Empirically testing Tonnetz, voice-leading, and spectral models of perceived triadic distance

References

• Bachem, Albert. 1950. “Tone Height and Tone Chroma as Two Different Pitch Qualities.” Acta Psychologica 7 80–88. doi: 10.1016/0001-6918(50)90004-7
   Web of Science ®Google Scholar
• Balzano, Gerald J. 1980. “The Group-Theoretic Description of 12-Fold and Microtonal Pitch Systems.” Computer Music Journal 4 (4): 66–84. doi: 10.2307/3679467
   Web of Science ®Google Scholar
• Bernstein, Joshua G., and Andrew J. Oxenham. 2003. “Pitch Discrimination of Diotic and Dichotic Tone Complexes: Harmonic Resolvability or Harmonic Number?” Journal of the Acoustical Society of America 113 (6): 3323–3334. doi: 10.1121/1.1572146
   PubMed Web of Science ®Google Scholar
• Bharucha, Jamshed Jay, and Carol L. Krumhansl. 1983. “The Representation of Harmonic Structure in Music: Hierarchies of Stability as a Function of Context.” Cognition 13 (1): 63–102. doi: 10.1016/0010-0277(83)90003-3
   PubMed Web of Science ®Google Scholar
• Bigand, Emmanuel, Richard Parncutt, and Fred Lerdahl. 1996. “The Perception of Musical Tension in Short Chord Sequences: The Influence of Harmonic Function, Sensory Dissonance, Horizontal Motion, and Musical Training.” Perception and Psychophysics 58 (1): 125–141. doi: 10.3758/BF03205482
   Web of Science ®Google Scholar
• Bregman, Albert S. 1990. Auditory Scene Analysis. Cambridge, MA: MIT Press.
   Google Scholar
• Callender, Clifton. 2004. “Continuous Transformations.” Music Theory Online 10 (3). http://www.mtosmt.org/issues/mto.04.10.3/mto.04.10.3.callender.pdf.
   Google Scholar
• Callender, Clifton, Ian Quinn, and Dmitri Tymoczko. 2008. “Generalized Voice-Leading Spaces.” Science 320 (5874): 346–348. doi: 10.1126/science.1153021
   PubMed Web of Science ®Google Scholar
• Capuzzo, Guy. 2014. “Neo-Riemannian Theory and the Analysis of Pop-Rock Music.” Music Theory Spectrum 26 (2): 177–199. http://dx.doi.org/10.1525/mts.2004.26.2.177. doi: 10.1525/mts.2004.26.2.177
   Web of Science ®Google Scholar
• Castellano, Mary A, J. J. Bharucha, and Carol L. Krumhansl. 1984. “Tonal Hierarchies in the Music of North India.” Journal of Experimental Psychology: General 113 (3): 394–412. doi: 10.1037/0096-3445.113.3.394
   PubMed Web of Science ®Google Scholar
• Chalmers, John. 1990. Divisions of the Tetrachord, edited by Larry Polansky and Carter Scholz. Lebanon, NH: Frog Peak Music.
   Google Scholar
• Chew, Elaine. 2006. “Slicing It All Ways: Mathematical Models for Tonal Induction, Approximation, and Segmentation Using the Spiral Array.” INFORMS Journal on Computing 18 (3): 305–320. http://dx.doi.org/10.1287/ijoc.1050.0134. doi: 10.1287/ijoc.1050.0134
   Web of Science ®Google Scholar
• Cohen, David E. 2002. “Notes, Scales, and Modes in the Earlier Middle Ages.” In The Cambridge History of Western Music Theory, edited by T. Christensen. Cambridge, UK: Cambridge University Press.
   Google Scholar
• Cohn, Richard. 1997. “Neo-Riemannian Operations, Parsimonious Trichords, and Their ‘Tonnetz’ Representations.” Journal of Music Theory 41 (1): 1–66. doi: 10.2307/843761
   Web of Science ®Google Scholar
• Cohn, Richard. 1998. “Introduction to Neo-Riemannian Theory: A Survey and a Historical Perspective.” Journal of Music Theory 42 (2): 167–180. doi: 10.2307/843871
   Web of Science ®Google Scholar
• Deutsch, Diana. 1982. “The Processing of Pitch Combinations.” In The Psychology of Music, edited by Diana Deutsch. New York, NY: Academic Press.
   Google Scholar
• Douthett, Jack, and Peter Steinbach. 1998. “Parsimonious Graphs: A Study in Parsimony, Contextual Transformations, and Modes of Limited Transposition.” Journal of Music Theory 42 (2): 241–263. doi: 10.2307/843877
   Web of Science ®Google Scholar
• Drobisch, Moritz Wilhelm. 1855. “Über musikalische Tonbestimmung und Temperatur.” In Abhandlungen der mathematisch-physischen Classe Königlich sächsichen Gesellschaft der Wissenschaften. Leipzig: S. Hirzel. https://archive.org/stream/bub_gb_SxoWAAAAYAAJ#page/n11/mode/2up.
   Google Scholar
• Euler, Leonhard. 1739. Tentamen novae theoriae musicae ex certissismis harmoniae principiis dilucide expositae. Saint Petersburg: Saint Petersburg Academy. http://eulerarchive.maa.org/pages/E033.html.
   Google Scholar
• Gollin, Edward. 2011. “From Matrix to Map: Tonbestimmung, the Tonnetz, and Riemann's Combinatorial Conception of Interval.” Chap. 9 in The Oxford Handbook of Neo-Riemannian Music Theories, edited by Edward Gollin and Alexander Rehding, 271–293. Oxford, UK: Oxford University Press.
   Google Scholar
• Holland, Simon. 1994. “Learning about Harmony with Harmony Space: An Overview.” In Music Education: An Artificial Intelligence Approach, edited by M. Smith, A. Smaill, and G. Wiggins. London: Springer-Verlag. https://ccrma.stanford.edu/files/papers/stanm88.pdf.
   Google Scholar
• Huron, David. 1989. “Voice denumerability in polyphonic music of homogeneous timbres.” Music Perception 6 (4): 361–382. doi: 10.2307/40285438
   Web of Science ®Google Scholar
• Huron, David. 2001. “Tone and Voice: A Derivation of the Rules of Voice-Leading from Perceptual Principles.” Music Perception 19 (1): 1–64. doi: 10.1525/mp.2001.19.1.1
   Web of Science ®Google Scholar
• Hyer, Brian. 1995. “Reimag(in)ing Riemann.” Journal of Music Theory 39 (1): 101–138. doi: 10.2307/843900
   Web of Science ®Google Scholar
• Iacobucci, Dawn. 2001. “Measurement.” Journal of Consumer Psychology 10 (1&2): 55–69.
   Google Scholar
• Janata, Petr, Jeffrey L. Birk, John D. Van Horn, Marc Leman, Barbara Tillmann, and Jamshed J. Bharucha. 2002. “The Cortical Topography of Tonal Structures Underlying Western Music.” Science 298 (5601): 2167–2170. doi: 10.1126/science.1076262
   PubMed Web of Science ®Google Scholar
• Kessler, Edward J., Christa Hansen, and Roger N. Shepard. 1984. “Tonal Schemata in the Perception of Music in Bali and in the West.” Music Perception 2 (2): 131–165. doi: 10.2307/40285289
   Web of Science ®Google Scholar
• Krumhansl, Carol L. 1990. Cognitive Foundations of Musical Pitch. Oxford, UK: Oxford University Press.
   Google Scholar
• Krumhansl, Carol L. 1998. “Perceived Triad Distance: Evidence Supporting the Psychological Reality of Neo-Riemannian Transformations.” Journal of Music Theory 42 (2): 265–281. doi: 10.2307/843878
   Web of Science ®Google Scholar
• Krumhansl, Carol L, and Edward J. Kessler. 1982. “Tracing the Dynamic Changes in Perceived Tonal Organization in a Spatial Representation of Musical Keys.” Psychological Review 89 (4): 334–368. doi: 10.1037/0033-295X.89.4.334
   PubMed Web of Science ®Google Scholar
• Longuet-Higgins, H. C. 1962. “Letter to a Musical Friend.” The Music Review 23 (3): 244–248.
   Google Scholar
• Longuet-Higgins, H. C. 1962. “Second Letter to a Musical Friend.” The Music Review 23 (4): 271–280.
   Google Scholar
• McLachlan, Neil M., David J. T. Marco, and Sarah J. Wilson. 2012. “Pitch Enumeration: Failure to Subitize in Audition.” PLoS ONE 7 (4): e33661. http://dx.doi.org/10.1371/journal.pone.0033661.
   Google Scholar
• Milne, Andrew J. 2009. “A Psychoacoustic Model of Harmonic Cadences.” Master's thesis, University of Jyväskylä, Finland. https://jyx.jyu.fi/dspace/bitstream/handle/123456789/21724/URN_NBN_fi_jyu-200908173596.pdf?sequence=1.
   Google Scholar
• Milne, Andrew J., Robin Laney, and David B. Sharp. 2015. “A Spectral Pitch Class Model of the Probe Tone Data and Scalic Tonality.” Music Perception 32 (4): 364–393. doi: 10.1525/mp.2015.32.4.364
   Web of Science ®Google Scholar
• Milne, Andrew J., Robin Laney, and David B. Sharp. 2016. “Testing a Spectral Model of Tonal Affinity with Microtonal Melodies and Inharmonic Spectra.” Musicae Scientiae. Advance online publication. http://dx.doi.org/10.1177/1029864915622682.
   Google Scholar
• Milne, Andrew J., William A. Sethares, Robin Laney, and David B. Sharp. 2011. “Modelling the Similarity of Pitch Collections with Expectation Tensors.” Journal of Mathematics and Music 5 (1): 1–20. doi: 10.1080/17459737.2011.573678.
   Web of Science ®Google Scholar
• Milne, Andrew J., William A. Sethares, and James Plamondon. 2008. “Tuning Continua and Keyboard Layouts.” Journal of Mathematics and Music 2 (1): 1–19. doi: 10.1080/17459730701828677.
   Web of Science ®Google Scholar
• Moore, Brian C. J. 1973. “Frequency Difference Limens for Short-Duration Tones.” Journal of the Acoustical Society of America 54 (3): 610–619. http://dx.doi.org/10.1121/1.1913640. doi: 10.1121/1.1913640
   PubMed Web of Science ®Google Scholar
• Moore, Brian C. J. 2005. Introduction to the Psychology of Hearing. London: Macmillan.
   Google Scholar
• Parncutt, Richard. 1988. “Revision of Terhardt's Psychoacoustical Model of the Root(s) of a Musical Chord.” Music Perception 6 (1): 65–94. doi: 10.2307/40285416
   Web of Science ®Google Scholar
• Révész, Geza. 1913. Zur Grundlegung der Tonspsychologie. Leipzig: Veit.
   Google Scholar
• Rodríguez, Juan Diego, Aritz Pérez, and Jose Antonio Lozano. 2010. “Sensitivity Analysis of k-Fold Cross Validation in Prediction Error Estimation.” IEEE Transactions on Pattern Analysis and Machine Intelligence 32 (3): 569–575. doi: 10.1109/TPAMI.2009.187
   PubMed Web of Science ®Google Scholar
• Rogers, Nancy, and Clifton Callender. 2006. “Judgments of Distance between Trichords.” In Proceedings of the 9th International Conference on Music Perception and Cognition, 22–26 August 2006, Bologna, edited by Mario Baroni, Anna Rita Addessi, Roberto Caterina, and Marco Costa, 1686–1691. http://myweb.fsu.edu/ccallender/icmpc-proceedings.pdf.
   Google Scholar
• Serrà, Joan, Gopala K. Koduri, Marius Miron, and Xavier Serra. 2011. “Assessing the Tuning of Sung Indian Classical Music.” In Proceedings of the 12th International Society for Music Information Retrieval Conference (ISMIR), 24–28 October 2011, Miami, FL, 157–162. http://ismir2011.ismir.net/papers/OS2-2.pdf.
   Google Scholar
• Shepard, Roger N. 1982. “Geometrical Approximations to the Structure of Musical Pitch.” Psychological Review 89 (4): 305–333. doi: 10.1037/0033-295X.89.4.305
   PubMed Web of Science ®Google Scholar
• Shepard, Roger N. 1987. “Toward a Universal Law of Generalization for Psychological Science.” Science 237 (4820): 1317–1323. doi: 10.1126/science.3629243
   PubMed Web of Science ®Google Scholar
• Toiviainen, Petri, and Carol L. Krumhansl. 2003. “Measuring and Modeling Real-Time Responses to Music: The Dynamics of Tonality Induction.” Perception 32 (6): 741–766. doi: 10.1068/p3312
   PubMed Web of Science ®Google Scholar
• Tymoczko, Dmitri. 2006. “The Geometry of Musical Chords.” Science 313 (5783): 72–74. doi: 10.1126/science.1126287
   PubMed Web of Science ®Google Scholar
• Tymoczko, Dmitri. 2011. A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Oxford, UK: Oxford University Press.
   Google Scholar
• Tymoczko, Dmitri. 2012. “The Generalized Tonnetz.” Journal of Music Theory 56 (1): 1–52. doi: 10.1215/00222909-1546958
   Web of Science ®Google Scholar
• Xenakis, Iannis. 1992. Formalized Music: Thought and Mathematics in Composition. Revised ed. Hillsdale, NY: Pendragon Press.
   Google Scholar