Clarify transpose octave-change documentation

[webern]

Why does the transpose element have both chromatic and diatonic elements? Are these both necessary? What is an example of when they would not be saying the same thing? i.e., it seems like they would always look like this...

diatonic, chromatic, name
-1      , -2       , Bb
-2      , -4       , Ab
-3      , -6       , Gb
-4      , -7       , F
-5      , -9       , Eb
...etc

diatonic is optional. Is it ever required for disambiguation?

Thanks.

Cross-ref: webern/mx#115

[mscuthbert]

Yes, definitely they're needed, at very least for:

diatonic, chromatic, name
-4      , -6       , F#

in particular, as a clarinetist, I'm generally in "-1/-2 Bb" in a score, but what if the score goes to 6#s, am I expected to play in 8 sharps? Generally what happens is my passage will be notated in 4-flats instead, so my transpose in musicxml will now be given as

diatonic, chromatic, name
-2       , -2       , A#

which makes my life a lot easier.

[webern]

I see, so diatonic provides the 'letter'. So to write your F# example instead as Gb would be this?

diatonic, chromatic, name
-3      , -6       , Gb

I guess I was thinking F# could have been disambiguated from Gb by writing the transposition as chromatic: +6, and adding an octave offset of -1. I guess, by adding diatonic, MusicXML has given two ways of achieving the same thing? i.e. are these equivalent?

<transpose>
    <diatonic>-3</diatonic>
    <chromatic>-6</chromatic>
</transpose>

...is the same as?

<transpose>
    <chromatic>6</chromatic>
    <octave-change>-1</octave-change>
</transpose>

(BTW, I haven't figured out harmonic spelling algorithms, in general, yet... I guess, in my head, there's some sort of implicit spelling going on where -6 results in Gb and +6 results in F#)

[mdgood]

Octave offsets are used only for intervals greater than an octave, not for disambiguating within an octave. I thought we had clarified this in the documentation for a related case but it looks like we haven't. We should probably add a sentence to the effect that "The octave-change element should be included when using transposition intervals of an octave and more, and should not be present for intervals of less than an octave."

In general, intervals - whether for transposition or analysis - require some sort of two-dimensional representation in common Western music notation. A common example is to distinguish two different ways of spelling a tritone. Is it an augmented fourth (C to F#, diatonic = 3) or a diminished fifth (C to Gb, diatonic = 4)? The chromatic value is 6 in both cases.

There's a nice article on interval representation by Walter Hewlett at https://www.ccarh.org/publications/reprints/base40/. Base 40 is one way to represent these two dimensions; MusicXML's diatonic / chromatic is another; and Finale's interval and key alteration is yet another.

[webern]

Thank you! This discussion was very helpful and I will read that paper. This issue can be closed unless you want to repurpose it for the documentation tweak.

[mdgood]

I've renamed the issue to reflect the underlying documentation issue and added it to our 4.0 milestone.

[webern]

I guess another thing to clarify... the diatonic element is optional. In the absence of a diatonic element, is the interval well-defined? Is it this? Seems like the diatonic element should be required.

Chromatic	Name	Or?	Common	What I guess I would do	Diatonic
-11	In Db	in C#?		Db	-6
-10	in D			D	-6
-9	in Eb			Eb	-5
-8	in E			E	-5
-7	in F			F	-4
-6	in Gb			Gb	-3
-5	in G			G	-3
-4	in Ab			Ab	-2
-3	in A			A	-2
-2	in Bb			Bb	-1
-1	in Cb?	in B?		B	-1
0	in C			C	0
1	in C#	in Db?		Db	1
2	in D			D	1
3	in D#?	in Eb?	Eb is common	Eb	2
4	in E			E	2
5	in F			F	3
6	in F#			F#	3
7	in G			G	4
8	in G#	in Ab?		Ab	5
9	in A			A	5
10	in A#	in Bb?	Bb is common	Bb	6
11	in B			B	6

[mdgood]

The diatonic interval is not well-defined unless it is specified. I expect your table is pretty common but it's not mandated. The <diatonic> element is optional in order to support software that may not have a complete representation for transposition. This is the type of thing that I expect will be required in MNX while remaining optional In MusicXML.