[CAUT] Unison Tuning

[James Ellis]

Ladies, Gentlemen:

This is a continuation of a subject under a different title "Sacrifice (was
tuners-technology)".  I'm using a new title that addresses the current
discussion a little better, i.e., the unision going slightly falt when all
three strings are tuned.  Several things are happening here, and they are
getting glossed over as generalities, which they are not.

Virgil Smith is correct about some things, incorrect about others.  Jim
Coleman is correct within the bounds of his statements.  But there is more
to it than that.

Fred Sturm is right on target here.  Measuring single strings (in a piano)
to an accuracy of 0.1 cent is puching the limit, if it isn't already past
it, and that's not the fault of the ETD.  It's just a limitation of pure
statistics - the data available to the ETD - limited by the decay rate of
the various paritals and the stability of the string's vibration.

All other things being equal, I would expect the fundamental of the note to
go a tiny, tiny, tiny but flat during the "prompt sound" when all three
strings are tuned due to the mutual coupling at the bridge.  But after
that, I would expect it to turn around and go the other way during the
"after-sound" due to the fact that the three strings, sooner or later, WILL
go out of phase, no matter how accurately the unison is tuned.  It's a
basic law of physics.  I'm saying the pitch produced by in-phase strings
will be ever-so-slightly lower than that produced by out-of-phase strings
due to the mutual coupling, and that will depend upon how much mutual
coupling there is, and how fast the decay is.

Another thing no one so far has mentioned is the fact that the bridge
itself is NOT rock solid.  When pressure is applied to a bridge pin, it
DOES move - by a microscopic amount - but it moves - and the movement of
one pin will move the next one a little bit.  Wood grain is springy.  I'll
bet that if you very carefully measure (on the same note of the same piano)
unison tuning going from sharp to flat, you will find this effect is not
the same as when you tune going from flat to sharp.  I have not done this
experiment, but that is what I would expect to see if I did.  Again, as
Fred points out, we are making measurements that are on the fringe area of
the resolution we can obtain in a real piano, and we are bound to get
scatter in the results.

One more thing that Fred also mentioned:  If all three strings of a unison
are within about 0.5 cent of each other, the fundamental will lock in due
to mutual coupling, and it won't beat, but some of the higher partials
will.  As you get the unison more closely tuned, the higher partials will
begin to lock in, and not beat.  I have done those experiments, and they
prove to be true.  When you aurally fine-tune unisons, you are actually
listening to the higher-pitched partials, as the fundamentals have long
since stopped beating.

We are looking at something here that is very complex, and we cannot
account for it with one single, simple, explanation - but it CAN be explained.

Sincerely,  Jim Ellis