Fairchild Method making FAC tuning

[Robert Scott]

John M. Formsma wrote:

 >>>>>>
Yes, the numbers change after a pitch raise, but would not the recalculated
tuning result in the same tuning, regardless of when the nubmers are
obtained? My guess, which is completely a guess, is that second FAC numbers
will be a ratio of the first FAC numbers, resulting in the same tuning when
calculated.
   ....
I would love to know for sure if the tuning is the same regardless of when
the FAC numbers are obtained.
<<<<<<

John, are you assuming that the FAC numbers are in some way representative
of the pitch? (So that after a pitch raise they all go up proportionally?)
This is not the case.  The FAC numbers are purely a measurement of
inharmonicity and are only indirectly related to pitch.  The tuning will be
the same if and only if the FAC numbers are the same.  The question of
whether the numbers will be different after the first pass of a pitch
raise does not depend on the new pitch, but it does depend on factors
that are affected at the same time as the pitch, such as a change in
the stiffness at the termination points.

Just to review, the FAC numbers are defined as follows:

   "F" number = the difference in cents between the  8th partial
    of F3 and two times the 4th partial of F3.

   "A" number = the difference in cents between the 4th partial
    of A4 and two times the 2nd partial of A4.

   "C" number = the difference in cents between the 2nd partial
    of C6 and the two times the fundamental of C6.

(source: Sanderson's patent # 5,285,711)

-Robert Scott
  Ypsilanti, Michigan