On Oct 22, 2008, at 12:14 AM, Richard Brekne wrote: > In the treble the stretch starts to develop a bit steeper then > traditional octave priority approaches... but the top octave ends up > quite moderately stretched. I rarely see C8 over 36 cents... > depends on the pianos built in inharmonicity. I find that on smoothly scaled pianos (certainly including most quality grands), the 6:3:1 and the 8:4:1 relations coincide pretty closely through about C6. In octave 6, there begins to be a divergence between 3:1 and 6:1, and a similar divergence between 4:1 and 8:1 (3:1 and 4:1 stay close to one another, as do 6:1 and 8:1). At C7, the divergence accelerates, and there is commonly an additional significant divergence between 8:1 and 6:1 in the top six or so notes. So if you are doing a stretch that compromises between 3:1 and 6:1, and favor 3:1 a bit, I agree that 36 cents may be the highest for C8 for the most part. If you favor 6:1, though, that number becomes higher. If you ignore 3:1 and just follow 6:1, C8 will often be as high as 45 to 50 cents. If you follow 8:1, C8 can get to 60 or occasionally higher. While this sounds like a big difference, it appears almost entirely in octaves 6 and 7, with the bulk of the difference in octave 7, and the bulk of the octave 7 difference in the top few notes. It's a matter of a curve that becomes fairly steep at the end. I prefer to follow the 6:1 and 8:1 (if they diverge too much, I favor 6:1) because I get very good support for octaves 5 and 6 (from higher partials of all the notes tuned below - as there is very little difference from 3:1 and 4:1 at that point), but then get more of a correspondence to the "psycho-acoustic" phenomenon ("the desire for high notes to be sharp") in the top of the range, where single octave beats and the like become pretty much irrelevant (hard to pick out and hear). Of course, if the customer prefers less stretch in the top, it is easy to drop those top two octaves - the rest of the tuning is "reasonably conservative." But I have yet to come across a customer who asked for less stretch. Maybe I lead a sheltered life <G>. Regards, Fred Sturm University of New Mexico fssturm at unm.edu
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