[CAUT] SAT numbers

[Fred Sturm]

On 8/22/07 1:47 PM, "Jeff Tanner" <jtanner at mozart.sc.edu> wrote:

> 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
>> 
> 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
> 

Hi Jeff,
    Interesting. I get significantly different numbers on my old (1995) SAT,
including for your library tuning, using those numbers. I don¹t 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 doesn¹t 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 number¹s 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. That¹s what they always said). But I am puzzled by the
difference between your ³library² and my calculation of the same numbers.
The degree of difference doesn¹t 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

 
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