The neo-Pythagorean view of musical structure in the light of music psychology

  • Piotr Podlipniak Adam Mickiewicz University in Poznań, Institute of Musicology
Keywords: musical structure, neo-Pythagoreanism, tonality, mental representations of music, musicology


The aim of this paper is to show why the neo-Pythagorean claims concerning musical structure are out-of-date and require the incorporation of contemporary psychological knowledge. The neo-Pythagorean view of musical structure has been analyzed and confronted with the contemporary neuropsychological view of music perception. It has been also suggested that musical intervals exist solely in human brains as a kind of interpretation of acoustic sounds. These sounds can be interpreted differently depending on many factors, which the popular speech-to-song illusion clearly illustrates. Another example of neo-Pythagorean ideas about musical structure that need psychological knowledge is tonal hierarchy, which also exists solely in human brains. Therefore, the popular musicological description of musical intervals in terms of mathematical proportions is misleading. It has been proposed that current musicological theories should always be confronted and consistent with contemporary psychological knowledge. This implies closer cooperation between musicology and the psychology of music.


Berent, I. (2013). The phonological mind. Trends in Cognitive Sciences, 17(7), 319–327.

Bharucha, J., Curtis, M., & Paroo, K. (2011). Musical communication as alignment of brain states. In P. Rebuschat, M. Rohrmeier, J. A. Hawkins, & I. Cross (Eds.), Language and music as cognitive systems (pp. 139–155). Oxford, New York: Oxford University Press.

Bregman, A. S. (1990). Auditory scene analysis: The perceptual organization of sound. Cam-bridge, London: The MIT Press.

Brown, S., Merker, B., & Wallin, N. L. (2000). An introduction to evolutionary musicology. In N. L. Wallin, B. Merker, & S. Brown (Eds.), The origins of music (pp. 3–24). Cambridge, London: The MIT Press.

Caleon, I., & Ramanathan, S. (2008). From music to physics: The undervalued legacy of Pythagoras. Science & Education, 17(4), 449–456.

Cook, N. (1987). The perception of large-scale tonal closure. Music Perception: An Interdisciplinary Journal, 5(2), 197–205.

Crocker, R. L. (1964). Pythagorean mathematics and music. The Journal of Aesthetics and Art Criticism, 22(3), 325.

Deutsch, D., Henthorn, T., & Lapidis, R. (2011). Illusory transformation from speech to song. The Journal of the Acoustical Society of America, 129(4), 2245–2252.

Deutsch, D., Lapidis, R., & Henthorn, T. (2008). The speech-to-song illusion. The Journal of the Acoustical Society of America, 124(4), 2471.

Fitch, W. T., & Jarvis, E. D. (2013). Birdsong and other animal models for human speech, song, and vocal learning. In M. A. Arbib (Ed.), Language, music and the brain (pp. 499–539). Cambridge, London: The MIT Press.

Gibson, J. J. (1983). The senses considered as perceptual systems. Westport, CT, US: Greenwood Press.

Handschin, J. (1948). Der Toncharakter: eine Einführung in die Tonpsychologie [The sound character: An introduction to the psychology of sound]. Zürich, Swiss: Atlantis.

Hauser, M. D. (1996). The evolution of communication. Cambridge, London: The MIT Press.

Hauser, M. D. (2000). The sound and the fury: Primate vocalizations as reflections of emotion and thought. In N. L. Wallin, S. Brown, & B. Merker (Eds.), The origins of music (pp. 77–102). Cambridge, MA, US: The MIT Press.

Hed, S., Gjerdingen, R. O., & Levin, D. (2015). Pitch-and-rhythm interrelationships and musical patterns: Analysis and modelling by subdivision schemes. Journal of Mathematics and Music, 9(1), 45–73.

Helmholtz, H. von (1954). On the sensations of tone as a physiological basis for the theory of music (A. J. Ellis, Trans.) (2nd ed.). New York, NY, US: Dover Publications.

Huang, J., Gamble, D., Sarnlertsophon, K., Wang, X., & Hsiao, S. (2012). Feeling music: Integration of auditory and tactile inputs in musical meter perception. PLoS ONE, 7(10), e48496.

Huron, D. B. (2006). Sweet anticipation: Music and the psychology of expectation. Cambridge, London: The MIT Press.

Kivy, P. (1990). Music alone: Philosophical reflections on the purely musical experience. Ithaca, London: Cornell University Press.

Krumhansl, C. L., & Cuddy, L. L. (2010). A theory of tonal hierarchies in music. In M. R. Jones, R. R. Fay, & A. N. Popper (Eds.), Music perception (pp. 51–87). New York, Dordrecht, Heidelberg, London: Springer New York.

Large, E. W., & Almonte, F. V. (2012). Neurodynamics, tonality, and the auditory brainstem response. Annals of the New York Academy of Sciences, 1252(1), E1–E7.

Large, E. W., & Tretakis, A. E. (2005). Tonality and nonlinear resonance. Annals of the New York Academy of Sciences, 1060(1), 53–56.

Lerdahl, F. (2013). Musical syntax and its relation to linguistic syntax. In M. A. Arbib (Ed.), Language, music, and the brain (pp. 257–272). Cambridge, London: The MIT Press.

Lerdahl, F., & Jackendoff, R. (1983). A generative theory of tonal music. Cambridge, London: The MIT Press.

Levitin, D. J., Grahn, J. A., & London, J. (2018). The psychology of music: Rhythm and movement. Annual Review of Psychology, 69(1), 51–75.

London, J. (2012). Three things linguists need to know about rhythm and time in music. Empirical Musicology Review, 7(1–2), 5–11.

Matyja, J. R. (2016). Embodied music cognition: Trouble ahead, trouble behind. Frontiers in Psychology, 7, 1891.

Matyja, J. R., & Schiavio, A. (2013). Enactive music cognition: Background and research themes. Constructivist Foundations, 8(3), 351–357.

McAdams, S., & Bregman, A. (2014). Musical streams. Computer Music Journal, 3(4), 26–43.

Merker, B. (2002). Music: The missing Humboldt system. Musicae Scientiae, 6, 3–21.

Merker, B. (2003). Is there a biology of music? And why does it matter? In R. Kopiez, A. C. Lehmann, I. Wolther, & C. Wolf (Eds.), Proceedings of the 5th Triennial ESCOM Conference (pp. 402–405). Hanover: Hanover University of Music and Drama.

Nikolsky, A. (2015). Evolution of tonal organization in music mirrors symbolic representation of perceptual reality. Part-1: Prehistoric. Frontiers in Psychology, 6, 1405.

Nolan, C. (2002). Music theory and mathematics. In T. Christensen (Ed.), The Cambridge history of Western music theory (pp. 272–304). Cambridge: Cambridge University Press.

Panksepp, J., & Bernatzky, G. (2002). Emotional sounds and the brain: The neuro-affective foundations of musical appreciation. Behavioural Processes, 60(2), 133–155.

Papadopoulos, A. (2002). Mathematics and music theory: From Pythagoras to Rameau. The Mathematical Intelligencer, 24(1), 65–73.

Parncutt, R., & Hair, G. (2018). A psychocultural theory of musical interval: Bye bye Pythagoras. Music Perception: An Interdisciplinary Journal, 35(4), 475–501.

Podlipniak, P. (2016). The evolutionary origin of pitch centre recognition. Psychology of Music, 44(3), 527–543.

Podlipniak, P. (2017a). The role of the Baldwin effect in the evolution of human musicality. Frontiers in Neuroscience, 11, 542.

Podlipniak, P. (2017b). Tonal qualia and the evolution of music. Avant, 8(1), 33–44.

Raftopoulos, A. (2009). Cognition and perception: How do psychology and neural science inform philosophy? Cambridge, MA, US: The MIT Press.

Rakowski, A. (2009). The domain of pitch in music. Archives of Acoustics, 34(4), 429–443.

Reybrouck, M. (2005). A biosemiotic and ecological approach to music cognition: Event perception between auditory listening and cognitive economy. Axiomathes, 15(2), 229–266.

Reybrouck, M., & Podlipniak, P. (2019). Preconceptual spectral and temporal cues as a source of meaning in speech and music. Brain Sciences, 9(3), 53.

Roederer, J. G. (2008). The physics and psychophysics of music: An introduction. New York, NY, US: Springer.

Schiavio, A., & van der Schyff, D. (2016). Beyond musical qualia. Reflecting on the concept of experience. Psychomusicology: Music, mind, and brain, 26(4), 366–378.

Scruton, R. (1999). The aesthetics of music. Oxford, New York: Oxford University Press.

Sethares, W. A. (1998). Tuning, timbre, spectrum, scale. London: Springer.

Shannon, R. V. (2016). Is birdsong more like speech or music? Trends in Cognitive Sciences, 20(4), 245–247.

Shepard, R. N. (1982). Structural representations of musical pitch. In D. Deutsch (Ed.), Psychology of music (1st ed., pp. 343–390). New York, NY, US: Academic Press.

Stein, B. E., Wallace, M. T., & Stanford, T. R. (2001). Brain mechanisms for synthesizing information from different sensory modalities. In E. B. Goldstein (Ed.), Blackwell handbook of perception (pp. 710–736). Malden, MA, Oxford: Blackwell.

Su, Y.-H., & Salazar-López, E. (2016). Visual timing of structured dance movements resembles auditory rhythm perception. Neural Plasticity, 2016, Article ID 1678390.

Todd, N. P. M., & Cody, F. W. (2000). Vestibular responses to loud dance music: A physiological basis of the “rock and roll threshold”? The Journal of the Acoustical Society of America, 107(1), 496–500.

Todd, N. P. M., Cody, F. W., & Banks, J. R. (2000). A saccular origin of frequency tuning in myogenic vestibular evoked potentials?: Implications for human responses to loud sounds. Hearing Research, 141(1–2), 180–188.

Trainor, L. J., Gao, X., Lei, J., Lehtovaara, K., & Harris, L. R. (2009). The primal role of the vestibular system in determining musical rhythm. Cortex, 45(1), 35–43.

Varela, F. J., Thompson, E., & Rosch, E. (1991). The embodied mind: Cognitive science and human experience. Cambridge, MA, US, London: The MIT Press.

Wiley, R. H. (2015). Noise matters: The evolution of communication. Cambridge, London: Harvard University Press.

Zatorre, R. J., & Baum, S. R. (2012). Musical melody and speech intonation: Singing a different tune. PLoS Biology, 10(7), Article ID e1001372.

Zimmermann, E., Leliveld, L., & Schehka, S. (2013). Toward the evolutionary roots of affective prosody in human acoustic communication: A comparative approach to mammalian voices. In E. Altenmüller, S. Schmidt, & E. Zimmermann (Eds.), Evolution of emotional communication: From sounds in nonhuman mammals to speech and music in man (pp. 116–132). Oxford, New York: Oxford University Press.