FAC numbers

[Joe & Penny Goss]

HI Jim,
What are the advantages of tuning FAC as opposed to F4?
Was the F4 curve better for some scaled pianos?
Joe

----------
> Hi richard:
> 
> The F, A, and C were chosen for very important reasons. If you know what
the
> inharmonicity of F3 is and can locate that note, you know how you want to
> tune Bb0 (it is the 6th partial of Bb0). If you know the inharmonicity of
> A4, you can accurately locate A4, A3, A5, A6 and A7. If you know the 
> inharmonicity of C6, you can locate C6, C7, and C8. If you can locate 
> all of these, then you can do a mathematical smooth curving of the
plotted
> points and have a complete tuning for the piano. Sure, you could measure
> all of the notes and make a more precise tuning (maybe), but it is not 
> practical except in Lab work. It takes a very lengthy computer program to
> do this. There is another wise choice Dr. Sanderson made in choosing
these
> notes and the partials by which all notes are to be tuned. The Bass is
tuned
> from A0 thru B2 using the 6th partials. The section from C3 thru B4 is 
> tuned using the 4th partial. The section from C5 thru B5 is tuned using
the
> 2nd partial. In each of these section these are the most important and 
> usually the strongest partials to be heard.
> 
> The reason for measuring the difference between the 4th and 8th partials
> of F3 is because you get more consistent answers as to the the general 
> inharmonicity of that note. The same goes for the A4 (using 2nd and 4th 
> partials) and for C6 (using 1st and 2nd partials).
> 
> There is no attempt to try to tune the 5ths. If the scale of the piano
> is rather decent, they will come out pretty good. If the scale is not
good,
> you cant do much better anyway. Oh sure, you could give more attention 
> to the 5ths, but this would be at the expense of consistency in 3rds, 
> double octaves, 10ths etc. You can't have it all on a poor scale even as
> "you can't make a silk purse out of a sow's ear".
> 
> Once an inharmonicity curve is plotted, you can tune any note by any 
> partial you wish. Just think how many intervals are controlled by the 4th
> partial which is used in the most critical part of the tuning. Octaves 
> (4-2 relationship), M3rds (4-5 relationships), 5ths (6-4 relationships),
> P4ths (3-4 relationships), m7ths (4-7 relationships). I just can't think
of
> any other partial which affects so many intervals. Oh, I forgot Double 
> Octaves (4-1 relationships).
> 
> Tuning Octave 5 by the 2nd partials gives more accuracy than tuning by 
> the fundamental. Above that, the fundamental is strongest and best to
tune
> by.