[CAUT] Unison Tuning

[Don]

Hi Jim,

As usual you are offering wonderful clarity.

I did mention the coupling effect in my post. Correct me if I'm wrong but
my understanding is that the coupled motion in a "standard" piano occurs
because the bridge is not a fixed termination point.

I'm aware that pendulum clocks will also sync themselves. 

http://www.its.caltech.edu/~sciwrite/journal03/tan.html

At 10:47 AM 3/4/2005 -0500, you wrote:
>Ladies, Gentlemen:
>
>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.

>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.
>Sincerely,  Jim Ellis 
Regards,
Don Rose, B.Mus., A.M.U.S., A.MUS., R.P.T.
Non calor sed umor est qui nobis incommodat

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