Stretch Vs.Temperament, (was Beat Rates)

[Ron Nossaman]

>Ron writes:
> >I never have liked the strings of a unison moving in opposition theory.
> >I  don't think that's even possible in a piano.
>
>     Hot damn,  chaos comes again!

Oh now, there's always room for one more source of aggravation.


>   This is how it seems to me:
>     If two strings are struck, it is not logical to me that the system will
>be so perfect that they move in phase, and the least bit out of phase will
>create, due to coupling, an alternating system of energy transfer between the
>two.  In a coupled system, if one string is unstruck and another is,  the
>unstruck string will begin moving, but it will NOT move in phase with the
>first.  It will absorb energy from the struck string and, in an attempt to
>"catch-up",  will lag behind.  At some point, energy will equalize and the
>two strings will go in and out of phase, but the period at which they will be
>in phase is temporal.

Yes and no. If their oscillation period is the same, one will lag, the 
other will accelerate, and they will synchronize. In a system with no 
damping in the shared flexible termination, they would oscillate back and 
forth, but there's enough damping in the system as seen in the piano, that 
they converge and stay there. At least that's what I hear. That yeowwwww 
effect you get in the attack from a unison not leveled to the hammer pulls 
together quickly and yeowwwwws no more until you hit it again. But that's a 
case of two or more strings not being started in phase. How is it possible 
to get two strings of a unison moving in opposition - that's 180° out of 
phase from each other - by hitting a unison with a hammer in a real piano 
during the course of a tuning? That would impress me. Even if it were 
possible to start them this way, they would pull together fairly quickly 
because they share a common flexible termination.


>    With three strings struck, there is a tertiary transfer created which is
>far more complex and contains more resultant modes of vibration, and the
>three strings will never be totally in phase.

Again, in theory, but I'm not sure that is the case in the piano. Of course 
they can be in phase and not be in acceptable  tune, but you already know that.


>think a really good tuner can manipulate the unison to give the best
>compromise.  Setting three strings of all unisons to "dead-on" ETD setting
>will not only create some unisons better than others, but will often create
>unisons that lack the sustain of the micro-mistuned ones.  I think the ear is
>the better judge of unisons because of this.

Absolutely, and I'm not that convinced that it takes a really good tuner so 
much as a hard head. Just like tuning an octave, there is a wider range of 
what constitutes "acceptable" in a unison than we take the time to explore. 
The same problems we have trying to decide which of repeated attempts 
concentrating on minimizing different ranges of aural garbage in a 
(shudder) wrapped trichord unison constitutes the "best" compromise, are 
available to us in (hopefully) lesser degree in any unison. Most times, we 
accept the first "minimum garbage" version we achieve that meets the 
criteria for the piano and the venue, and move on rather than spending all 
day trying to enhance the luster of fecal material to no rational end. I 
wouldn't know where to start trying to code the concept of "acceptably 
least bad" into ETD software, but the wetware does this naturally (if not 
necessarily well) with every action we take - tuning or not. "You're not 
going to eat that are you?" "Who picked out that shirt?"



>       My normal unison is formed by setting two strings to the SAT, and then
>tuning the middle string aurally. This allows a more consistant sounding set
>of unisons, and I feel like the piano's sustain is brought under my control.
>It also side-steps the question of flattening of the unison by the addition
>of the second or third string.  I don't see that in my results, and even so,
>it appears that what Virgil Smith is pointing out as an effect of unison
>flattening is in the .3 or less cent range, and that is easily obviated by
>choice of stretch made earlier.
>Regards,
>Ed Foote

Yep, about what you'd expect from opening the door and letting in a little 
winter chill on the way out. Then there's the strip muters. If the pitch 
falls 0.3 cents through the whole forest, how can you tell by comparing trees?

Ron N