Tuning a guitar

[From Rick Marken (940807.2110)]

Peter Cariani (940805) --

Me:

I would have more confidence in (and understanding of) the
"periodicity" alternative to neural currents (the current cherished
neurophysiological assumption of PCT) if you could post a computer
model of a control system that operates on the basis of neural signals
carried in the form of spike periods.

Peter:

J.C.R. Licklider in the 1950's proposed a neural network with delay
lines...Richard Lyon, Roy Patterson, BCJ Moore, Meddis & Hewitt, and
others have developed models for pitch based on Licklider's
concepts

I guess I wasn't clear. I am familiar with the Licklider and related
models. These are transduction models -- describing processes that will
transform variations in auditory waveforms into pulse train variations
that correspond to what subjects report as variations in the pitch of the
waveform. Licklider's is a model of what in PCT is one possible type of
perceptual function, where the output of the function varies in terms of the
interval between spikes, rather than spike rate.

What I was asking for was a model of a _control system_ that controls
the perceptual signal that is the output of such a function. This control
system would be a model of what I used to do (in the 60's) when I
tuned my guitar. I would pluck, say, the low E string. Then, assuming
the E was correct (a false but usually irrelevant assumption) I would
adjust the pitch of the B string to match the remembered relationship
to what E sounded like. So I had a reference (from memory) for the
pitch of the B string; I had the actual perception of the pitch of the B
string, and I had an output (the tuning peg) that could be used to bring
the perceived pitch of to the reference.

The periodicity theory of pitch suggests that variations in pitch (at least
of low frequency sounds, including "beats" I presume) are "coded" by
the interval between neural spikes. What I want to see is a pitch
control (guitar tuning) system based on the idea that the controlled
perception is represented by inter-spike interval. I don't doubt that
such a system could be built; I just want to see how it might be done.
Then we can compare the neurological plausibility of such a system to
the system suggested by the PCT "neural current" model. A guitar tuning
system is, of course, very easy to build if you assume that the
perceptual function transforms the acoustical waveform into a "neural
current" representation of pitch

Oh, and the "guitar tuning" control system should have a variable
reference input. The actual pitch to which I tuned, say, the B string,
could be varied (by me) for various reasons, such as changes in what I
took as the actual pitch of E or to produce a "modal" tuning.

Once we design a control system that can tune the guitar, maybe we can
work on a high level system (one that will please all those skeptical AI
types) that can play the PCT theme song -- "The times they are a'
changin'":wink:

Best

Rick

Rick Marken (940807.2110) wrote --

What I was asking for was a model of a _control system_ that controls
the perceptual signal that is the output of such a function. This
control system would be a model of what I used to do (in the 60's)
when I tuned my guitar. I would pluck, say, the low E string. Then,
assuming the E was correct (a false but usually irrelevant
assumption) I would adjust the pitch of the B
string to match the remembered relationship
to what E sounded like. So I had a reference (from memory) for the
pitch of the B string; I had the actual perception of the pitch of
the B string, and I had an output (the tuning peg) that could be used
to bring the perceived pitch of to the reference.

Rick, I think it's not a tall order to come up with a system that
uses intervals. The basic idea is to run the reference signal and
the test signal into a coincidence detector (with some inhibition)
that penalizes noncorrelated inputs. For the sake of discussion
we will assume here that memory permits particular temporal
patterns to circulate for a long time or to be generated at
will by neural assemblies.

Let's consider the most primitive case. I can take as my reference
signal a spike train with many intervals of 10 msec (-> 100 Hz) and
minimally I can measure the output rate of the coincidence detector.
The closer the test pattern to the reference pattern, the more the
coincidence detector will fire. So if I have a means of steering the
test pattern (via muscular actions) so that I get a higher
temporal correlation, I have a control system.

Now I used to play the violin (badly, I'm afaid), but in tuning the
violin I would play a scale on one string and then match the pitch
of the fingered string with that of the open string.
When one gets a fairly close pitch match one generates "beats,"
which are also directly represented in temporal discharge
patterns -- when one got close to the correct tuning,
one could attempt to minimize the perception of the beats by
minimizing the presence of very long interspike intervals
corresponding to the beats. Here the longer intervals harmonically
unrelated to that of the primary tones interfere with the
correlation, so maximizing the correlation brings the strings into
tune.

It is notable in these systems that small interval ratios (2:1, 3:2,
4:3, etc) will also produce higher correlations (this has
implications for theories of tonal fusion and of consonance and
dissonance).

Now, I find the above example unsatisfactory for a few reasons, the
main one being that the temporal code has been transformed into a
non-temporal one, whereas one wants the basic processing operations
to produce the same kinds of signals that they have as inputs.
Alternately, we could also observe that the output of the simple
coincidence detector above will also have temporal structure, and
that this temporal structure is then fed iteratively into other
similarly structured assemblies, so that those stimuli evoking a
highly coherent temporal coincidence patterns (with those ref.
signals that are already circulating), tend to persist longer and
become reinforced, whereas those that do not become extinguished.

This is the problem which I find conceptually difficult, trying to
visualize how a network could be organized using spatiotemporal
patterning in order to generate coherent behavior. Moshe Abeles
is probably the furthest along on this path, with his "synfire
chains" (he has a very nice simulation demonstration), but I think
nobody really has a firm idea of how to organize these timing nets
and how to train them. Thus incorporating temporal structure into
the existing connectionist conceptual framework is relatively
easy; what is hard is developing an alternative framework with
somewhat different operational primitives.

I hope this helps.
Peter