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Re: harmonic extraction

(Jim Bashford is having problems getting the listserv to accept his
messages, so I'm forwarding this on his behalf -- DAn.)

---------- Forwarded message ----------
From: James Bashford
Date: Sun, Mar 29, 2009 at 5:29 PM

Dear Al,

I’ve listened to a number of conditions, including the odd-through-all
harmonic alternation you mentioned (with 0.5 sec half-cycle and no
silence between the alternating tones).  Most of my observations have
used a 6-component “all-harmonic” base stimulus, because I have
determined that, for me at least, the capture of individual harmonics
from a complex tone (alternating with a lone sinusoid) does not
readily occur for the seventh and higher harmonics.  For the
six-harmonic stimulus conditions, the even-through-all and the
odd-through-all stimuli behave as I reported earlier: I hear an
intermittent complex tone that matches the pitch and timbre of the
all-harmonic stimulus presented alone, and I hear a continuous complex
tone having the pitch and timbre of the three-component stimulus
(comprised of either even or odd harmonics).  These observations were
made for stimuli having fundamental frequencies of 100 Hz and also 300
Hz.  So it appears that duplexity prevails when all harmonics are
resolved by the auditory system.

 I also listened to the original stimulus condition employing the
first 10 harmonics and did hear the effect you anticipated when the
fundamental frequency was 100 Hz.  Along with the continuous
odd-harmonic signal having a pitch of 100 Hz, I do hear an
intermittent 200 Hz having a rich timbre (one has to be careful with
these judgments since it is easy to spontaneously hear out the “pure”
sounding second harmonic).  Your prediction did not hold when the
fundamental frequency was at 300 Hz.  At that frequency, the percept
of the intermittent all-harmonic stimulus retains the pitch and timbre
heard when the stimulus is presented alone.

On Mar 27, 2009, at 6:27 PM, Al Bregman wrote:

Dear Jim,

Imagine your experiment in "reverse".  Alternate the all-harmonic tone
with an ODD-harmonic inducer.  Then if the inducer captures the odd
harmonics from the all-harmonic tone, the residual will be the set of
even harmonics, and their fundamental is 2f not f.  So you ought to
hear a continuous tone at frequency f, accompanied by a pulsing tone
an octave higher. I am quite sure that this will occur if there is no
silence between the tones.  In fact I'll turn in my badge if it
doesn't come out that way.

This method makes it easier to determine whether the residual
harmonics are used to make their own tone, because it requires a pitch
judgment rather than the more difficult timbre judgment that you
reported.  If the outcome is as I expect, there will be no need to
evoke an explanation in terms of duplex perception for this
odd-full-odd-full stimulus pattern.

But even so, this wouldn't prove that there had been no duplex
perception in the example that YOU reported (even-full-even-full).  It
may be that the partitioning of the spectrum is more ambiguous with
your stimulus, and that this could lead to duplex perception.  It is
possible that duplex perception is a top-down process that tries to
make sense of an ambiguous input.


Albert S. Bregman, Emeritus Professor
Psychology Department, McGill University
1205 Docteur Penfield Avenue
Montreal, QC, Canada H3A 1B1.
Office:  Phone: (514) 398-6103
             Fax: (514) 398-4896