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

[Dean L. Reyburn, RPT]

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>

>If you have been using SATs for any length of time you may have
>noticed that FAC measurements tend to change from one season to
>another.  The "A" measurement especially will rise with the
>increase of humidity.  This will skew the tuning of a good piano
>unpleasantly.
>
>I dislike seeing "A" above 8 and 9 which happens in summer
>humidity.
>
The A measurement in the FAC system is only used for setting the pitch of
the overall tuning, if I understand FAC properly.  F and C are used for
setting the stretch.  So if the "A" is too high, just offset the SAT
flat, if that turns out to be needed.  It really shouldn't be though.

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.

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.

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
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