Subject: Re: Pitch of a complex tone From: Peter Cariani <peter(at)epl.meei.harvard.edu> Date: Wed, 4 Feb 1998 14:12:14 +0000Alexander 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 Hi Alex, 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 high-CF regions). 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 is heard. 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 repetition period. 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. --Peter Cariani