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:
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:
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
> 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.
> Ani Patel
> Aniruddh D. Patel
> 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>