<HTML> <HEAD> <TITLE>Re: [CAUT] SAT numbers</TITLE> </HEAD> <BODY> On 8/22/07 1:47 PM, "Jeff Tanner" <jtanner@mozart.sc.edu> wrote: <BLOCKQUOTE>Temperament 41 is the library tuning for Baldwin Hamilton - F/A/C = 17.9/6.2/6.0 (old curve) Temperament 1 is the same FAC recalculated to SAT III curve Temperament 2 is same as Temperament 1, with F number changed to 10.0 <BLOCKQUOTE> </BLOCKQUOTE>Note Temperament 1 2 41 (old curve) A0 -20.6 -13.4 -11.9 C1 -16.5 -10.6 -10.5 C2 -4.3 -2.6 -4.7 B2 +3.2 +2.2 +3.0 C3 -3.6 -2.3 -5.0 F3 -1.0 -0.4 -2.0 A3 +0.8 +1.0 +0.3 C4 +2.2 +2.4 +2.1 F4 +5.0 +5.0 +5.1 A4 +7.7 +7.7 +7.8 C5 +2.6 +2.5 +2.5 C6 +4.4 +3.8 +3.7 C7 +11.4 +11.2 +10.7 C8 +35.0 +34.2 +33.4 </BLOCKQUOTE> Hi Jeff,     Interesting. I get significantly different numbers on my old (1995) SAT, including for your library tuning, using those numbers. I don’t have any explanation. For the record, here are my results: Note Tuning (first is 17.9/6.2/6.0, second 10.0/6.2/6.0) A0 –17.6  -13.2 C1 –13.5  -10.3 C2 –3.4  -2.7 B2 1.9  1.7 C3 –2.7  -2.0 F3 –0.6  -0.4 A3 1.0  1.0 C4 2.4  2.4 F4 5.0  5.0 A4 7.7  7.7 C5 2.4  2.4 C6 3.4  3.3 C7 10.6  10.5 C8 33.5  33.3     It just doesn’t jibe at all with your numbers.     I do grant that the differences (on my machine) from F3 down to C3 would be somewhat significant, so if you do a C3 to E4 temperament, that would be part of the temperament (I did a C#3 to F4, nearly the same span). And, again with my machine, I preferred a default low F number’s results. But even going down that far, the differences are gradual and reach a maximum of 0.7 cents, hardly earthshaking.     Obviously the SAT III produces different calculations, and what I have been writing applies only to SAT I/II (same mathematical guts in both I and II, as far as I know. That’s what they always said). But I am puzzled by the difference between your “library” and my calculation of the same numbers. The degree of difference doesn’t make any sense.     The B2 to C3 shift (6th partial to 4th partial) is probably the most troublesome spot on the SAT, or used to be. A spot to keep a close eye on, and possibly to do a little intervention to smooth it out. But the difference in the B2D#3 M3s between my two FAC tunings is a pretty negligible 0.2 cents (B2 moved up 0.2, D#3 up 0.4), not the 2 cent difference you found. I guess the SAT III is a far different animal. As I had remembered, no note from F3 through C8 changed value more than 0.2 cents with a change in F number of as much as 8.0. So I guess that we are talking at cross-purposes to some extent, as we have different machines. Regards, Fred Sturm University of New Mexico   </BODY> </HTML>