A Cognitive Information Theory of Music (CITM)

This project contains the code and data for Chan (2008). Portions of the project are based on Yang and Speidel (2005), Eerola et al. (2007, 2001), and Cilibrasi et al. (2004); see the AUTHORS file for details.

Introduction

CITM is a novel information model which quantifies human music cognition in bits. It models musical complexity, similarity, and preference using tools from algorithmic information theory, statistical distances, and complex systems. This project is organized as follows. The information, similarity, and fitness directories contain the code and data from Chapters 3, 4, and 5, respectively. The information directory consists of the following:

Directory	Description
chan	My proposed and reduced measures
cilibrasi	Baseline measure from Cilibrasi (2004)
conley	Complexity for Conley (1981)
shmulevich	Complexity for Shmulevich and Povel (2000)
heyduk	Complexity for Heyduk (1975)

while the similarity directory includes the following:

File	Description
experiment-1	Similarity for Cambouropoulos (2001)
experiment-2	Similarity for Eerola et al. (2007, 2001)
experiment-3	My similarity experiment

and the fitness directory includes the following:

File	Description
experiment-1	Replication of Chan and Wiggins (2005)
experiment-2	My fitness experiment
experiment-3	Fitness for Jeong et al. (1998)
experiment-4	Fitness for Heyduk (1975)
experiment-5	Fitness for Vitz (1966)

Additional tools are placed under the utilities directory:

File	Description
asymmetry.m	Calculates departure from symmetry
esac.y	Parses EsAC
mutate.c	Mutates OPM files
nb2opm.c	Converts NB to OPM
opm2mid.c	Converts OPM to MIDI
opmcat.c	Concatenates OPM files
printcor.m	Prints correlation with gMDL+
random.c	Generates random music (Jeong et al., 1998)
shares.pl	Converts EsAC files into a shell archive
triangle.m	Calculates departure from triangle inequality
trilmat.m	Row-major version of squareform('tovector')
trilvec.m	Row-major version of squareform('tomatrix')
vitz.c	Generates tone sequences (Vitz, 1966)

The non-M-files are only used if you regenerate the stimuli for Chapter 5 (see below). The EsAC format is described in Schaffrath (1997). A note-beat (NB) file consists of note statements of the form Note [ontime] [offtime] [pitch] plus beat statements of the form Beat [time] [level], as defined by Temperley and Sleator (1999). An OPM or onset-pitch-metrical level file consists of the number of notes on the first line, followed by OPM statements of the form [time] [pitch] [level] on subsequent lines. Symmetricity and triangle inequality violations are calculated as per Johnson et al. (2002).

Requirements

In additional to the GNU development environment (bash, g++, gcc, make, and yacc), we require the following.

• A recent version of MATLAB (or Octave), Perl 5, Ruby 2, and mftext from abcmidi.

• To regenerate the stimuli, we need the sources for Melisma and Dynamic Creator under the utilities directory:

  cd citm/utilities
  curl http://www.link.cs.cmu.edu/melisma/melisma2003.tar.gz | tar zxvf -
  curl http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/DC/dcmt0.1.tgz | tar zxvf -
  cd ../..

• To replicate the psychological experiments, we need Objective-C and Xcode on Mac OS X 10.3 (unsupported).

Compilation and Execution

Perform the following steps under the citm directory.

1. Type make to compile the code.
2. Type make regenerate if you wish to regenerate the musical fitness stimuli using current time as seed (results will differ).
3. Type make reproduce, then run analysis.m under each of the results subdirectories (see Appendix for a transcript).
4. The similarity/Experiment and fitness/Experiment directories contain Xcode projects for the validation experiments. They could be useful if you wish to extend the psychological experiments herein (unsupported).

Erratum

The baseline results in Chapter 3 are wrong because part of the workflow was done in text mode. To simulate this error, insert exit(0) if n == mn into cilibrasi.rb, right before na.each.

Tak-Shing Chan

20 December 2017

References

Cambouropoulos, E. (2001). Melodic cue abstraction, similarity, and category formation: A formal model. Music Perception, 18(3), 347-370.

Chan, T.-S. T. and Wiggins, G. A. (2005, July). A computational memetics approach to music information and aesthetic fitness. Paper presented at the IJCAI Workshop on Computational Creativity.

Chan, T.-S. T. (2008). A cognitive information theory of music: A computational memetics approach (Unpublished doctoral dissertation). University of London, London, UK.

Cilibrasi, R., Vitanyi, P., & de Wolf, R. (2004). Algorithmic clustering of music based on string compression. Computer Music Journal, 28(4), 49-67.

Conley, J. K. (1981). Physical correlates of the judged complexity of music by subjects differing in musical background. British Journal of Psychology, 72, 451-464.

Eerola, T., & Bregman, M. (2007). Melodic and contextual similarity of folk song phrases. Musicae Scientiae, Discussion Forum 4A, 211-233.

Eerola, T., Jarvinen, T., Louhivuori, J., & Toiviainen, P. (2001). Statistical features and perceived similarity of folk melodies. Music Perception, 18(3), 275-296.

Heyduk, R. G. (1975). Rated preference for musical compositions as it relates to complexity and exposure frequency. Perception and Psychophysics, 17(1), 84-91.

Jeong, J., Joung, M. K., & Kim, S. Y. (1998). Quantification of emotion by nonlinear analysis of the chaotic dynamics of electroencephalograms during perception of 1/f music. Biological Cybernetics, 78(3), 217-225.

Johnson, D. S., Gutin, G., McGeoch, L. A., Zhang, W., & Zverovitch, A. (2002). Experimental analysis of heuristics for the ATSP. In G. Gutin & A. Punnen (Eds.), The Traveling Salesman Problem and Its Variations (pp. 445-487). Dordrecht: Kluwer Academic Publishers.

Schaffrath, H. (1997). The Essen Associative Code: A code for folksong analysis. In E. Selfridge-Field (Ed.), Beyond MIDI: The Handbook of Musical Codes (pp. 343-361). Cambridge, MA: MIT Press.

Shmulevich, I., & Povel, D.-J. (2000). Measures of temporal pattern complexity. Journal of New Music Research, 29(1), 61-69.

Temperley, D., & Sleator, D. (1999). Modeling meter and harmony: A preference-rule approach. Computer Music Journal, 23(1), 10-27.

Vitz, P. C. (1966). Affect as a function of stimulus variation. Journal of Experimental Psychology, 71(1), 74-79.

Yang, J., & Speidel, U. (2005, September). A T-decomposition algorithm with O(n log n) time and space complexity. Paper presented at the International Symposium on Information Theory. https://doi.org/10.1109/ISIT.2005.1523285

Appendix. Transcript of Results

A MATLAB diary is appended below (after make reproduce):

>> addpath /home/takshingchan/citm/utilities
>> % 3.8.1 Experiment 1
>> cd information/shmulevich/results
>> analysis
ncf-ftd         r(33) = 0.44174 (p = 0.0039457), gMDL+ = 0.81111
plain-ftd       r(33) = -0.44841 (p = 0.99655), gMDL+ = 1.2704
cilibrasi       r(33) = 0.10458 (p = 0.27496), gMDL+ = 1.2704
>> % 3.8.2 Experiment 2
>> cd ../../conley/results/1
>> analysis
ncf-ftd
- Graduate  r(14) = 0.41527 (p = 0.054848), gMDL+ = 1.8282
- Sophomore r(14) = 0.66564 (p = 0.0024427), gMDL+ = -0.67028
- Non-major r(14) = 0.59758 (p = 0.0072504), gMDL+ = 0.29844
plain-ftd
- Graduate  r(14) = 0.48901 (p = 0.027287), gMDL+ = 1.3615
- Sophomore r(14) = 0.72824 (p = 0.00068984), gMDL+ = -1.8584
- Non-major r(14) = 0.65668 (p = 0.0028605), gMDL+ = -0.52605
cilibrasi
- Graduate  r(14) = 0.57495 (p = 0.0099071), gMDL+ = 0.56324
- Sophomore r(14) = 0.78453 (p = 0.00016001), gMDL+ = -3.2844
- Non-major r(14) = 0.8041 (p = 8.6895e-05), gMDL+ = -3.8921
>> % 3.8.3 Experiment 3
>> cd ../2
>> analysis
ncf-ftd
- Graduate  r(14) = 0.48571 (p = 0.028238), gMDL+ = 1.3864
- Sophomore r(14) = 0.68993 (p = 0.0015497), gMDL+ = -1.0916
- Non-major r(14) = 0.62716 (p = 0.0046565), gMDL+ = -0.088188
plain-ftd
- Graduate  r(14) = 0.54564 (p = 0.014398), gMDL+ = 0.8701
- Sophomore r(14) = 0.73447 (p = 0.00059722), gMDL+ = -1.997
- Non-major r(14) = 0.66793 (p = 0.0023442), gMDL+ = -0.70808
cilibrasi
- Graduate  r(14) = 0.64777 (p = 0.003331), gMDL+ = -0.38797
- Sophomore r(14) = 0.81385 (p = 6.2481e-05), gMDL+ = -4.2227
- Non-major r(14) = 0.81005 (p = 7.1206e-05), gMDL+ = -4.0915
>> % 3.8.4 Experiment 4
>> cd ../../../heyduk/results
>> analysis
ncf-ftd         r(2) = 0.98768 (p = 0.0061589), gMDL+ = -3.6414
plain-ftd       r(2) = 0.87465 (p = 0.062673), gMDL+ = -0.37071
cilibrasi       r(2) = 0.83806 (p = 0.080972), gMDL+ = -0.058764
>> % 4.4.1 Model Selection with Three Experiments (p. 69)
>> % - Correlation with Deliege's (1996) Experiment
>> cd ../../../similarity/results/cambouropoulos
>> analysis
bach-dist1      r(24) = 0.2987 (p = 0.069134), gMDL+ = 2.491
bach-dist2      r(24) = 0.38291 (p = 0.026757), gMDL+ = 1.9257
bach-dist3      r(24) = 0.42199 (p = 0.015882), gMDL+ = 1.5534
>> % - Correlation with Eerola et al.'s (2001) Experiment
>> % - Correlation with Eerola and Bregman's (2007) Experiment
>> cd ../eerola
>> analysis
eerola01-dist1  r(103) = 0.42047 (p = 3.9895e-06), gMDL+ = -4.0067
eerola01-dist2  r(103) = 0.45405 (p = 5.726e-07), gMDL+ = -5.8189
eerola01-dist3  r(103) = 0.4178 (p = 4.6141e-06), gMDL+ = -3.872
eerola07-dist1  r(188) = 0.51983 (p = 7.6054e-15), gMDL+ = -22.556
eerola07-dist2  r(188) = 0.45283 (p = 2.6947e-11), gMDL+ = -14.611
eerola07-dist3  r(188) = 0.49928 (p = 1.1309e-13), gMDL+ = -19.922
eerola01        asymmetry = 0, triangle = 0.0034313
eerola07        asymmetry = 0, triangle = 0.0035215
eerola01-dist1  asymmetry = 0.0025063, triangle = 0
eerola01-dist2  asymmetry = 0, triangle = 0
eerola01-dist3  asymmetry = 0.0058994, triangle = 0
eerola07-dist1  asymmetry = 0.0061873, triangle = 0
eerola07-dist2  asymmetry = 2.8793e-05, triangle = 0
eerola07-dist3  asymmetry = 0.016385, triangle = 0
>> % 4.4.2 Validation of H1
>> cd ../chan
>> analysis
chopin-dist1    r(76) = 0.61654 (p = 9.2944e-10), gMDL+ = -12.367
chopin-dist1    asymmetry = 0.0015351, triangle = 0
chopin          asymmetry = 0, triangle = 0
chopina         asymmetry = 0.078926, triangle = 0.00018017
>> % 5.3.3 Model Selection with Three Experiments
>> % - Correlation with Vitz's (1966) Experiment
>> cd ../../../fitness/results/vitz
>> analysis
vitz-uid1       r(4) = 0.84667 (p = 0.01673), gMDL+ = -0.72447
vitz-uid2       r(4) = 0.94361 (p = 0.00234), gMDL+ = -2.9889
vitz-uid3       r(4) = 0.86956 (p = 0.012205), gMDL+ = -1.0712
>> % - Correlation with Heyduk's (1975) Experiment
>> cd ../heyduk
>> analysis
heyduk_uid1     r(2) = 0.74572 (p = 0.12714), gMDL+ = 0.42395
heyduk-uid2     r(2) = 0.74938 (p = 0.12531), gMDL+ = 0.41026
heyduk-uid3     r(2) = 0.93187 (p = 0.034063), gMDL+ = -1.1768
>> % - Correlation with Jeong et al.'s (1998) Experiment
>> cd ../jeong/2
>> analysis
jeong-uid1      r(1) = 0.8459 (p = 0.17906), gMDL+ = 0.020653
jeong-uid2      r(1) = 0.99657 (p = 0.026362), gMDL+ = -3.5428
jeong-uid3      r(1) = -0.99235 (p = 0.96061), gMDL+ = -0.058892
>> % 5.3.4 Validation of H2 and H3
>> cd ../../chan
>> analysis
essen-uid1      r(176) = 0.18205 (p = 0.0075047), gMDL+ = 3.0835
essen-uid2      r(176) = 0.66223 (p = 3.9205e-24), gMDL+ = -43.726
essen-uid3      r(176) = 0.66943 (p = 8.5045e-25), gMDL+ = -45.242