Re: Neural mechanisms of octave equivalence

[Pierre Divenyi <pdivenyi@xxxxxxxxxxxxxxxxxx>]

Hi Alain, hi Dick,

Another thought: would Terhardt's pitch salience measure also show this octave phenomenon? I will take a look at it next week (I am traveling), but what is your first reaction?

-Pierre

On 9/24/16 12:29 PM, Richard F. Lyon wrote:

Alain, right, I didn't mention harmonic templates; yes, that mechanism can work, but if birds mostly use narrowband harmonic-poor songs, and don't develop such templates, but do match on individual peaks, then no octave equivalence would be expected.

Personally, I don't think the harmonic template approach is plausible. It's too hard to see how to make it work with plausible mechanisms that follow what the cochlea does, in either birds or mammals.

Dick

On Sat, Sep 24, 2016 at 10:17 AM, Alain de Cheveigne <alain.de.cheveigne@xxxxxx> wrote:

Hi Dick,

The mechnanisms I mentioned don’t depend on the tones having harmonics.  This is easy to see for autocorrelation: the property we invoke is that peaks for the lower tone coincide with peaks of the octave tone, which is true whether or not the tones have harmonics.  The same holds for pattern matching: the fundamental and and harmonics of the octave tone match the harmonic template defined by the lower tone (whether that tone contains harmonics or not).  The harmonic template is an abstract pattern that can be matched by a harmonic spectrum but also by a single component.

Of course it could be that we (or birds) do perceive octave similarity by matching patterns formed by the harmonics of the tones.  That would be yet another model.

Alain

> On 24 Sep 2016, at 18:39, Richard F. Lyon <dicklyon@xxxxxxx> wrote:
>
> I agree with Alain, but looked at the paper and have a few more comments:
> https://www.researchgate.net/profile/Lauren_Guillette/publication/235376278_Chickadees_fail_standardized_operant_tests_for_octave_equivalence/links/09e4151228c5ace7d7000000.pdf
>
> 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.
>
> Dick
>
>
> On Sat, Sep 24, 2016 at 12:59 AM, Alain de Cheveigne <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.
>
> 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/
>