FAC numbers

[Jim Coleman, Sr.]

Hi Joe:

For a few strange pianos the F4 stretch number works better, but then you
have to pigtail on the treble and Bass. If you see a problem with the FAC,
then switch over to the F4 Stretch system. Sometimes the F3 just doesn't 
fit the rest of the piano.

Jim Coleman, Sr.

On Sun, 23 Aug 1998, Joe & Penny Goss wrote:

> 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.
> 
> 
>