User-agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.11; rv:45.0) Gecko/20100101 Thunderbird/45.3.0
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
On 9/24/16 12:29 PM, Richard F. Lyon
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
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.
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.
> On 24 Sep 2016, at 18:39, Richard F. Lyon <dicklyon@xxxxxxx>
> 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
> 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
> 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
> 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
> 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
> 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).
> > On 23 Sep 2016, at 13:06, Patel, Aniruddh D.
> > Dear List,
> > Is anyone aware on theoretical or empirical
papers on the neural mechanisms of octave equivalence in
> > 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
> > Azrieli Program in Brain, Mind, &
> > a.patel@xxxxxxxxx
> > http://ase.tufts.edu/psychology/people/patel/