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Re: Pitch of a complex tone
Alexander Galembo wrote:
> It is classical that the pitch of a periodic complex tone is independent on
> phases of harmonics.
> I would appreciate to be informed about any publications providng a doubt
> in this phase independence (if exist).
> Thank you,
> Alex Galembo
Several years ago I went through the literature on phase effects in
conjunction with our work on population-interspike interval
representations of the pitches of complex tones.
Cariani, Peter A., and Bertrand Delgutte. 1996.
Neural correlates of the pitch of complex tones.
I. Pitch and pitch salience. II. Pitch shift,
pitch ambiguity, phase-invariance, pitch circularity,
and the dominance region for pitch.
J. Neurophysiology 76 (3) : 1698-1734. (2 papers)
What I concluded from my readings was that:
0. Phase structure is much more important for nonstationary sounds
(in which a particular phase structure is not repeated at some
fixed recurrence time) than for stationary ones (where a particular
phase structure is repeated at some fixed recurrence time, 1/F0).
For nonstationary sounds, phase structure is very important for
timbre (as Roy Patterson has demonstrated).
1. For stationary sounds, phase does not seem to affect the pitch
of sounds with lower frequency harmonics (say below 1-2 kHz).
For stationary sounds, phase also does not seem to affect
the timbre of sounds with lower frequency harmonics.
E.g. I think it's v. hard to alter either the pitch
or timbre of vowels by altering the phase spectrum.
However, phase spectrum can affect the salience (strength)
of the pitch that is heard. (A waveform with a higher peak
factor probably generates more F0-related intervals in
2. Phase has limited effects for higher frequency harmonics. Only
special phase manipulations alter the pitch of such complexes,
and when they do, they result in octave shifts (up). There seems to
be no way that one can get arbitrary pitch shifts from phase
manipulations (someone correct me if I'm wrong).
In terms of interspike interval models, the intervals produced by
higher frequency harmonics are related mainly to the envelopes
of the cochlear filtered stimulus waveform. Phase alterations
that give rise to the octave jumps do so by halving envelope periods,
thereby producing intervals at 2*F0 (or potentially, n*F0).
One could think of the Flanagan-Gutman alternating polarity click
trains and the Pierce tone pip experiments in these terms. For high
frequency components, these phase manipulations produce envelopes
with large modulations at multiples of F0, and the intervals
produced follow these envelopes. In our study of pitch in the
auditory nerve (above), we observed that if you consider only
fibers with CF's above 2 kHz (as would be the ANF subpopulation mainly
excited by a high-pass filtered alternating click train,
where these effects are most pronounced), the most frequent
interspike interval corresponds to the click rate (here 2*F0)
rather than the true fundamental (F0). THis corresponds with what
However, if one takes the entire ANF population (all CF's), the
predominant interval is always at 1/F0, which is not what is heard
at low click rates (one hears a pitch at the click rate, an octave
above F0). My thinking on this is that intra-channel
interspike intervals may not be the whole story; that for such
stimuli (esp. under high-pass filtering) strong interchannel
interval patterns and synchronies are set up, and these might also
play a factor in the central interval analysis.
3. Despite the largely phase-invariant nature of our perception of
stationary sounds, this doesn't mean that phase isn't important.
If one takes a segment of noise of 5 msec long and repeats
it many times, one will hear a pitch at 200 Hz. If you scramble
the phase spectrum of the noise segment in each period, you will
no longer hear the repetition pitch. (One can do a similar
periodicity-detection experiment with random click trains with
recurrence times of seconds.)
I therefore think that phase coherence is important even
for those aspects of auditory
perception that appear to be largely insensitive to which
particular phase configuration is chosen.
According to an all-order interval-based theory, one needs
constant phase relations spanning at least 2 periods to
preferentially create intervals related to the
There is even a more general way of thinking about
detection of periodicity that involves the fusing together of
phase-relations that are constant into auditory objects, and
separating those relations that continually change. If we
think of 2 diff. vowels with diff. F0's added together, the
composite waveform contains 2 sets of internally-invariant
phase relations (two periods of each vowel's waveform)
plus the changing phase relations between the
two vowel periods (pitch period asynchronies). If one had a
means of detecting invariant phase structure, then one could
separate these two auditory objects. I think Roy Patterson's strobed
auditory image model moves in this direction, as do the kinds of
recurrent timing models I am working on.
Because of phase-locking of auditory nerve fibers, the timings of
individual spike discharges provide a representation of the
running stimulus phase spectrum. Interspike interval distributions
are then one way of neurally representing recurrent phase relations.
The formation of interval patterns depends crucially upon
phase structure, but once intervals are formed,
then the resulting representations are phase-independent.