Perfect tunings (S.A.T.'s?)

[Jim Coleman, Sr.]

On Sat, 27 Apr 1996, Dean L. Reyburn, RPT wrote:

> Newton Hunt writes:
> >Now is the time for all good tuners to tune to _S_scientific
> >_A_ural _T_emperaments.
> >
> So that's what S.A.T. stands for! <g>
>

> I dislike seeing "A" above 8 and 9 which happens in summer
> >humidity.

Dean, and Newton,   The A stretch number controls the width of the Temp-
erament octave and in addition it will have more effect on the octave
stretch than the F and C will if you deviate from the measured stretch
of A.  One can deviate this number if he does not like the amount of
stretch in the A3 to A4 octave.  Preferably deviations of only a few
tenths of a cent will not cause much trouble.

If you are tuning a spinet with short strings, you better have an A
value above 8 or 9 cents, or you will will end up with a narrow Temp-
erament octave.


> The question is: *WHY* do the stretch numbers change from season to
> season?  Maybe the piano is telling us something.  Presumably when a
> tuner does an FAC tuning, he measures "stretch numbers" which are
> considered to be a measure of inharmonicity (IH).  But if you look at the
> IH formulae, they are based on string tension, diameter, length, and
> weight.  Which one of these changes to alter the IH?  The answer is none
> of course, so why do the stretch numbers change from summer to winter?
> We all know they do.

I suspect that the impedance changes as the soundboard rises or falls.
An additional thing may happen in conjuntion with this and that is the
the effectual length actually changes during the aging of a piano, in
that the curvature of the string passing around bridge pins and V-bars
will more closely conform to the curvature of the pin or V-Bar. This
removal of some of the curvature stress may let the string think it is
longer.  (yes, I know the strings don't really think)  Try settling the
strings at the various contact points and see how the stretch changes.

> Even the tunings calculated by my Chameleon-2 system (on the same piano)
> change with the season.
>
> I've been working on this problem for some time, and have not come up
> with all the answers yet, but here is what I think at least part of the
> answer is:
>
> The bridge and soundboard are not rigidly supported, but can move in
> response to the string's motion.  This movement induces an effect sort of
> like "backwards inharmonicity", which lowers the actual frequency of the
> lower partials the most.  This effect changes with the moisture content
> in the wood, and therefore with the season.
>
> There must be some other causes too, especially on wound bass strings.  I
> have measured wound strings where the IH was (apparently) negative!!   I
> measured some strings for which the IH was all over the map, not
> consistent with any formulae I know of.

Wrapped strings have more possibility of uneven loading, especially where
one end of a single wound string may have deliberately over-wrapped its
own end.  This makes some bass octaves impossible to tune.

 >
> BTW, Don't miss my class in July/Dearborn ("The Digital-Aural Tuner")
> where I will be showing some interesting research I have done, and am
> doing right now on this subject!
>
> (Also see Dave Merrill "The Puzzles of Inharmonicity" Piano Technicians
> Journal, pages 23-24, November, 1980.)  If several people are interested,
> I could type this in.  It is real interesting, way ahead of its time.
>
> If you really want to record and save those "_S_scientific _A_ural
> _T_emperaments", and don't have a SAT yet, try my Web page below, we have
> several great packages.
>
> Dean
>
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>  Dean L. Reyburn, RPT                    Sanderson Accu-Tuner
>  REYBURN PIANO SERVICE, INC.             Authorized Distributor
>  2695 Indian Lakes Rd, NE               "Software Solutions
>  Cedar Springs, MI  49319  USA           for Piano Technicians"
>  616-696-0500  Fax: 616-696-8121         email:  dean@reyburn.com
>
>           See our software at our new Web site:   www.reyburn.com
> ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
>
Keep up the good work Dean and Newt.

Jim Coleman, Sr.