Hi Ani,Alain's point that the equivalence/resemblance of a tone and its octave is asymmetric could be also substantiated by even a superficial combing through musical examples of upward vs. downward leaps in melodies, or of the composer achieving continuity of a melodic line with its segments appearing either an octave higher or lower. It would be an interesting project for a student to gather examples and counterexamples of such melodic treatments, and then to see how they relate to the various pitch theories (or vice-versa).
On 9/24/16 2:59 AM, Alain de Cheveigne wrote:
Hi Ani, Octave “equivalence” is an emergent property of both pattern-matching and autocorrelation models of pitch. All harmonics of the tone at the octave belong to the harmonic series of the lower tone. Likewise autocorrelation peaks of the lower tone coincide with peaks of the tone at the octave. Some neural instantiations of these models are Shihab Shamma’s harmonic template model, or Cariani’s work on autocorrelation (based on Licklider’s ideas), and there are many others. Whether or not any specific model is supported by anatomical or electrophysiological data is less clear. Actually “equivalence” is a misnomer. The relation is not commutative: the harmonics of the lower tone do not all belong to the harmonic series of the octave. Likewise peaks of the autocorrelation of the octave tone are not all peaks of the lower tone. Thus these models would predict an asymmetry in the perceptual similarity between octaves (i.e. an octave tone “resembles” the lower tone but not vice-versa). I don’t know of any relevant behavioral data or music-theoretical results on this. Alain — de Cheveigné, A. (2005) Pitch perception models. In: Pitch - Neural coding and perception (Plack C, Oxenham A, eds). New York: Springer, 169-233. (http://audition.ens.fr/adc/pdf/2005_pitch_SHAR.pdf) Shamma S, and Klein D (2000) The case of the missing pitch templates: how harmonic templates emerge in the early auditory system. J Acoust Soc Am 107:2631-2644. Cariani PA, and Delgutte B (1996b) Neural correlates of the pitch of complex tones. II. Pitch shift, pitch ambiguity, phase-invariance, pitch circularity, rate-pitch and the dominance region for pitch. J Neurophysiol 76:1717-1734. Licklider JCR (1951) A duplex theory of pitch perception (reproduced in Schubert 1979, 155-160). Experientia 7:128-134.On 23 Sep 2016, at 13:06, Patel, Aniruddh D. <a.patel@xxxxxxxxx> wrote: Dear List, Is anyone aware on theoretical or empirical papers on the neural mechanisms of octave equivalence in auditory perception? Interestingly, recent works suggests that songbirds may not perceive octave equivalence: Hoeschele, M., Weisman, R. G., Guillette, L. M., Hahn, A. H., & Sturdy, C. B. (2013). Chickadees fail standardized operant tests for octave equivalence. Animal cognition, 16(4), 599-609. Thanks, Ani Patel Aniruddh D. Patel Professor Dept. of Psychology Tufts University 490 Boston Ave. Medford, MA 02155 Senior Fellow Canadian Institute for Advanced Research (CIFAR) Azrieli Program in Brain, Mind, & Consciousness a.patel@xxxxxxxxx http://ase.tufts.edu/psychology/people/patel/