SAT III FAC Calculation Assumptions?

[J Patrick Draine]

On Thursday, October 31, 2002, at 08:43  PM, Dave Smith wrote:

> In other words, is it trying to hit exact 6:3 octaves all the way down 
> into
> the bass and exact 2:1 octaves all the way up into the treble?

I *think* you'll find the bass octaves are slightly expanded from 6:3, 
and the high treble is expanded from 2:1, probably closer to a 4:1 
octave.
It should be quite easy to check a calculated tuning to see if this is 
true. For example, after executing the FAC tuning on the piano, with 
the SAT set on the calculated reading for A0, observe the display when 
A0 is played (it shouldn't be rotating), then check note A1. The 
pattern would be drifting very slightly sharp if the 6:3 octave is 
expanded.
Likewise, with the FAC displaying for A7, play A6 and A5. If the A5 key 
keeps the display stable you've got a 4:1 octave.
I'm not sure where (or if) this is documented.

Patrick Draine