[From Bill Powers (960509.1440 MDT)]
Martin Taylor 960509 13:30 --
Replying to Rick Marken:
I read Peter differently, as dealing with a variable that changes
continuously as frequency changes. If that is so, then you wouldn't
have a problem with using it in a controller for pitch, would you?
The signal representation makes a difference in the kind of computation
you have to do in order to represent the frequency (or interval)
difference, the error signal.
The auditory system is a special case, because the physical input
quantity is periodic, and it is periodic in the same range as normal
neural signals. In going from, say, a temperature to a signal
representing temperature, there is no problem with the neural
frequencies, because they lie in a range well above the range in which
temperatures vary. But how do you convert a pitch in a range from, say,
100 to 10,000 HZ into a neural signal with a frequency representing
pitch? A one-to-one conversion is most unlikely. In the rate universe,
you'd have to go through an analog stage in which the input is converted
to some analog variable (a post-synaptic potential, for example), and
then the analog variable modulates the frequency of a neural signal
generator over a more reasonable range, like 10 to 500 HZ. Of course if
there is significant modulation of the analog variable at the input
frequency, then you'd expect some degree of harmonic locking between
input and output, so that output frequencies that are subharmonics of
the input frequency would tend to put stair-steps into the overall
conversion. You might even get frequency division -- the output
perceptual-signal frequency abruptly dropping to the next lower
suharmonic of the input. This could possibly relate to the natural
harmonic musical scales, the perceptual similarity of octaves, and so
on. I think that in a rate model you can come up with many of the same
phenomena that interval treatments would show.
I have found that when people do pitch control in Demo 1, they can
become confused between harmonics of the square-wave signal being
applied to the PC loudspeaker. In some people there is a tendency to
maintain a note a 5th above the reference tone, and in others to
maintain a tone an octave above the fundamental of the reference tone.
Of course some people can't do it at all!
What looks to me like a difficult problem is that of comparing one
temporal code with another to get a measure of the difference between a
reference signal and a perceptual signal. In terms of frequencies this
is easy, but if there is complex internal structure in the codes, the
comparison looks more difficult to me. Just what would a pitch error
signal look like? How would it be computed? And of course we also have
to worry about converting from temporal code signals to the frequency-
domain signals that drive muscles -- we don't have much choice there.
···
-----------------------------------------------------------------------
Best,
Bill P.