Altering FAC Settings 2

[FSSturm@aol.com]

Dear list,

In this continuation of my last post, I'll focus on the upper treble, and on
the "C number". The "C number" is a measurement of the difference between he
1st and 2nd partials of C6. This number is used by the FAC program to produce
a tuning curve for C7 to C8.

As stated in my earlier post, the difference between the 1st and 2nd partials
is 1/4 the difference between the 2nd and 4th partials. Therefore, if we know
the difference between the 1st and 2nd partials, we can multiplt that figure
by 5 to project the 4th partial's value.

The FAC program wants C8 to form a slightly wide 4:1 double octave with C6.
To obtain a value for C8, the FAC multiplies the "C number" by 5, adds that
result to the value it has calculated for the 1st partial of C6, and adds an
additional 0.5-1.0 cents. (Well, the FAC program may not do it exactly that
way, but that is the result it produces, consistently, regardless of input
numbers).

I have found the "C number" more inconsistent than the "A number", or, I
should say, more consistent in producing anomolies. On too many occasions I
have found C7 - C8 not forming close 4:1 octaves with C5 - C6 when I have
followed the instructions in the manual. My solution has been to read the
difference between the 1st and 4th partials of C6, and divide that number by
5 to arrive at my "C number". (Tune C6 to 0.0 cents. 8ve up to C8 and
measure. It is usually most convenient to use cents up to get to 30-40 cents,
then use the measure button to get a reading. Sometimes plucking the string
is necessary).

I kept records for a while, of about 50 readings, comparing the readings I
got at C7 to the readings I got at C8. 50-60% of the time, these measurements
aere in a 1:5 ratio, within 0.2 cents (at the C7 level). 20-25% of the time
it was 0.2-1.0 cents plus or minus. The remaining ca. 20% of my readings
there was a discrepancy greater than 1.0 cents, sometimes quite large. Since
this multiplies by 5, a 1.0 discrepancy at C7 translates to a 5.0 cent
discrepancy at C8.

Since I have been reading C8 instead of C7 to arrive at my "C number", my
results have been very consistent. I think much of the inconsistency at the
C7 level comes from the difficulty in obtaining a reliable measurement of the
2nd partial of C6 - lots of falseness, and not that strong a signal for the
SAT to pick up. Although the reading of the 4th partial (at C8) may also be
"jumpy", it is more reliable because less accuracy is required: if you are
within 1.0 cents at C8, it is the same as being within 0.2 cents at C7.

Like Jim Coleman, I want more stretch in the upper treble, with clean 8:1
triple octaves where possible. I fudge my "C number" up by 1.5 cents or so as
a rule. This puts C8 sharp by 7.5 cents, which is usually within 2 - 3 cents
of where I want it. So far so good.

However, the FAC program uses the "C number" only for C7 - C8. It takes the
value it has produced from the "A number" for C7, and the number it has
produced from the "C number" for C8, and creates a logarithmic curve between
those values. Thus, most of the effect of increasing the "C number" appears
near the top, in the F7 - C8 area, with much less effect from C7 to E7. I
find that the upper notes are close to where I want them, but the 4:1 double
octaves between 8ves 5 and 7 are too wide for my taste, among other problems.

As I pointed out in my earlier post, the FAC program "dampens" the stretch of
C5 - C7 by insisting on slightly wide 4:1 double octavews with C3 - C5. My
empirical solution is as follows:

For C5 - B5, I increase each note by 0.3 - 1.0 cents (or up to 0.5 - 1.5
cents). In concrete terms, C5 and C#5 plus 0.3; D5 plus 0.4, D#5 and E5 plus
0.5, etc. up to B5 plus 1.0. (Or C5 and C#5 plus 0.5, etc. up to B5 plus 1.5
cents).

C6 I increase by the same amount as I increased B5. Then I play C4, C3, and
F3, and observe the lights. I expect C4 to produce lights moving not too fast
flat (wide 4:1 double octave), C3 to produce lights moving just flat (just
wide 8:1 triple octave), and F3, well, that varies, but I want to know.

I alter the cents setting to maintain this pattern of just wide 8:1 triple
octaves up to C7, as long as the 4:1 double octaves don't become too wide
(check by ear and eye). From C7 to C8 I usually allow the triple octaves to
become gradually narrow, compromising between the double and triple octave -
making the triple octave not quite as narrow as the double octave is wide as
I approach C8. This can be estimated by eye, matching the speed the lights
rotate when playing the double and triple octaves below the note to be tuned.
(The double octave will cause the lights to rotate flat, the triple to rotate
sharp. I adjust the cents value until they rotate fairly equally. I also
remember from note to note how much I changed the previous one, and make the
changes even and gradual). I find that maintaining triple octaves to the top
usually produces double and single octaves too wide for my taste. My taste
may change with time.

It's a little more complicated than I have described. Pianos with large jumps
in inharmonicity at the tenor break need to be treated differently, for
example. But I have gone on at much more length than I intended, so I'll call
a halt here, and later send a final post on the "F number", the tenor break,
and the bass.

Regards,
Fred Sturm
Albuquerque