String coupling.

[Robert Scott]

Kent Swafford asks:

>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.

Speaking for TuneLab, I can tell you that the phase display will be
somewhat erratic if there are really three different frequencies blended
together.  Once the three pitches have been mixed together they appear
to TuneLab to be the same as one tone that is wavering in both pitch
and amplitude.  You cannot draw any conclusions about the average pitch.
About the best you can say is that an instantaneous pitch indication
reflects a pitch somewhere between the minimum and maximum of the
component pitches.  It is sometimes suggested that a more accurate
pitch determination can be made by observing the "long term trend" of
the phase display.  But in the case of a blend of pitches or false beats,
the phase display often has an ambiguous long term trend.  That is, the
phase display will appear to be moving in one direction and then,
suddenly, will jump 180 degrees.  You can't tell if the jump was 
forward or backward because each case is just as close to the previous
phase.  This happens in the SAT as well, and probably in the RCT too.

But getting back to the original question of pitch depression in
unisons, I have two comments.  One is that if the phenomenon works
as hypothsized, then the effect will likely be the same on all three
strings.  So if all three strings go down in pitch together in a unision,
then you don't need to worry about what happens to VTDs when presented
with multiple pitches because the drop you expect to observe should be
larger than the spread of individual string pitches.

My second point is that if you really do want to measure the pitch
of a single string while it is sounding as part of a unison, then
take a look at the optical pickup device that I described in my
article in the June 1993 PTG Journal, page 44.  Use the signal
from such a pickup instead of a microphone and you should get just 
one string.


Also, Ron Nossaman observed:

> tuning each
> string of a unison as perfectly as I was able to the Tunelab display, the
> unison did indeed drop when all were sounded together, just like you said.
> Also in every case, the unison sounded rougher than I can tune it aurally.
> Touching up aurally, the unison pitch drop disappeared again, or was
> greatly reduced. Checking each string individually against the display,
> they weren't precisely the same anymore, but the unison as a whole was on
> pitch and sounded good.
> 
> Why?

Ron, I think you know why the aurally-tuned unison sounded better.  You
listen to all the partials while TuneLab listens to only one at a time.
But I was interested in the observation that the aurally-tuned unison
did not exhibit pitch drop.  I think I can explain this one.  Pitch drop,
if it exists, would be based on coupling through the bridge.  When the
unison is tuned with TuneLab, the selected partial is perfectly matched
across all three strings (even though other partials may not be).  And
when all three strings push the bridge up and down in unison the bridge
appears more resiliant (to the selected partial only) and thus the
effective termination point is moved a little further back and the pitch
drops (for the selected partial only).  When the interval is tuned
aurally, you make compromises that are better overall, but perhaps a
little worse for the one selected partial that TuneLab is using.  So
at that partial, the three strings are not pushing exactly together
and the bridge does not appear more resiliant and the pitch drop
does not happen.  Sound plausible?

-Robert Scott
 Real-Time Specialties