716
Views
20
CrossRef citations to date
0
Altmetric
Articles

An Information Theoretic Approach to Chord Categorization and Functional Harmony

, &
Pages 219-244 | Received 01 Apr 2014, Accepted 25 Mar 2015, Published online: 22 Sep 2015

References

  • Agmon, E. (1995). Functional harmony revisited: a prototype-theoretic approach. Music Theory Spectrum, 17(2), 196–214.
  • Ariza, C., & Cuthbert, M. (2010). music21: A Toolkit for Computer-Aided Musicology and Symbolic Music Data. In: Proceedings of the International Symposium on Music Information Retrieval, pp. 637–42.
  • Boyd, S., & Vandenberghe, L. (2004). Convex optimization. Cambridge: Cambridge University Press.
  • Brown, P. F., deSouza, P. V., Mercer, R. L., Pietra, V. J. D., & Lai, J. C. (1992). Class-based n-gram models of natural language. Computational Linguistics, 18(4), 467–479.
  • Chechik, G., Globerson, A., Tishby, N., & Weiss, Y. (2005). Information bottleneck for Gaussian variables. Journal of Machine Learning Research, 6(1), 165–188.
  • Cohn, R. (1998). Introduction to Neo-Riemannian theory: A survey and a historical perspective. Journal of Music Theory, 42(2), 167–180.
  • Conklin, D. (2010). Discovery of distinctive patterns in music. Intelligent Data Analysis, 14(5), 547–554.
  • Cover, T. M., & Thomas, J. A. (2012). Elements of information theory. New York, NY: Wiley.
  • De Clercq, T., & Temperley, D. (2011). A corpus analysis of rock harmony. Popular Music, 30, 47–70.
  • Feller, W. (1950). An introduction to probability theory and its applications. New York, NY: Wiley.
  • Friedman, A., & Goldberger, J. (2013). Information theoretic pairwise clustering. In E. Hancock & M. Pelillo (Eds.), SIMBAD 2013 (Lecture Notes in Computer Science 7953 (pp. 106–119). Berlin, Heidelberg: Springer-Verlag.
  • Friedman, N., Mosenzon, O., Slonim, N., & Tishby, N. (2001). Multivariate information bottleneck. Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence (UAI). Cambridge, MA: MIT Press.
  • Gasparini, F. (1715). L’Armonico Pratico al Cimbalo. Venice.
  • Hastie, T., Tibshirani, R., Friedman, J., & Franklin, J. (2005). The elements of statistical learning: data mining, inference and prediction. The Mathematical Intelligencer, 27(2), 83–85.
  • Hecht, R.M., Noor, E., & Tishby, N. (2009, Sept). Speaker recognition by gaussian information bottleneck. Paper presented at Tenth Annual Conference of the International Speech Communication Association (INTERSPEECH 2009); Brighton, UK,
  • Heinichen, J.D. (1728). Der Generalbass in der Komposition. Dresden.
  • Huron, D. (2006). Sweet anticipation: Music and the psychology of expectation. Cambridge, MA: MIT Press.
  • Kirenberg, J.P. (1774). Die Kunst des reinen Satzes in der Musik. Berlin und K\"{o}nigsberg: G. J. Decker und G. L. Hartung.
  • Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680.
  • Kostka, S. M., & Payne, D. (1984). Tonal harmony: With an introduction to twentieth-century music (1st ed.). New York: A.A. Knopf.
  • Lerdahl, F., & Jackendoff, R. S. (1983). A generative theory of tonal music. Cambridge, MA: MIT Press.
  • Loui, P. (2012). Learning and liking of melody and harmony: Further studies in artificial grammar learning. Topics in Cognitive Science, 4(4), 554–567.
  • Loui, P., & Wessel, D. (2007). Harmonic expectation and affect in Western music: Effects of attention and training. Perception & psychophysics, 69(7), 1084–1092.
  • Loui, P., Wessel, D.L., & Kam, C.L.H. (2010). Humans rapidly learn grammatical structure in a new musical scale. Music perception, 27(5), 377–388.
  • Mavromatis, P. (2009). Minimum description length modelling of musical structure. Journal of Mathematics and Music, 3(3), 117–136. doi:10.1080/17459730903313122.
  • Mavromatis, P. (2012). Exploring the rhythm of the Palestrina style: A case study in probabilistic grammar induction. Journal of Music Theory, 56(2), 169–223.
  • Meeús, N. (2000). Toward a post-Schoenbergian grammar of tonal and pre-tonal harmonic progressions. Music Theory Online, 6(1).
  • Niedt, F.E. (1706). Musikalische Handleitung. Hamburg.
  • Pearce, M.T., & Wiggins, G.A. (2006). Expectation in melody: The influence of context and learning. Music Perception, 23(5), 377–405.
  • Pereira, F., Tishby, N., & Lee, L. (1993, June). Distributional clustering of English words. Paper presented at the 31st Annual Meeting on Association for Computational Linguistics; Columbus, OH USA.
  • Praetorius, M. (1615). Syntagma musicum III (3 Vols). Wittenberg: Johannes Richter.
  • Quinn, I. (2005, Nov). Harmonic function without primary triads. Paper presented at the Annual Meeting of Society for Music Theory, Boston/Cambridge, MA, USA.
  • Quinn, I., & Mavromatis, P. (2011). Voice-leading prototypes and harmonic function in two chorale corpora. In C. Agon, M. Andreatta, G. Assayag, E. Amiot, J. Bresson, & J. Mandereau (Eds.), Mathematics and computation in music, Vol. 6726 (pp. 230–240). Berlin: Springer.
  • Raphael, C., & Stoddard, J. (2004). Functional harmonic analysis using probabilistic models. Computer Music Journal, 28(3), 45–52.
  • Rohrmeier, M. (2005). Towards modelling movement in music: Analysing properties and dynamic aspects of pc set sequences in Bach’s chorales (MPhil dissertation), University of Cambridge, UK. (Published as Darwin College Research Report 04.)
  • Rohrmeier, M., & Cross, I. (2008, Aug.). Statistical properties of harmony in Bach’s chorales. Paper presented at the the 10th International Conference on Music Perception and Cognition, Sapporo, Japan,
  • Sadai, Y., Davis, J., & Shlesinger, M. (1980). Harmony in its systemic and phenomenological aspects. Jerusalem, Israel: Yanetz.
  • Schenker, H. (1925). Das Meisterwerk in der Musik, Vol. 1. New York, NY: G. Olms.
  • Schenker, H. (1935/1979). Der frei Satz. Vienna: Universal Edition. [Published in English as Free Composition (trans. and ed. E. Oster). London: Longman.]
  • Schneiderman, E., Slonim, N., Tishby, N. (2002). Analyzing neural codes using the information bottleneck method (Technical Report). Jerusalem, Israel: The Hebrew University.
  • Schoenberg, A. (1969). Structural functions of harmony. New York, NY: WW Norton & Company.
  • Shannon, C. E. (2001). A mathematical theory of communication. ACM SIGMOBILE Mobile Computing and Communications Review, 5(1), 3–55.
  • Slonim, N., Friedman, N., & Tishby, N. (2006). Multivariate information bottleneck. Neural Computation, 18(8), 1739–1789.
  • Slonim, N., & Tishby, N. (2000). Document clustering using word clusters via the information bottleneck method. In SIGIR ’00 Proceedings of the 23rd annual international ACM SIGIR conference on research and development in information retrieval (pp. 208-215) New York, NY: ACM.
  • Temperley, D. (2007). Music and probability. Cambridge, MA: MIT Press.
  • Temperley, D. (2009). A statistical analysis of tonal harmony. http://theory.esm.rochester.edu/temperley/kp-stats/index.html
  • Temperley, D., & VanHandel, L. (2013). Introduction to the special issues on corpus methods. Music Perception: An Interdisciplinary Journal, 31(1), 1–3.
  • Tillmann, B., & Bigand, E. (2004). The relative importance of local and global structures in music perception. The Journal of Aesthetics and Art Criticism, 62(2), 211–222.
  • Tishby, N., Pereira, F., & Bialek, W. (1999, Sept.). The information bottleneck method. Paper presented at the 37th Annual Allerton Conference on Communication, Control and Computing; Allerton, IL, USA.
  • Tishby, N., & Polani, D. (2011). Information theory of decisions and actions. In V. Cutsuridis, A. Hussain, & J. G. Taylor (Eds.), Perception-action cycle (pp. 601–636). Berlin: Springer.
  • Tymoczko, D. (2003). Progressions fondamentales, functions, degrés: Une grammaire de l’harmonie tonale élémentaire. Musurgia, 10(3–4), 35–64.
  • Tymoczko, D. (2006). The geometry of musical chords. Science, 313(5783), 72–74.
  • Tymoczko, D. (2011). A geometry of music: Harmony and counterpoint in the extended common practice. New York, NY: Oxford University Press.
  • White, C.W., & Quinn, I. (2014). The Yale-classical archives corpus. In International Conference for Music Perception and Cognition: Seoul, Korea. http://ycac.yale.edu

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.