[CAUT] SAT numbers

[Fred Sturm]

On Aug 20, 2007, at 1:53 PM, Jeff Tanner wrote:

>
> On Aug 20, 2007, at 10:03 AM, Fred Sturm wrote:
>
>> I came to believe, based on things I had read and conversations I  
>> had had (which I'm afraid are hazy at this point) that Al  
>> Sanderson had made a change to the FAC calculations to give more  
>> stretch to the bass, in response to criticism by people using the  
>> SAT for concert tuning.
>
> Paul told me the curve had been recalculated for the SATIII, but I  
> didn't realize it was for that reason.

I'm not talking about SAT III. THe original SAT I. Way back in the  
mists of time. I have no idea what was done in the transition from  
SAT I to SAT III. No doubt it was for the good.
>
>
>> And I came to the conclusion that it was a "patch" that didn't  
>> actually make any sense for pianos with an inharmonicity profile  
>> that happened to have a plain wire, low tension F3. (Note that the  
>> Hamilton 243 and the various flavors of Acrosonic are essentially  
>> the same scale, somewhat foreshortened. But the smaller Acrosonics  
>> happen to have wound strings for F3. Why should there be that much  
>> difference in their tuning?)
>
>
> I have tried using your idea at times and thought that the  
> temperament section turns out funky.  It really does take a stretch  
> of 18 or 19 for the temperament to work out right in the Hamilton,  
> and in most cases I haven't thought the bass was too stretched  
> either.  Using the numbers in the "library" for the Baldwin  
> Hamilton doesn't work, because they are the "pre-recalculated"  
> numbers.  Way too narrow.

The F number doesn't affect the temperament octave. At all. Try it.  
Do two calculated tunings, one with F at 18, the other with F at 10  
(A and C the same for both). Read the numbers and compare. I did that  
(and all sorts of other permutations as well), and found out there  
was no more than 0.1 and occasionally 0.2 cents difference for any  
note above F3, based on changes of any amplitude in the F number.

> snip
>
>> (I had found that with those larger numbers, I was constantly  
>> needing to intervene and narrow the octaves).
>> 	I also always tuned the bass downwards (never started at A0) so  
>> that I would know what was happening and be able to intervene.
>
> The problems I've had with "intervening" is that I wind up with a  
> whole string of affected notes that have to be changed just to make  
> one fit better in one spot.  IOW, trading one compromise for  
> another, or a whole bunch of them.  For example, D#3 might be  
> wound, and doesn't work well with the scale of the plain strings in  
> the octave above it, so we tweak it aurally to work better in the  
> temperament.  But that can set a whole series of problems with bass  
> tuning beginning with B2, and all the other related notes going  
> down in the bass, and it may well affect double octave and other  
> coincident partials in the scales above the temperament.

Yep, I agree. You certainly shouldn't go for the sound of one octave  
in isolation. But when all the octaves are obviously too wide in the  
calculated tuning, reducing their width in a systematic way is often  
a good solution. I would typically just do a 6:3 (play the octave  
above, stop the lights to that note, then tune the lower note).  
Occasionally I would do a slightly narrowed 6:3. And usually I would  
only have to do this for a short section before the calculated tuning  
was fine.
>
> snip
> But the FAC was right.  It had produced a scale that was the best  
> compromise overall, and the smallest of aural corrections just made  
> things worse.  In my experience, this happens far more often than  
> the reverse.  I find it to be a very rare occurrence that aural  
> corrections are an improvement.

Again, I agree. But not with those enormous F numbers. Hence my  
policy to reduce to a default 8 - 10. Once I started doing that, I  
rarely did any "intervention."
>
> Jeff
>
>
>
> Jeff Tanner, RPT
> University of South Carolina


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