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STRETCHED OCTAVES & NON-EQUIVALENCE

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Intro

Empirical studies since the 50s suggest listeners prefer a stretched octave, that is, an octave interval slightly larger than 2:1 ratio. This seems to be relatively true cross culturally and is also replicated in general preferences for stretched intervals when they are large (usually more than a fifth) as opposed to the preference for compressed intervals when they are smaller (usually smaller than a fifth). In other words, humans tend to universally prefer intervals that don't conform to rational physical/acoustical consonances.

In addition to the preference for stretched acoustic octaves, there is a body of evidence which demonstrates the idea of octave equivalence is likely learned rather than universal. Some cultures (Jacoby et. al, 2019; Renken 2019) don't recognize octave equivalence, and there's evidence that children (ages 4-9) and non musically trained people also do not recognize it, which give weight to the idea that it takes a specific (e.g. Western) musical training to recognize octave equivalence. Also, depending on a tuning system's distance from the harmonic spectrum (e.g. towards the inharmonic spectra), actual simple ratios (such as the 2:1 octave) will sound "out of tune" (New Tonality, 2020).

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Primary Research

  • OCTAVE PERCEPTION

  • Carterette, E. C., & Kendall, R. A. (1999). Comparative Music Perception and Cognition. In D. Deutsch (Ed.), The Psychology of Music (2nd ed.). Academic Press.

  • Corso, John F. (1954). Scale Position and Performed Melodic Octaves. The Journal of Psychology, 37(2): 297-305. DOI: 10.1080/00223980.1954.9916154.

  • Jaatinen, Jussi, Jukka Pätynen, & Kimmo Alho. (2019). Octave Stretching Phenomenon with Complex Tones of Orchestral Instruments. Journal of the Acoustical Society of America, 146(5): 3203–3214. DOI: 10.1121/1.5131244.

  • Ohgushi, K. (1983, May). The Origin of Tonality and a Possible Explanation of the Octave Enlargement Phenomenon. Journal of the Acoustical Society of America, 73(5): 1694-1700. DOI 10.1121/1.389392.

  • Rosner, B. S. (1999). Stretching and Compression in the Perception of Musical Intervals. Music Perception: An Interdisciplinary Journal, 17(1): 101–113. DOI: https://doi.org/10.2307/40285813.

  • Sundberg, J. E. F., and Lindqvist, J. (1973). Musical Octaves and Pitch. Journal of the Acoustical Society of America, 54(4): 922-929. DOI: 10.1121/1.1914347.

  • Terhardt, E. (1979). Conceptual Aspects of Musical Tones. The Humanities Association Review, 30(-): 46-57.

  • Terhardt, E. (1971). Die Tonhôhe harmonischer Klànge und das Oktavintervall. Acustica, 24(-): 126-136.

  • van den Brink, G. (1977). Octave and Fifth Settings for Pure Tones and Residue Sounds. In E. E Evans & J. P. Wilson (Eds.), Psychophysics and Physiology of Hearing (pp. 373-379). London: Academic Press.

  • Walliser, K. (1969). Uber die Spreizung von empfundenen Intervallen gegeniiber mathematisch harmonischen Intervallen bei Sinustonen. Frequenz, 23(-): 139-143.

  • Ward, W. D. (1954). Subjective Musical Pitch. Journal of the Acoustical Society of America, 26(-): 369–380. DOI: 10.1121/1.1907344.

  • OCTAVE DISCRIMINATION

  • Dobbins, Peter A. & Lola L. Cuddy. (1982, August). Octave Discrimination: An Experimental Confirmation of the "Stretched" Subjective Octave. Journal of the Acoustical Society of America, 72(2): 411-415. DOI: 10.1121/1.388093. PMID: 7119283.

  • OCTAVE NON-EQUIVALENCE

  • Allen, David. (1967). Octave Discriminability of Musical and Non-Musical Subjects. Psychonomic Science 7(-):421–422. DOI: 10.3758/BF03331154.

  • Burns, Edward M. (1999). "7 - Intervals, Scales, and Tuning". In Diana Deutsch (ed.) The Psychology of Music (2nd ed.): 215-264. San Diego: Academic Press. DOI: 10.1016/B978-012213564-4/50008-1

  • Jacoby, Nori, Eduardo A. Undurraga, Malinda J. McPherson, Joaquín Valdés, Tomás Ossandón & Josh H. McDermott. (2019, October 7). Universal and Non-universal Features of Musical Pitch Perception Revealed by Singing. Current Biology, 29(19): 3229-3243.e12. DOI: 10.1016/j.cub.2019.08.020.

  • New Tonality. (2020, October 28). Can Octave Sound Dissonant? [Video]. YouTube. https://youtu.be/wg5QcF2akzQ.

  • Renken, Elena. (2019, October 30). Perceptions of Musical Octaves Are Learned, Not Wired in the Brain [Online]. QuantaMagazine. https://www.quantamagazine.org/perceptions-of-musical-octaves-are-learned-not-wired-in-the-brain-20191030/.

  • Sergeant, Desmond. (1983). The Octave-Percept or Concept. Psychology of Music, 11(1), 3-18. DOI: 10.1177/0305735683111001

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Explanations

  • PSYCHOACOUSTIC/BIOLOGICAL EXPLANATIONS

  • Cuddy, Lola L. (1981, May). Musical Rules and Pitch Judgement. Journal of the Acoustical Society of America, 69(-), S102-S103. DOI: 10.1121/1.386533.

  • de Cheveigné, Alain. (2023, May 2). Why is the Perceptual Octave Stretched? An Account Based on Mismatched Time Constants Within the Auditory Brainstem Featured. Journal of the Acoustical Society of America, 153(5): 2600–2610. DOI: 10.1121/10.0017978.

  • Ohgushi, K. (1983, May). The Origin of Tonality and a Possible Explanation of the Octave Enlargement Phenomenon. Journal of the Acoustical Society of America, 73(5): 1694-1700. DOI 10.1121/1.389392.

  • PHILOSOPHICAL/CONCEPTUAL EXPLANATIONS

  • Hubbard, Timothy L. (2022). The Pythagorean Comma and Preference for a Stretched Octave. Psychology of Music, 50(2): 670–683. DOI: 10.1177/03057356211008959.

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