Unison coupling

[Ron Nossaman]

 Hi Roger,
I'll try this again. I had a reply for you at lunch time, but the operating
system I got from the richest man in the country crashed Eudora during the
(incredibly demanding of system resources) spell check. Anyway, here's a
reply... maybe.

>Hi Ron,
>           What I think is happening, each partial takes time to develop,
>and is added to the fundamental to for a progressively more complex wave
>form. The negative inharmonicity of the partials aids in lowering the pitch.

* Perhaps, but how does inharmonicity, negative or otherwise, lower pitch?
I know how it works with octaves and such, but for a single string?


>The inharmonicty increases with a more powerful blow, and is there for mor
>noticable with a firm blow.

* This is contrary to what Ric's quoted article said. What's your source?
This isn't a trap, honest, I'm just trying to resolve conflicting information.


>I'm convincinced that many factors conspire, damping or impedence of the
>board, the wire, the hardness of the hammer, the velocity, the regulation,
>and so the list goes on.
>Just some half baked musings.
>Roger

Musings from just inside the door of the Mezzo-Thermoneal Stabilizer, eh?
Alright, let's bake a little. 

The generally accepted explanation for the pitch drop moving from the
attack phase of the envelope, to the dwell, is roughly this: At the
beginning of the attack, the string vibrational amplitude is at it's
widest. At the strings widest deviation from a straight line between bridge
pin and, say, agraffe, the string's path is longer than the supposed
speaking length. That means the string has to stretch, which raises the
tension, which raises the pitch. As the soundboard assembly, duplex
segments, air resistance, internal friction, and whatever else you might
think of reduces the vibrational amplitude, the string assumes a much
straighter line as it enters the dwell. Since it isn't stretched as much as
in the attack, the pitch drops to what you've "tuned" it to for the bulk of
the duration of the dwell, then further drops (less dramatically) through
the decay as the string straightens out still further. It seems to me that
this requires that the elastic recovery rate of the string increases as the
tension gets closer to the yield point. I would assume that it does, since
the elongation factor changes proportionally to the proximity of tension to
yield point. Otherwise, the string would act like a pendulum, and the
oscillation period (frequency) would remain constant whatever the amplitude
of oscillation.

I still like this explanation. It's simple, logical, and doesn't require a
cast of thousands, so it's understandable. That's not what we're after
though. The original question here, is what makes the pitch drop when a
second string is tuned in. Is the perceived drop just a difference in the
timing of the attack/dwell transition, or is there actually another pitch
drop in the dwell phase, in which case we have TWO pitch drops occurring.

Just trying to drag this back into focus.

Ron N