the three kinds of rhythm, dactylic, iambic and cretic (answering to
common, triple, and quintuple time). Surely the four elements of all
musical scales of which Plato speaks are not four kinds of scale
(_Harmonien-Klassen_), but the four ratios which give the primary
musical intervals--viz. the ratios 2: 1, 3: 2, 4: 3 and 9: 8, which
give the Octave, Fifth, Fourth and Tone.]

[Footnote 2: If Hypo-phrygian is the same as the older Ionian (p.
11), the coincidence is complete for the time of Aristotle. Plato
treats the claim of Ionian to rank among the Hellenic modes as
somewhat doubtful (_Laches_, p. 188).]

It may be urged that this hypothesis is inconsistent with our
interpretation of the passage of the _Problems_ about the tonic
character of the Mese. If _a_ is key-note, it was argued, the mode is
that of the _a_-species (Hypo-dorian, our Minor), or at most--by
admitting the tetrachord Synemmenon--it includes the _e_-species
(Dorian of Helmholtz). The answer may be that the statement of the
_Problems_ is not of this absolute kind. It is not the statement of a
technical writer, laying down definite rules, but is a general
observation, or at best a canon of taste. We are not told how the
predominance of the Mese is shown in the form of the melody. Moreover
this predominance is not said to be exercised in music generally, but
in all _good_ music ([Greek: panta gar ta chresta mele pollakis te
mese chretai]). This may mean either that tonality in Greek music was
of an imperfect kind, a question of style and taste rather than of
fixed rule, or that they occasionally employed modes of a less
approved stamp, unrecognised in the earlier musical theory. Sec. 36.
_Conclusion._

The considerations set forth in the last chapter seem to show that if
difference of mode or species cannot be entirely denied of the
classical period of Greek music, it occupied a subordinate and almost
unrecognised place.

The main elements of the art were, (1) difference of _genus_,--the
sub-divisions of the tetrachord which Aristoxenus and Ptolemy alike
recognise, though with important discrepancies in detail; (2)
difference of pitch or _key_; and (3) _rhythm_. Passing over the
last, as not belonging to the subject of _Harmonics_, we may now say
that genus and key are the only grounds of distinction which are
evidently of practical importance. No others were associated with the
early history of the art, with particular composers or periods, with
particular instruments, or with the ethos of music. This, however, is
only true in the fullest sense of Greek music before the time of
Ptolemy. The main object of Ptolemy's reform of the keys was to
provide a new set of scales, each characterised by a particular
succession of intervals, while the pitch was left to take care of
itself. And it is clear, especially from the specimens which Ptolemy
gives of the scales in use in his time, that he was only endeavouring
to systematise what already existed, and bring theory into harmony
with the developments of practice. We must suppose, therefore, that
the musical feeling which sought variety in differences of key came
to have less influence on the practical art, and that musicians began
to discover, or to appreciate more than they had done, the use of
different 'modes' or forms of the octave scale. Along with this
change we have to note the comparative disuse of the Enharmonic and
Chromatic divisions of the tetrachord. The Enharmonic, according to
Ptolemy, had ceased to be employed. Of the three varieties of
Chromatic given by Aristoxenus only one remains on Ptolemy's list,
and that the one which in the scheme of Aristoxenus involved no
interval less than a semitone. And although Ptolemy distinguished at
least three varieties of Diatonic, it is worth notice that only one
of these was admitted in the tuning of the lyre,--the others being
confined to the more elaborate cithara. In Ptolemy's time, therefore,
music was rapidly approaching the stage in which all its forms are
based upon a single scale--the natural diatonic scale of modern
Europe.

In the light of these facts it must occur to us that Westphal's
theory of seven modes or species of the Octave is really open to an
_a priori_ objection as decisive in its nature as any of the
testimony which has been brought against it. Is it possible, we may
ask, that a system of modes analogous to the ecclesiastical Tones can
have subsisted along with a system of scales such as the genera and
'colours' of early Greek music? The reply may be that Ptolemy himself
combines the two systems. He supposes five divisions of the
tetrachord, and seven modes based upon so many species of the
Octave--in all thirty-five different scales (or seventy, if we bring
in the distinction of octaves [Greek: apo netes] and [Greek: apo
meses]). But when we come to the scales actually used on the chief
Greek instrument, the cithara, the number falls at once to six.
Evidently the others, or most of them, only existed on paper, as the
mathematical results of certain assumptions which Ptolemy had made.
And if this can be said of Ptolemy's theory, what would be the value
of a similar scheme combining the modes with the Enharmonic and the
different varieties of the Chromatic genus? The truth is, surely,
that such a scheme tries to unite elements which belong to different
times, which in fact are the fundamental ideas of different stages of
art.

The most striking characteristic of Greek music, especially in its
earlier periods, is the multiplicity and delicacy of the intervals
into which the scale was divided. A sort of frame-work was formed by
the division of the octave into tetrachords, completed by the
so-called disjunctive tone; and so far all Greek music was alike. But
within the tetrachord the reign of diversity was unchecked. Not only
were there recognised divisions containing intervals of a fourth, a
third, and even three-eighths of a tone, but we gather from several
things said by Aristoxenus that the number of possible divisions was
regarded as theoretically unlimited. Thus he tells us that there was
a constant tendency to flatten the 'moveable' notes of the Chromatic
genus, and thus diminish the small intervals, for the sake of
'sweetness' or in order to obtain a plaintive tone[1];--that the
Lichanos of a tetrachord may in theory be any note between the
Enharmonic Lichanos (_f_ in the scale _e-e*-f-a_) and the Diatonic
(_g_ in the scale _e-f-g-a_)[2];--and that the magnitude of the
smaller intervals and division of the tetrachord generally belongs to
the indefinite or indeterminate element in music[3]. Moreover, in
spite of the disuse of several of the older scales, much of this
holds good for the time of Ptolemy. The modern diatonic scale is
fully recognised by him, but only as one of several different
divisions. And the division which he treats as the ordinary or
standard form of the octave is not the modern diatonic scale, but one
of the so-called 'soft' or flattened varieties. It is clear that in
the best periods of Greek music these refinements of melody, which
modern musicians find scarcely conceivable, were far from being
accidental or subordinate features. Rather, they were as much bound
up with the fundamental nature of that music as complex harmony is
with the music of modern Europe.

[Footnote 1: Aristox. _Harm._ p. 23 Meib. [Greek: hoi men gar te nun
katechouse melopoiia ounetheis monon ontes eiktos ten ditonon
lichanon] (_f_ in the scale _e-a_) [Greek: exorizousi; suntonoterais
gar chrontai schedon hoi pleistoi ton nun. toutou d' aition to
boulesthai glukainein aei. semeion de hoti toutou stochazontai,
malista men gar kai pleiston chronon en to chromati diatribousin.
hotan d' aphikontai pote eis ten harmonian engus tou chromatos
prosagousi, sunepismomenou tou ethous.]]

[Footnote 2: Ibid. p. 26 [Greek: noeteon gar apeirous ton arithmon
tas lichanous. hou gar an steses ten phonen apodedeigmenon lichano
topou lichanos estai; diakenon de ouden esti tou lichanoeidous topou,
oude toiouton hoste me dechisthai lichanon]. And p. 48 [Greek: epeide
per ho tes lichanou topos eis apeirous temnetai tomas].]

[Footnote 3: Aristox. _Harm._ p. 69 Meib. [Greek: kata men oun ta
megethe ton diastematon kai tas ton phthongon taseis apeira pos
phainetai einai ta peri to melos, kata de tas dynameis kai kata ta
eide kai kata tas theseis peperasmena te kai tetagmena.]]

The mediaeval modes or Tones, on the other hand, are essentially
based on the diatonic scale,--the scale that knows only of tones and
semitones. To suppose that they held in the earliest Greek music the
prominent place which we find assigned to the ancient Modes or
[Greek: harmoniai] is to suppose that the art of music was developed
in Greece in two different directions, under the influence of
different and almost opposite ideas. Yet nothing is more remarkable
in all departments of Greek art than the strictness with which it
confines itself within the limits given once for all in the leading
types, and the consequent harmony and consistency of all the forms
which it takes in the course of its growth.

The dependence of artistic forms in their manifold developments upon
a central governing idea or principle has never been more luminously
stated than by the illustrious physicist Helmholtz, in the thirteenth
chapter of his _Tonempfindungen_. I venture to think that in applying
that truth to the facts of Greek music he was materially hindered by
the accepted theory of the Greek modes. The scales which he analyses
under that name were certainly the basis of all music in the Middle
Ages, and are much more intelligible as such than in relation to the
primitive Greek forms of the art[1].

[Footnote 1: The ecclesiastical Modes received their final shape in
the _Dodecachordon_ of Glareanus (Bale, 1547). They are substantially
the Greek modes of Westphal's theory, although the Greek names which
Glareanus adopted seem to have been chosen at haphazard. But the
ecclesiastical Modes, as Helmholtz points out, were developed under
the influence of polyphonic music from the earlier stages represented
by the Ambrosian and Gregorian scales. It would be a singular chance
if they were also, as Greek modes, the source from which the
Ambrosian and Gregorian scales were themselves derived.

Some further hints on this part of the subject may possibly be
derived from the musical scales in use among nations that have not
attained to any form of harmony, such as the Arabians, the Indians,
or the Chinese. A valuable collection of these scales is given by Mr.
A. J. Ellis at the end of his translation of Helmholtz (Appendix XX.
Sect. K, _Non-harmonic Scales_). Among the most interesting for our
purpose are the eight mediaeval Arabian scales given on the authority
of Professor Land (nos. 54-61). The first three of these--called
'Ochaq, Nawa and Boas[=i]li--follow the Pythagorean intonation, and
answer respectively to the Hypo-phrygian, Phrygian, and Mixo-lydian
species of the octave. The next two--Rast and Zenkouleh--are also
Hypo-phrygian in species, but the Third and Sixth are flatter by
about an eighth of a tone (the Pythagorean comma). In Zenkouleh the
Fifth also is similarly flattened. The last two scales--Hhosa[=i]ni
and Hhidjazi--are Phrygian: but the Second and Fifth, and in the case
of Hhidjazi also the Sixth, are flatter by the interval of a comma.
The remaining scale, called Rahawi, does not fall under any species,
since the semitones are between the Third and Fourth, and again
between the Fifth and Sixth. It will be seen that in general
character--though by no means in details--this series of scales bears
a considerable resemblance to the 'scales of the cithara' as given by
Ptolemy (_supra_, p. 85). In both cases the several scales are
distinguished from each other partly by the order of the intervals
(_species_), partly by the intonation, or magnitude of the intervals
employed (_genus_). This latter element is conspicuously absent from
the ecclesiastical Modes.]




Sec. 37. _Epilogue--Speech and Song._

Several indications combine to make it probable that singing and
speaking were not so widely separated from each other in Greek as in
the modern languages with which we are most familiar.

(1) The teaching of the grammarians on the subject of accent points
to this conclusion. Our habit of using Latin translations of the
terms of Greek grammar has tended to obscure the fact that they
belong in almost every case to the ordinary vocabulary of music. The
word for 'accent' ([Greek: tonos]) is simply the musical term for
'pitch' or 'key.' The words 'acute' ([Greek: oxys]) and 'grave'
([Greek: barys]) mean nothing more than 'high' and 'low' in pitch. A
syllable may have two accents, just as in music a syllable may be
sung with more than one note. Similarly the 'quantity' of each
syllable answers to the time of a musical note, and the rule that a
long syllable is equal to two short ones is no doubt approximately
correct. Consequently every Greek word (enclitics being reckoned as
parts of a word) is a sort of musical phrase, and every sentence is a
more or less definite melody--[Greek: logodes ti melos], as it is
called by Aristoxenus (p. 18 Meib.). Moreover the accent in the
modern sense, the _ictus_ or stress of the voice, appears to be quite
independent of the pitch or 'tonic' accent: for in Greek poetry the
_ictus_ ([Greek: arsis]) is determined by the metre, with which the
tonic accent evidently has nothing to do. In singing, accordingly,
the tonic accents disappear; for the melody takes their place, and
gives each syllable a new pitch, on which (as we shall presently see)
the spoken pitch has no influence. The rise and fall of the voice in
ordinary speaking is perceptible enough in English, though it is more
marked in other European languages. Helmholtz tells us--with tacit
reference to the speech of North Germany--that an affirmative
sentence generally ends with a drop in the tone of about a Fourth,
while an interrogative is marked by a rise which is often as much as
a Fifth[1]. In Italian the interrogative form is regularly given, not
by a particle or a change in the order of the words, but by a rise of
pitch. The Gregorian church music, according to a series of rules
quoted by Helmholtz (_l. c._), marked a comma by a rise of a Tone, a
colon by a fall of a Semitone; a full stop by a Tone above, followed
by a Fourth below, the 'reciting note'; and an interrogation by a
phrase of the form _d b c d_ (_c_ being the reciting note).

These examples, however, do little towards enabling modern scholars
to form a notion of the Greek system of accentuation. In these and
similar cases it is the _sentence as a whole_ which is modified by
the tonic accent, whereas in Greek it is the individual _word_. It is
true that the accent of a word may be affected by its place in the
sentence: as is seen in the loss of the accent of oxytone words when
not followed by a pause, in the anastrophe of prepositions, and in
the treatment of the different classes of enclitics. But in all these
instances it is the intonation of the word as such, not of the
sentence, which is primarily concerned. What they really prove is
that the musical accent is not so invariable as the stress accent in
English or German, but may depend upon the collocation of the word,
or upon the degree of emphasis which it has in a particular use.

[Footnote 1: _Tonempfindungen_, p. 364 (ed. 1863).]

(2) The same conclusion may be drawn from the terms in which the
ancient writers on music endeavour to distinguish musical and
ordinary utterance.

Aristoxenus begins his _Harmonics_ by observing that there are two
movements of the voice, not properly discriminated by any previous
writer; namely, the _continuous_, which is the movement
characteristic of speaking, and the _discrete_ or that which proceeds
by _intervals_, the movement of singing. In the latter the voice
remains for a certain time on one note, and then passes by a definite
interval to another. In the former it is continually gliding by
imperceptible degrees from higher to lower or the reverse[1]. In this
kind of movement the rise and fall of the voice is marked by the
_accents_ ([Greek: prosodiai]), which accordingly form the melody, as
it may be called, of spoken utterance[2]. Later writers state the
distinction in much the same language. Nicomachus tells us that the
two movements were first discriminated by the Pythagoreans. He dwells
especially on the ease with which we pass from one to the other. If
the notes and intervals of the speaking voice are allowed to be
separate and distinct, the form of utterance becomes singing[3].
Similarly Aristoxenus says that we do not rest upon a note, unless we
are led to do so by the influence of feeling ([Greek: an me dia
pathos pote eis toiauten kinesin anankasthomen elthein]).

[Footnote 1: Aristox., _Harm._ p. 3 Meib. [Greek: kineitai men gar
kai dialegomenon hemon kai melodounton ten eiremenen kinesin; oxy gar
kai bary delon hos en amphoterois toutois enestin.] Also p. 8 [Greek:
dyo tines eisin ideai kineseos, he te syneches kai he diastematike;
kata men oun ten syneche topon tina diexienai phainetai he phone te
aisthesei houtos hos an medamou histamene, k.t.l.] And p. 9 [Greek:
ten oun syneche logiken einai phanen, k.t.l.]]

[Footnote 2: Ibid. p. 18 Meib. [Greek: tou ge logodous kechoristai
taute to mousikon melos; legetai gar de kai logodes ti melos, to
synkeimenon ek ton prosodion ton en tois onomasin; physikon gar to
epiteinein kai anienai en to dialegesthai.]]

[Footnote 3: Nicomachus, _Enchiridion_, p. 4 [Greek: ei gar tis e
dialegomenos e apologoumenos tini e anaginoskon ge ekdela metaxy
kath' hekaston phthongon poiei ta megethe, diistanon kai metaballon
ten phonen ap' allou eis allon, ouketi legein ho toioutos oude
anaginoskein alla meleazein legetai.]]

According to the rhetorician Dionysius of Halicarnassus the interval
used in the melody of spoken utterance is approximately a Fifth, or
three tones and a half ([Greek: dialektou men oun melos heni
metreitai diastemati to legomeno dia pente, hos engista; kai oute
epiteinetai pera ton trion tonon kai hemitoniou epi to oxy oute
anietai tou choriou toutou pleion epi to bary][1]). He gives an
interesting example (quoted above on p. 91) from the _Orestes_ of
Euripides, to show that when words are set to music no account is
taken of the accents, or spoken melody. Not merely are the intervals
varied (instead of being nearly uniform), but the rise and fall of
the notes does not answer to the rise and fall of the syllables in
ordinary speech. This statement is rendered the more interesting from
the circumstance that the inscription discovered by Mr. Ramsay
(_supra_, p. 89), which is about a century later, does exhibit
precisely this correspondence. Apparently, then, the melody of the
inscription represents a new idea in music,--an attempt to bring it
into a more direct connexion with the tones of the speaking voice.
The fact of such an attempt being made seems to indicate that the
divergence between the two kinds of utterance was becoming more
marked than had formerly been the case. It may be compared with the
invention of recitative in the beginning of the seventeenth century.

Aristides Quintilianus (p. 7 Meib.) recognises a third or
intermediate movement of the voice, viz. that which is employed in
the recitation of poetry. It is probable that Aristides is one of the
latest writers on the subject, and we may conjecture that in his time
the Greek

[Footnote 1: _De Compositione Verborum_, c. 11, p. 58 Reisk.]

language had in great measure lost the original tonic accents, and
with them the quasi-melodious character which they gave to prose
utterance.

In the view which these notices suggest the difference between
speaking and singing is reduced to one of degree. It is analysed in
language such as we might use to express the difference between a
monotonous and a varied manner of speaking, or between the sounds of
an Aeolian harp and those of a musical instrument.

(3) What has been said of melody in the two spheres of speech and
song applies also _mutatis mutandis_ to rhythm. In English the time
or quantity of syllables is as little attended to as the pitch. But
in Greek the distinction of long and short furnished a prose rhythm
which was a serious element in their rhetoric. In the rhythm of
music, according to Dionysius, the quantity of syllables could be
neglected, just as the accent was neglected in the melody[1]. This,
however, does not mean that the natural time of the syllables could
be treated with the freedom which we see in a modern composition. The
regularity of lyric metres is sufficient to prove that the increase
or diminution of natural quantity referred to by Dionysius was kept
within narrow limits, the nature of which is to be gathered from the
remains of the ancient system of Rhythmic. From these sources we
learn with something like certainty that the rhythm of ordinary
speech, as determined by the succession of long or short syllables,
was the basis not only of metres intended for recitation, such as the
hexameter and the iambic trimeter, but also of lyrical rhythm of
every kind.

[Footnote 1: _De Comp._ c. 11, p. 64 [Greek: to de auto ginetai kai
peri tous rhythmous; he men gar peze lexis oudenos oute onomatos oute
rhematos biazetai tous chronous oude metatithesin, all' oias
pareilephe te physei tas syllabas, tas te makras kai tas bracheias,
toiautas phylattei; he de mousike te kai rhythmike metaballousin
autas meiousai kai parauxousai, oite pollakis eis tanantia
metachorein; ou gar tais syllabais apeuthynousi tous chronous, alla
tois chronois tas syllabas.]]

(4) As to the use of the stress accent in Greek prose we are without
direct information. In verse it appears as the metrical _ictus_ or
_arsis_ of each foot, which answers to what English musicians call
the 'strong beat' or accented part of the bar[1]. In the Homeric
hexameter the ictus is confined to long syllables, and appears to
have some power of lengthening a short or doubtful syllable. In the
Attic poetry which was written in direct imitation of colloquial
speech, viz. the tragic and comic trimeter, there is no necessary
connexion between the ictus and syllabic length: but on the other
hand a naturally long syllable which is without the ictus may be
rhythmically short. In lyrical versification the ictus does not seem
to have any connexion with quantity: and on the whole we may gather
that it was not until the Byzantine period of Greek that it came to
be recognised as a distinct factor in pronunciation. The chief
elements of utterance--pitch, time and stress--were independent in
ancient Greek speech, just as they are in music. And the fact that
they were independent goes a long way to prove our main contention,
viz. that ancient Greek speech had a peculiar quasi-musical
character, consequently that the difficulty which modern scholars
feel in understanding the ancient statements on such matters as
accent and quantity is simply the difficulty of conceiving a form of
utterance of which no examples can now be observed.

[Footnote 1: The metrical accent or ictus was marked in ancient
notation by points placed over the accented syllable. These points
have been preserved in Mr. Ramsay's musical inscription (see the
Appendix, p. 133) and in one or two places of the fragment of the
_Orestes_ (p. 130). Hence Dr. Crusius has been able to restore the
rhythm with tolerable certainty, and has made the interesting
discovery that in both pieces the ictus falls as a rule on a short
syllable. The only exceptions in the inscription are circumflexed
syllables, where the long vowel or diphthong is set to two notes, the
first of which is short and accented. The accents on the short first
syllables of the dochmiacs of Euripides are a still more unexpected
evidence of the same rhythmical tendency.]

       *       *       *       *       *

The conception which we have thus been led to form of ancient Greek
as it was spoken is not without bearing on the main subject of these
pages. For if the language even in its colloquial form had qualities
of rhythm and intonation which gave it this peculiar half musical
character, so that singing and speaking were more closely akin than
they ever are in our experience, we may expect to find that music was
influenced in some measure by this state of things. What is there,
then, in the special characteristics of Greek music which can be
connected with the exceptional relation in which it stood to
language?

Greek music was primarily and chiefly vocal. Instrumental music was
looked upon as essentially subordinate,--an accompaniment or at best
an imitation of singing. For in the view of the Greeks the words
([Greek: lexis]) were an integral part of the whole composition. They
contained the ideas, while the music with its variations of time
([Greek: rhythmos]) and pitch ([Greek: harmonia]) furnished a natural
vehicle for the appropriate feelings. Purely instrumental music could
not do this, because it could not convey the ideas or impressions
fitted to be the object of feeling. Hence we find Plato complaining
on this ground of the separation of poetry and music which was
beginning to be allowed in his time. The poets, he says, rend asunder
the elements of music; they separate rhythm and dance movements from
melody, putting unmusical language into metre, and again make melody
and rhythm without words, employing the lyre and the flute without
the voice: so that it is most difficult, when rhythm and melody is
produced without language, to know what it means, or what subject
worthy of the name it represents ([Greek: kai hoto eoike ton
axiologon mimematon]). It is utterly false taste, in Plato's opinion,
to use the flute or the lyre otherwise than as an accompaniment to
dance and song[1]. Similarly in the Aristotelian _Problems_ (xix. 10)
it is asked why, although the human voice is the most pleasing,
singing without words, as in humming or whistling, is not more
agreeable than the flute or the lyre. Shall we say, the writer
answers, 'that the human voice too is comparatively without charm if
it does not _represent_ something? ([Greek: e oud' ekei, ean me
mimetai, homoios hedy?]) That is to say, music is expressive of
_feeling_, which may range from acute passion to calm and lofty
sentiment, but feeling must have an object, and this can only be
adequately given by language. Thus language is, in the first instance
at least, the matter to which musical treatment gives artistic form.
In modern times the tendency is to regard instrumental music as the
highest form of the art, because in instrumental music the artist
creates his work, not by taking ideas and feelings as he finds them
already expressed in language, but directly, by forming an
independent vehicle of feeling,--a new language, as it were, of
passion and sentiment,--out of the absolute relations of movement and
sound.

The intimate connexion in Greek music between words and melody may be
shown in various particulars. The modern practice of basing a musical
composition--a long and elaborate chorus, for example--upon a few
words, which are repeated again and again as the music is developed,
would have been impossible in Greece.

[Footnote 1: Plato, _Legg._ p. 669.]

It becomes natural when the words are not an integral part of the
work, but only serve to announce the idea on which it is based, and
which the music brings out under successive aspects. The same may be
said of the use of a melody with many different sets of words. Greek
writers regard even the repetition of the melody in a strophe and
antistrophe as a concession to the comparative weakness of a chorus.
With the Greeks, moreover, the union in one artist of the functions
of poet and musician must have tended to a more exquisite adaptation
of language and music than can be expected when the work of art is
the product of divided labour. In Greece the principle of the
interdependence of language, metre, and musical sound was carried
very far. The different recognised styles had each certain metrical
forms and certain musical scales or keys appropriated to them, in
some cases also a certain dialect and vocabulary. These various
elements were usually summed up in an ethnical type, one of those
which played so large a part in their political history. Such a term
as Dorian was not applied to a particular scale at random, but
because that scale was distinctive of Dorian music: and Dorian music,
again, was one aspect of Dorian temper and institutions, Dorian
literature and thought.

Whether the Greeks were acquainted with harmony--in the modern sense
of the word--is a question that has been much discussed, and may now
be regarded as settled[1]. It is clear that the Greeks were
acquainted with the phenomena on which harmony depends, viz. the
effect produced by sounding certain notes together. It appears also
that they made some use of harmony,--and of dissonant as well as
consonant intervals,--in instrumental accompaniment ([Greek:
krousis]). On the other hand it was unknown in their vocal music,
except in the form of bass and treble voices singing the same melody.
In the instrumental accompaniment it was only an occasional ornament,
not a necessary or regular part of the music. Plato speaks of it in
the _Laws_ as something which those who learn music as a branch of
liberal education should not attempt[1]. The silence of the technical
writers, both as to the use of harmony and as to the tonality of the
Greek scale, points in the same direction. Evidently there was no
_system_ of harmony,--no notion of the effect of _successive_
harmonies, or of two distinct _parts_ or progressions of notes
harmonising with each other.

[Footnote 1: On this point I may refer to the somewhat fuller
treatment in Smith's _Dictionary of Antiquities_, art. MUSICA (Vol.
II, p. 199, ed. 1890-91).]

The want of harmony is to be connected not only with the defective
tonality which was probably characteristic of Greek music,--we have
seen (p. 42) that there is some evidence of tonality,--but still more
with the non-harmonic quality of many of the intervals of which their
scales were composed. We have repeatedly dwelt upon the variety and
strangeness (to our apprehension) of these intervals. Modern writers
are usually disposed to underrate their importance, or even to
explain them away. The Enharmonic, they point out, was produced by
the interpolation of a note which may have been only a passing note
or _appoggiatura_. The Chromatic also, it is said, was regarded as
too difficult for ordinary performers, and most of its varieties went
out of use at a comparatively early period. Yet the accounts which we
find in writers so remote in time and so opposed in their theoretical
views as Aristoxenus and Ptolemy, bear the strongest testimony to the
reality and persistence of

[Footnote 1: Plato, _Legg_. p. 812 d [Greek: panta oun ta toiauta me
prospherein tois mellousin en trisin etesi to tes mousikes chresimon
eklepsesthai dia tachous.]]

these non-diatonic scales. And we have the decisive fact that of the
six scales of the cithara given by Ptolemy (see p. 85) not one is
diatonic in the modern sense of the word. It may be alleged on the
other side that the ideal scale in the _Timaeus_ of Plato is purely
diatonic, and exhibits the strictest Pythagorean division. But that
scale is primarily a framework of mathematical ratios, and could not
take notice of intervals which had not yet been identified with
ratios. It is not certain when the discovery of Pythagoras was
extended to the non-diatonic scales. Even in the _Sectio Canonis_ of
Euclid there is no trace of knowledge that any intervals except those
of the Pythagorean diatonic scale had a numerical or (as we should
say) physical basis[1].

[Footnote 1: In Euclid's _Sectio Canonis_ the Pythagorean division is
assumed, and there is no hint of any other ratio than those which
Pythagoras discovered. Prop. xvii shows how to find the Enharmonic
Lichanos and Paranete by means of the Fourth and Fifth. Prop. xviii
proves against Aristoxenus (of course without naming him), that a
[Greek: pyknon] cannot be divided into two equal intervals; but there
is no attempt to explain the nature of the Enharmonic diesis. It is
worth notice that in these propositions the Lichanos and Paranete of
the Enharmonic scale are called [Greek: lichanos] and [Greek:
paranete] simply, as though the Enharmonic were the only genus--a
usage which agrees with that of the Aristotelian _Problems_ (supra,
p. 33).

According to Ptolemy (i. 13) the Pythagorean philosopher Archytas was
the author of a new division of the tetrachord for each of the three
genera. In it the natural Major Third (5: 4) was given for the large
interval of the Enharmonic, in place of the Pythagorean ditone (81:
64); and the Diatonic was the same as the Middle Soft Diatonic of
Ptolemy. But, as Westphal long ago pointed out (_Harmonik und
Melopoeie_, p. 230, ed. 1863), this scheme is probably the work of the
later Pythagorean school. It seems to be unknown to Plato and
Aristoxenus,--the latter wrote a life of Archytas--and also to
Euclid, as we have seen. The next scheme of musical ratios is that of
Eratosthenes, who makes no use of the natural Major Third.]

In Plato's time, as we can see from a well-known passage of the
_Republic_ (quoted on p. 53), the Enharmonic and Chromatic scales
were the object of much zealous study and experiment on the part of
musicians of different schools,--some seeking to measure and compare
the intervals directly by the ear, others to find numbers in the
consonances which they heard, and both, from the Platonic point of
view, 'setting ears above intelligence,' and therefore labouring in
vain[1].

The multiplicity of intervals, then, which surprises us in the
doctrine of the _genera_ and 'colours' was not an accident or
excrescence. And although some of the finer varieties, such as the
Enharmonic, belong only to the early or classical period, there is
enough to show that it continued to be characteristic of the Greek
musical system, at least until the revival of Hellenism in the age of
the Antonines. The grounds of this peculiarity may be sought partly
in the Greek temperament. We can hardly deny the Greeks the credit of
a fineness of sensibility upon which civilisation, to say the least,
has made no advance. We may note further how entirely it is in
accordance with the analogies of Greek art to find a series of
artistic types created by subtle variations within certain
well-defined limits. For the present purpose, however, it will be
enough to consider how the phenomenon is connected with other known
characteristics of Greek music,--its limited compass and probably
imperfect tonality, the thin and passionless quality of its chief
instrument, on the other hand the keen sense of differences of pitch,
the finely constructed rhythm, and finally the natural adaptation, on
which we have already dwelt, between the musical form and the
language. The last is perhaps the feature of greatest significance,
especially in a comparison of the ancient and modern types of the
art. The beauty and even the persuasive effect of a voice depend, as
we are more or less aware, in the first place upon the pitch or key
in which it is set, and in the second place upon subtle variations of
pitch, which give emphasis, or light and shade. Answering to the
first of these elements ancient music, if the main contention of this
essay is right, has its system of Modes or keys. Answering to the
second it has a series of scales in which the delicacy and variety of
the intervals still fill us with wonder. In both these points modern
music shows diminished resources. We have in the Keys the same or
even a greater command of degrees of pitch: but we seem to have lost
the close relation which once obtained between a note as the result
of physical facts and the same note as an index of temper or emotion.
A change of key affects us, generally speaking, like a change of
colour or of movement--not as the heightening or soothing of a state
of feeling. In respect of the second element of vocal expression, the
rise and fall of the pitch, Greek music possessed in the multiplicity
of its scales a range of expression to which there is no modern
parallel. The nearest analogue may be found in the use of modulation
from a Major to a Minor key, or the reverse. But the changes of genus
and 'colour' at the disposal of an ancient musician must have been
acoustically more striking, and must have come nearer to reproducing,
in an idealised form, the tones and inflexions of the speaking voice.
The tendency of music that is based upon harmony is to treat the
voice as one of a number of instruments, and accordingly to curtail
the use of it as the great source of dramatic and emotional effect.
The consequence is twofold. On the one hand we lose sight of the
direct influence exerted by sound of certain degrees of pitch on the
human sensibility, and thus ultimately on character. On the other
hand the music becomes an independent creation. It may still be a
vehicle of the deepest feeling: but it no longer seeks the aid of
language, or reaches its aim through the channels by which language
influences the mind of man.

[Footnote 1: The two schools distinguished by Plato seem to be those
which were afterwards known as the [Greek: harmonikoi] or
Aristoxeneans, and the [Greek: mathematikoi], who carried on the
tradition of Pythagoras. The [Greek: harmonikoi] regarded a musical
interval as a quantity which could be measured directly by the ear,
without reference to the numerical ratio upon which it might be
based. They practically adopted the system of equal temperament. The
[Greek: mathematikoi] sought for ratios, but by experiment 'among the
consonances which are heard,' as Plato says. Hence they failed
equally with those whose method never rose above the facts of sense.]

       *       *       *       *       *


                   APPENDIX


TABLE I.
_Scales of the seven oldest Keys, with the species of the same name._
[Music: Mixo-lydian. _b_-species.]
[Music: Lydian. _c_-species.]
[Music: Phrygian. _d_-species.]
[Music: Dorian. _e_-species.]
[Music: Hypo-lydian. _f_-species.]
[Music: Hypo-phrygian. _g_-species.]
[Music: Hypo-dorian. _a_-species.]

TABLE II.
_The fifteen Keys._
Mese.
[Music: Hyper-lydian.]
[Music: Hyper-aeolian.]
[Music: Hyper-phrygian.]
[Music: Hyper-ionian.]
[Music: Mixo-lydian.]
[Music: Lydian.]
[Music: Aeolian.]
[Music: Phrygian.]
[Music: Ionian.] Mese.
[Music: Dorian.]
[Music: Hypo-lydian.]
[Music: Hypo-aeolian.]
[Music: Hypo-phrygian.]
[Music: Hypo-ionian.]
[Music: Hypo-dorian.]


The moveable notes ([Greek: phthongoi kinoumenoi]) are distinguished
by being printed as crotchets.

The two highest of these keys--the Hyper-lydian and the
Hyper-aeolian--appear to have been added in the time of the Empire.
The remaining thirteen are attributed to Aristoxenus in the
pseudo-Euclidean _Introductio_ (p. 19, l. 30), and by Aristides
Quintilianus (p. 22, l. 30): but there is no mention of them in the
extant _Harmonics_. It may be gathered, however, from the criticism
of Heraclides Ponticus (see the passage discussed on pp. 9-12) that
the list of keys was being considerably enlarged in his time, and
Aristoxenus, though not named, is doubtless aimed at there. Music of
the 'Orestes' of Euripides (ll. 338-344).

[Symbols: II P C. P? 40 n] [Greek: katoloPHYROMAIZMATEROS haima sas]

[Symbols: Z (?)..1' "Z E E (?)] [Greek: ho s' anab AKCHEUEIZOMEGAS
olbos ou]

[Symbols:-ii P C. I' Z] [Greek: monimoSEMBROTOISZANA de laiphos]

[Symbols: C P-A C p-i?. c,] [Greek: hos tiSAKATOUTHOASTINAxas dai-]

[Symbols:] [Greek: mon KATEKLYSEN deinon]

[Symbols: Z re. z?] [Greek: ponoN[Symbols:???]OOSPONT ou]

[Symbols: I C: C: Pvl(?) 40(?)] [Greek: olethrIoiSIN en kymasin]

[Music: Restoration proposed by Dr. Crusius.

    [Greek: kat-o-lo-phu-ro-mai ma-te-ros ai-ma sas
    o s ana-bak-cheu-ei. o me-gas ol-bos ou
    mon-i-mos en Bro-tois a-na de lai-phos hos
    tis a-ka-tou tho-as ti-na-xas dai-mon
    kat-ek-ly-sen dei-non po-non hos pon-tou
    lab-rois o-leth-ri-oi-sin en ky-ma-sin]

]

The metre is dochmiac, each dochmius consisting of an iambus followed
by a cretic, [Symbols: u--u-]. The points which seem to mark the
ictus, or rhythmical accent, are found on the first syllable of each
of these two feet. If we assume that the first syllable of the iambus
has the chief accent, the dochmius will be correctly expressed as a
musical bar of the form--

[Music]

If the first syllable of the cretic is accented, the dochmius is
divided between two bars, and becomes--

[Music]

The accompaniment or [Greek: krousis], consisting of notes interposed
between the phrases of the melody, is found by Dr. Wessely and Dr.
Crusius in the following characters:

1. The character [Symbols:] appears at the end of every dochmius
shown by the papyrus. After the first, third and fifth it is written
in the same line with the text. After the seventh it is written above
that line, between two vocal notes. Dr. Crusius takes it to be the
instrumental [Symbols: Z], explaining the difference of shape as due
to the necessity or convenience of distinguishing it from the vocal
[Symbols: Z]. If that were so the form [Symbols: 1.] would surely
have been permanent, and would have been given in the schemes of
Alypius and Aristides Quintilianus. I venture to suggest that it is a
mark intended to show the end of the dochmius or bar.

2. The group [Symbols: 21 D] occurs twice, before and after the words
[Greek: deinon ponon]. There is a difficulty about the sign [Symbols:
2], which Dr. Crusius takes to be a _Vortragszeichen_. The other two
characters may be instrumental notes.

The double [Greek: o] of [Greek: hos] (written [Greek: OOS]) is
interesting because it shows that when more than one note went with a
syllable, the vowel or diphthong was repeated. This agrees with the
well-known [Greek: hei-ei-ei-ei-ei-eilissete] of Aristophanes (_Ran._
1314), and is amply confirmed by the newly discovered hymn to Apollo
(p. 134). _Musical part of the Seikelos inscription._

[Symbols: C Z Z KIZ I] [Greek: OSONZESPHAINOU]

[Symbols: K I Z IK O] [Greek: MEDENOLOSSY]

[Symbols: E., C O i; C K Z] [Greek: LYPOUPOSOLI]

[Symbols: I IC I K C OZ] [Greek: GONESTITOZEN]

[Symbols: C K O i [.Z]] [Greek: TOTELOSOCHRO]

[Symbols: K C [=C] C [.=X]] [Greek: NOSAPAITEI]

The inscription of which these lines form part was discovered by Mr.
W. M. Ramsay, and was first published by him in the _Bulletin de
correspondance hellenique_ for 1883, p. 277. It professes to be the
work of a certain [Greek: Seikelos]. The discovery that the smaller
letters between the lines are musical notes was made by Dr. Wessely.

The Seikelos inscription, as Dr. O. Crusius has shown (_Philologus_
for 1893, LII. p. 161), is especially valuable for the light which it
throws upon ancient rhythm. The quantity of the syllables and the
place of the _ictus_ is marked in every case, and we are able
therefore to divide the melody into bars, which may be represented as
follows:

[Symbols: V?--I v %.)..s 10-I? L, I/4 i v^%., L)? % i:\--%. i v1/4d]
[Greek: hoson | zes phai-| nou; meden | holos sy ly-| pou; pros
oli-|]

[Symbols: " \s 10 V1/4.0,? V? V V Lo V V V L.? I/4.?] [Greek: gon
esti to | zen; to telos | ho chronos apai-| tei.] _The hymns recently
discovered at Delphi._

Since these sheets were in type the materials for the study of
ancient Greek music have received a notable accession. The French
archaeologists who are now excavating on the site of Delphi have
found several important fragments of lyrical poetry, some of them
with the music noted over the words, as in the examples already
known. The two largest of these fragments have been shown to belong
to a single inscription, containing a hymn to Apollo, which dates in
all probability from the early part of the third century B.C. Of the
other fragments the most considerable is plausibly referred to the
first century B.C. These inscriptions have been published in the
_Bulletin de correspondance hellenique_ (viii-xii. pp. 569-610), with
two valuable commentaries by M. Henri Weil and M. Theodore Reinach.
The former scholar deals with the text, the latter chiefly with the
music.

The music of the hymn to Apollo is written in the vocal notation. The
metre is the cretic or paeonic ([Symbols:]), and the key, as M.
Reinach has shown, is the Phrygian--the scale of C minor, with the
conjunct tetrachord _c--d[Symbol: flat]--d--f_.

In the following transcription I have followed M. Reinach except in a
few minor points. When two notes are sung to the same syllable the
vowel or diphthong is repeated, as in the fragment of the Orestes (p.
132): but I have thought it best to adhere to the modern method.

[Music: A [Symbols: o r 4] [Greek: [Ton kithari]sei kly-ton pai-da
me-ga-lou [Dios a-]]

[Symbols: oruh.u4r] [Greek: eidete pa]r' a-kro-ni-phe ton-de pa-gon,
am[broth' hos]]]

[Music: [Symbols: #1? ZS A rty r M Y M] [Greek: pa-si thna-tois
pro-phai-neis [logia, tr]i-po-da man-]

[Symbols: 1M I O r O 4ruh.0] [Greek: tei-on hos hei[les, echthros hon
e-phr]ou-rei dra-kon;]

[Symbols: 4:I U!or 4 u] [Greek: ho-te te[oisi belesin e-tr]e-sas
ai-o-lon he-lik-tan[]

[Symbols: I omio r 4] [Greek:] sy-rig-math' hi-eis a-tho-pe[ut' eba;]
[Symbols: U ior.t. U]

[Greek: nyn] de Ga-la-tan a-res..n epe-ras' a-sep-t[os

[Symbols:] [Greek: sal-li-o](?) [Greek: gen-nan..n thalos phi-lon]

[Symbols:] [Greek: da-moi-o lo....ron e-phor..]

[Symbols:] [Greek: te-on k.. e-nai k..]]

(about 12 bars wanting.)] [Music: B [Symbols: I M G M Th I M] [Greek:
Helik]ona ba-thy-den-dron hai la[chete Dios eri]bro-mou]

[Symbols: I M U M Th Th I M I] [Greek: thy-ga-tres eu-o-le[noi]
mo-le[te] syn-o-mai-mon hi-na]

[Symbols: M U M U M W Th G W] [Greek: Phoi-bon o-dai-si mel-pse-te
chry-se-o-ko-man;]

[Symbols: Th O Ps O Th O Th I M Th] [Greek: hos a-na di-ko-ry-ni-a
Par-nas-si-dos tas-de pet-]

[Symbols: I M U M U M I Th I Th G O Ps G] [Greek:-ras he-dra-na
[me]ta kly-tais Del-phi-sin Kas-ta-li-dos]

[Symbols: O Ps O Th G L M] [Greek: eu-u-drou na-mat' e-pi-ni-se-tai,
Del-phon a-na]

[Symbols: G M I Th I M Ph G] [Greek: [pr]o-na man-tei-on e-phe-pon
pa-gon. [ithi] klyta]] [Music: [Symbols:] [Greek: me-ga-lo-po-lis
Ath-this, eu-chai-si phe-ro-ploi-o nai-]

[Symbols:] [Greek:-ou-sa Tri-to-ni-dos da[ped]on a-thrauston, ha-gi-]

[Symbols:] [Greek:-ois de bo-moi-sin Ha-phais-tos ai-thei ne-on]

[Symbols:] [Greek: me-ra tau-ron; ho-mou de nin A-raps at-mos es Y-

[Symbols:] [Greek:-lym-pon a-na-kid-na-tai; li-gy de lo-tos bre-mon]

[Symbols:] [Greek: ai-o-lois [me]le-sin o-dan kre-kei; chry-sea d']

[Symbols:] [Greek: ha-dy-throu[s ki]-tha-ris hym-noi-sin
a-na-mel-pe-tai;]

[Symbols:] [Greek: ho de [the]-o-ron pro-pas es-mos Ath-thi-da
lach[on]]] The notes employed in this piece of music cover about an
octave and a half, viz. from Parypate Hypaton to the Chromatic
Lichanos Hyperbolaion. In two of the tetrachords, viz. Synemmenon and
Hyperbolaion, the intervals employed are Chromatic (or possibly
Enharmonic): in the tetrachord Diezeugmenon they are Diatonic, while
in the tetrachord Meson the Lichanos, which would distinguish the
genus, is wanting. On the other hand there are two notes which do not
belong to the Phrygian key as hitherto known, viz. [Symbol: O], a
semitone below Mese, and [Symbol: B], a semitone below Nete
Diezeugmenon. If we assume that we have before us Chromatic of the
standard kind ([Greek: chroma toniaion]), the complete scale is--

[Music: [Symbols:]]

If the intervals are Enharmonic, or Chromatic of a different variety,
the moveable notes (in this case [Symbols: A K] and [Symbols: 4 3E])
will be somewhat flatter.

M. Reinach is particularly happy in tracing the successive changes of
genus and key in the course of the poem. The opening passage, as he
shows, is Diatonic. With the mention of the Gaulish invasion ([Greek:
Galatan ares]) we come upon the group [Symbols: U 4] (_g--a[Symbol:
b]--a_) of the Chromatic tetrachord Hyperbolaion. At the beginning of
the second fragment the intervals are again Diatonic, up to the point
where the poet turns to address the Attic procession ([Greek: ithi,
klyta megalopolis Aththis, k.t.l.]). From this point the melody lies
chiefly in the Chromatic tetrachord Synemmenon [Symbols: M AK r]
(_c--d[Symbol: o]--d--f_)--a modulation into the key of the
sub-dominant as well as a change of genus. At the end of the fragment
the poet returns to the Diatonic and the original key. With regard to
the _mode_--the question which mainly concerns us at present--M.
Reinach's exposition is clear and convincing. He appeals to three
criteria,--(1) the impression which the music makes on a modern ear;
(2) the endings of the several phrases and divisions; and (3) the
note which recurs most frequently. All these criteria point to a
Minor mode. The general impression made by the Diatonic parts of the
melody is that of the key of _C_ minor: the rhythmical periods end on
one or other of the notes _c-e[Symbol: flat]-g_, which form the chord
of that key: and the note _c_ distinctly predominates. This
conclusion, it need hardly be said, is in entire agreement with the
main thesis of the preceding pages.

The symbols [Symbol: O] and [Symbol: B], which do not belong to the
Phrygian scale, are explained by M. Reinach in a way that is in a
high degree plausible and suggestive. In other keys, he observes, the
symbol [Symbol: O] stands for the note _b_ (natural). Thus it holds
the place of 'leading-note' (_note sensible_) to the keynote, _c_. It
has hitherto been supposed that the standard scale of Greek music,
the octave _a-a_, differed from the modern Minor in the want of a
leading note. Here, however, we find evidence that such a note was
known in practice, if not as a matter of theory, to Greek musicians.
If this is so, it strongly confirms the view that _c_ was in fact the
key-note of the Phrygian scale. The symbol [Symbol: B], which occurs
only once, answers to our _g_[Symbol: flat], and may be similarly
explained as a leading note to _g_, the dominant of the key. We
infer, with M. Reinach, that the scale employed in the hymn is not
only like, but identical with, the scale of our Minor.

The fragment marked C by M. Weil resembles the hymn to Apollo in
subject, and also in metre, but cannot belong to the same work. The
melody is written in the Lydian key, with the notation which we have
hitherto known as the instrumental, but which is now shown to have
been used, occasionally at least, for vocal music. The fragment is as
follows:[Music: [Symbols]

[Greek: t' e-pi te-les-ko-pon tan[de] di-ko-ry-phon klei-tyn hym[in]
Pi-erides ai ni-pho-bo-lous mel-pe-te de Py-thi-on Phoi-bon on
e-tik-te L[a-to]]

M. Reinach connects this fragment with a shorter one, also in the
Lydian key, but not in paeonic metre, viz.--

[Music: [Symbols]

[Greek:.. thon es-che ma ... the-ra kat-ek-ta.... syrigm' a-per..]]

M. Reinach thinks that the mode may be the so-called Hypo-lydian (the
octave _f - f_). The materials are surely too scanty for any
conclusion as to this.

The fragment D, the only remaining piece which M. Reinach has found
it worth while to transcribe, is also written in the instrumental
notation of the Lydian key. The metre is the glyconic. The fragment
is as follows:--

[Music: [Symbols]

[Greek: ton man-to-sy[na klyton] o-leth' hy-gra ch ... despoti
Kre-sion.. ai nae-tas Delphon]] [Music: [Symbols]

[Greek: ...in ap-tais-tous Bak-chou [thiasous] ...te prospolois]]

[Symbols] [Greek: tan te do[u]ri[klyton ar-chan au-xet' a-ge-ra-to
thal ...]]

This piece also is referred by M. Reinach to the Hypo-lydian mode. It
may surely be objected that of three places in which we may fairly
suppose that we have the end of a metrical division, viz. those which
end with the words [Greek: Delphon, prospolois] and [Greek: agerato],
two present us with cadences on the Mese (_d_), and one on the Hypate
(_a_). This seems to point strongly to the Minor Mode.

On the whole it would seem that the only _mode_ (in the modern sense
of the word) of which the new discoveries tell us anything is a mode
practically identical with the modern Minor. I venture to think this
a confirmation, as signal as it was unexpected, of the main
contention of this treatise.

It does not seem to have been observed by M. Weil or M. Reinach that
in all these pieces of music there is the same remarkable
correspondence between the melody and the accentuation that has been
pointed out in the case of the Seikelos inscription (pp. 90, 91). It
cannot indeed be said that every acute accent coincides with a rise
of pitch: but the note of an accented syllable is almost always
followed by a note of lower pitch. Exceptions are, [Greek: aiolon,
hina] (which may have practically lost its accent, cp. the Modern
Greek [Greek: na]), and [Greek: molete] (if rightly restored). The
fall of pitch in the two notes of a circumflexed syllable is
exemplified in [Greek: manteion, heilen, Galatan, Phoibon, odaisi,
klytais, bomoisin, homou]: the opposite case occurs only once, in
[Greek: thnatois]. The observation holds not only of the chief hymn,
but of all the fragments.

INDEX OF PASSAGES DISCUSSED OR REFERRED TO.

      AUTHOR                             PAGE

_Anonymi Scriptio de Musica_, Sec. 28 (the modes employed on different
instruments), 27
  Secs. 63-64 ([Greek: topoi tes phones]), 64

Aristides Quintilianus (ed. Meib.):
  p. 10 (Lichanos), 31
  p. 13 (ethos of music), 63, 66
  p. 15 ([Greek: kata dieseis harmonia]), 53, 98
  p. 21 (Modes in Plato's _Republic_), 94-100
  p. 28 ([Greek: topoi tes phones]), 63

Aristophanes, _Eq._ 985-996 (Dorian Mode), 7, 42

Aristotle:
  _Metaphysics_, iv. 11, p. 1018 _b_ 26 ([Greek: arche]), 46
  Politics, iv. 3, p. 1290 a 20 (Dorian and Phrygian), 105
    viii. 5-7, pp. 1340-1342 (ethos of music), 9, 12, 13, 107
    viii. 7, p. 1342 _a_ 32 (Phrygian Mode), 12, 13, 107
  Problems, xix. 20, p. 919 a 13 (Mese), 43, 82, 102, 107
      26, p. 919 _b_ 21 ([Greek: harmonia]=System), 55
      33, p. 920 _a_ 19 (Hypate), 44
      36, p. 920 _b_ 7 (Mese), 44
      47, p. 922 _b_ 3 (heptachord scales), 33
      48, p. 922 _b_ 10 (modes used by chorus), 14
      49, p. 922 _b_ 31 (high and low pitch), 15

  _Rhetoric_, iii. 1, p. 1403 b 27 ([Greek: tonos] and
[Greek: harmonia]), 15
Aristoxenus (ed. Meib.):
  _Harm._ p. 2, l. 15 (diagrams of [Greek: harmoniai]), 49
    p. 3 (melody of speech),  115
    p. 6 (nomenclature by [Greek: thesis] or position), 81
    p. 6, l. 20 (species of the Octave), 50
    p. 8 (speaking and singing), 115
    p. 8, l. 12 (perfect System), 36
    p. 18 (melody of speech),  90, 115
    p. 23 (Chromatic and Enharmonic), 110
    p. 26, l. 14 (Lichanos indefinite), 110
    p. 27, l. 34 (diagrams), 52
    p. 36, l. 29 (seven [Greek: harmoniai]), 51, 54
    p. 37 ([Greek: tonoi] or keys), 17-19
    p. 48, l. 13 (Lichanos indefinite), 110
    p. 69, l. 6 (nomenclature by position), 81
    _ibid._ (indefinite element in music), 111


Bacchius (ed. Meib.), p. 11 (topoi tes phones), 65
  p. 19 (theseis tetrachordon), 82


Dionysius Hal.:
  c. 11, p. 58 Reisk. (accent and melody), 90, 115
  c. 11, p. 64 Reisk. (rhythm and quantity), 115


Euclid (ed. Meib.):
  _Introductio_, p. 19 (ten-stringed lyre), 38
    p. 20 (modulation), 104
  _Sectio Canonis_, Prop. xvii, xviii, 123

Euripides, _Orest._ 338-343 (musical setting), 92, 130


Heraclides Ponticus ap. Athen. xiv. pp. 624-626 (modes), 9-11, 76


Lasus ap. Athen. xiv. p. 624 _e_ ([Greek: Aiolis harmonia]), 6


Nicomachus (ed. Meib), p. 4 (speaking and singing), 115
  p. 7 (heptachord scales), 34


Pausanias, iv. 27, 4 (Sacadas and Pronomus), 75

Pherecrates ap. Plut. _de Mus._ c. 30, 38

Pindar, _Nem._ iv. 45 (Lydian), 7

Plato:
  _Phileb._ p. 17 ([Greek: harmonia] = System), 55
  _Laches_, p. 188 (Dorian, Ionian, Phrygian, Lydian), 8
  _Repub._ p. 398 (use of modes in education), 7, 8
    p. 399 ([Greek: aulos--poluchordia])., 39, 41
    p. 531 A (study of music), 53, 123
  _Laws_, p. 669 (instrumental music), 120
    p. 812 D (harmony), 122
Plutarch:
  _De Musica_, c. 6 ([Greek: harmoniai]), 25
    cc. 15-17 (Platonic modes), 21-25, 103
    c. 19 ([Greek: tonos, harmonia]), 26

    _De gener. Mundi_, p. 1029 _c_ (Proslambanomenos), 39

Pollux, _Onom._ iv. 78 ([Greek: harmoniai auletikai]), 22, 28

Pratinas ap. Athen. xiv. p. 624 _f_ ([Greek: mete syntonon k.t.l.]), 5

Ptolemy:
  Harm. i. 13 (musical ratios of Archytas), 123
    i. 16 ([Greek: hegemon]=highest note), 45
    _ibid._ (scales of the cithara), 84-86, 102, 123
    _ibid._ (Pythagorean division), 87
    ii. 6 (modulation), 67
    ii. 7 (pitch of scales), 80
    ii. 16 (scales of the cithara), 84-86, 102


Seikelos inscription, 89, 132


Telestes ap. Athen. xiv. p. 625 _f_ (Phrygian and Lydian), 6

Theon Smyrnaeus, c. 8 (enlargement of scale), 37



THE END


_Note on the Seikilos Inscription_ (pp. 89-91, 133).


Since the publication of this work, the Seikilos inscription has been
examined afresh by Mr. J. A. R. Munro (of Lincoln College, Oxford).
The result of his examination is to show that the last note of the
melody has been misread. From a squeeze which he has kindly placed at
my disposal it appears that the word [Greek: apaitei] is written--

[Symbols: c x] [Greek: APAITEI]

The line drawn under the three notes [Symbols: C X I] has caused the
last to be read as [Symbol: 3], which has no meaning here. In fact it
is a reversed Gamma ([Greek: g apestrammenon]), and answers to our
_e_ natural.

Hence the last line of the transcription on pp. 89-90 should be as
follows:

[Music: [Greek: to te-los ho chro-nos a-pai--tei]]

The importance of this correction is obvious. The scale employed is
now seen to be the octave--


          _e f# g a b c# d e_


If, as I ventured to suggest on p. 90, the mode is the Hypo-phrygian
(the scale of our Major mode, but with a flat Seventh), the key-note
will be _a_. The close on the Dominant _e_ will then have to be noted
as a fact supporting the belief that in Greek music the close on the
Dominant or Hypate was the usual one (see p. 45).

The line drawn under the three symbols [Symbols: C N1] is found in
several other cases where the melody gives more than one note for a
syllable. So [Symbols: 1K] (l. 2), and [Symbols: 04)] (l. 3),
[Symbols: K1] and [Symbols: 04)] (l. 4). It does not appear however
under [Symbols: K I Z] (l. 1).


                                                  D. B. M.






End of the Project Gutenberg EBook of The Modes of Ancient Greek Music, by
David Binning Monro

*** 