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Re: Neural mechanisms of octave equivalence

I believe that Humans can start to estimate pitch within two periods. This argues more for a time domain processing approach. Harmonic and octave tracking requires a much higher level of signal processing, and the process would take much more time. It also doesnt consider what happens when the pitch is changing, which is sort of the whole point of pitch signal processing.

My 2 cents.


On 09/24/2016 11:39 AM, Richard F. Lyon wrote:
I agree with Alain, but looked at the paper and have a few more comments:

Octave equivalence is pretty strong for tones with enough harmonics,
for reasons that Alain describes.  This paper shows that humans have
some octave generalization even with pure sine waves, and that the
birds do not.  This likely points to different mechanisms.

For matching based on common frequencies of partials, you need some
partials in common, which is not the case here, due to the signals
being sine waves (no upper partials). For matching based on common
periods, or common peaks in autocorrelation functions, sine waves an
octave apart are close, because the higher one is also periodic at the
period of the lower one.

So maybe this argues that humans use more period-based matching and
birds use only frequency (cochlear place) matching?  Maybe the
experiment should be repeated with tones that have at least a second
harmonic, and see if that leads to birds doing octave generalization
by matching one tone's fundamental to another's second harmonic?  This
would be a better way to get at pitch height versus chroma, perhaps.


On Sat, Sep 24, 2016 at 12:59 AM, Alain de Cheveigne
<alain.de.cheveigne@xxxxxx <mailto:alain.de.cheveigne@xxxxxx>> 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.


    de Cheveigné, A. (2005) Pitch perception models. In: Pitch -
    Neural coding and perception (Plack C, Oxenham A, eds). New York:
    Springer, 169-233.
    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
    <mailto: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 <mailto:a.patel@xxxxxxxxx>
    > http://ase.tufts.edu/psychology/people/patel/