Greetings:

    The Klepac chart from Travis' Guide to Restringing that Terry
Smythe posted may be as good a place to start as any, if the piano in
question has no strings and no other data is available. After all, this
kind of *rule-of-thumb* approach is what many manufacturers used for
years because they would not or could not spend money on their own
research.

    Just for fun, I plugged those numbers into my spreadsheet
adaptation of Dave Roberts' formulas. I used Klepac's chart to modify
and then evaluate an existing scale for a medium sized grand that I had
rebuilt recently. The resulting *Klepac* scale would certainly be
acceptable if no other data nor means of derivation were available. The
piano would not implode from excess tension. However, the inharmonicity
and loudness progressions are pretty sloppy without a whole lot of
*fine tuning*, which the Klepac chart, of course, does not supply. And,
Klepac's chart offers no assistance whatsoever in the matter of wound
strings, nor the critical transition between wound and plain wire
strings.

    One can begin to appreciate that the higher quality pianos of
yesteryear, the ones that sound good, are stable, and easy to tune,
became so through a tremendous amount of experimentation at the
factory. The scales were derived empirically, not by mathematical
modeling, nor by simple adherence to rule-of-thumb scaling schemes.

    When Travis first wrote his book, the *only* quantifiable factor
available to him was tension, and that only for plain wire strings.
Inharmonicity was certainly recognized, and at least partially
understood, but accurate formulae for _predicting_ inharmonicity (nor
any other quantifiable audible factor) did not exist until fifteen or
twenty years ago. The rule-of-thumb approach will get you in the
ballpark, but will not enable you to optimize the scale to any degree
whatsoever. Where Travis' book _is_ invaluable is in the wire gauge
data that he had gathered for so many American pianos.  That data
doesn't really exist anywhere else in such concentrated form.

Cheers

Doug Rhodes