String coupling.

[Ron Nossaman]

>So this variable is a mismatch in inharmonicity, just as we experience every
>day in wound bass strings.

Hi Kent,
And in plain wire unisons too, possibly. The inharmonicity differences in
wound strings within a unison can be pretty dramatic, given their
construction. Has anyone measured unison pitch drop proportional to unison
frequency in wound strings? It ought to be a proportionally greater drop
than in plain wire, by my theory of the day.  


>This is but one variable with which we are dealing. There is every reason to
>think that there are also other variables at work.

No doubt. I haven't abandoned the impedance thing just yet. It may well
serve as an inharmonicity modifier/modulator in the oscillator feedback
coupling with both adjacent strings and duplex effects. I'm tending to
think at this point that the inharmonicity is the primary effect though.
Tomorrow could change all that.   

>Another variable is the pitch envelope of a sounding note. Piano strings do
>not necessarily vibrate at a stable pitch, but rather can vibrate at a
>continuously changing frequency. We know this because out VTD's exceed the
>stability of vibrating piano strings and can display the changing pitch
>while a note is sounding; this is the cause of the VTD's display changing
>speed and/or direction while a string is sounding. Two strings which have
>similar pitch envelopes can be tuned together no matter how unstable;
>strings that have different pitch envelopes cannot really be tuned together.

Yes, but the envelope isn't a cause, it's a result. The amplitude, pitch,
and duration of all phases of the envelope are the result of the physical
characteristics of the generator. You said yourself that you had noticed
the attack phase pitch rise duration (bla bla) to be shortened as the
second ant third string of a unison is tuned in. I'd be more likely to see
the envelope as another meter to read, other than a variable to account for.


>Another variable which is rarely discussed is the behavior of a VTD display
>in the presence of more than one frequency. Does the VTD display the lower
>pitch, the higher pitch, the average pitch, the loudest pitch, or a random
>combination of all the above? This is an important question to ask, isn't
>it? Do we know the answer? I don't think we do.

Excellent question, I think, and I have no idea whatsoever what the answer
is. Anyone done any research along these lines? 


>In order to answer the questions about string coupling, we need to know a
>bit more about how VTD's work, in my opinion. If we are going to claim that
>3 strings vibrating together do so at a frequency different from the same 3
>strings vibrating individually, we must learn about how blended frequencies
>are displayed on a VTD. We concentrate on the fact that readings seem to
>change, but do we know enough about VTD behavior to know that the
>frequencies actually change, or does the inevitable mix of frequencies just
>display differently?
>
>Kent Swafford

Another perspective here: One of the more vocal proponents of the idea of
pitch drop in unison tuning is Virgil Smith, an aural tuner. Of course, we
don't really know how our aural equipment works either, so that's probably
not a point to try to make after all. Never mind. Let's see, by the back
door method, if a comparison of string partial pitches within a unison
transmogrifies, by my proposed rounding down at whatever (?) partial in any
way resembles what the ETD readout shows us. Since thinking is more
flexible than measuring, we might get lucky and get a reasonable fit.

Anyone care to contribute a few measurements?

Ron N