[CAUT] Interesting boo-boo

[Fred Sturm]

On 5/19/05 1:34 PM, "Jeff Tanner" <jtanner@mozart.sc.edu> wrote:

> by accident, I measured C5, rather than C6.
> 
> I didn't realize I had done it until I had tuned all the way up to C5.
> The only reason I noticed it then, was that I had had to tap the bridge
> pin to eliminate the false beat so I could measure the string, and I
> realized then, at that point that it was C5 that I had measured for the
> FAC rather than C6.
> 
> Hmm.  It worked anyway.  The stretch for C (at C5) was something like
> 7.8, which was in line with the other two measurements, so no warning
> bells had gone off.  All the octaves sounded very clean, and there
> didn't seem to be any problem with intervals anywhere.  The client was
> due for choir rehearsal at 6:30, so I was pressed for time, and decided
> to keep going and finish, rather than start completely over.  Piano
> sounded great, maybe even better than I remember previous tunings
> sounding.

Hi Jeff,
    It's not particularly surprising that a tuning generated with a
mis-measured C number would sound fine. The C number in the FAC program has
a very minor (unnoticeable) affect from C6 to C7. Its major affect is from
C7 to C8. So it mostly determines the stretch of the top octave.
    BTW, the F number operates almost exclusively in octaves 1 and 2. The A
number is the vital one. Most of the reason the FAC and other mathematical
constructs work (in the sense of creating "equal temperament" in the form of
progressing beat rates) lies in the choice of tuning partial, together with
smoothly increasing numbers. The measured input numbers (eg, FAC) give the
size and stretch of the octaves, and intermediate numbers are extrapolated.
It's far simpler and less mysterious than it looks or seems to the average
tuner. 
    Differences of 0.5 cents for The A input number are negligible from the
point of view of how the tuning will sound. For the F and C numbers,
variances of 2 to 5 cents will produce acceptable tunings. When I used an
SAT, I always added 0.5 to the A number, and 5.0 to the C number to start
with, to produce the basic structure of stretch I wanted (I would then alter
on the fly, but this gave me a close starting point). The F I usually left
alone unless it was high, in which case I capped it at a default 10.0.
Regards,
Fred Sturm
University of New Mexico