Jim,
Regarding your analysis of voicing and inharmonicity, it is gratifying to
see such thoroughness and attention to detail . Now I see why people who
have been on this list longer than I have hold you in such high regard.
It is interesting that where I had looked at harder than normal voicing
(using a wooden paint stirring stick) you used softer than normal voicing
with the nameboard felt strip.
Looking at your first experiment,
>F3 partial 4
w/o felt w/felt
> 3.83 3.80
> 3.90 4.08
> 3.76 3.98
> 3.83 3.90
> 3.92 3.91
> 3.92 3.77
> 3.88 3.86
> 3.73 3.83
> 3.86 3.79
> 3.86 3.77
> ===== =====
> Average 3.849 3.869 difference = .020 cents
Std.Dev .061 .096
It is clear from the standard deviation that it was absolutely essential
that you averaged a number of readings. A single reading would not
have been very meaningful. But it does appear that you are measuring
a real effect.
For F3 partial 3 you got a difference of .086 cents with standard deviations
of .108 and .150, an even more significant result.
Your result for partial 2 is a little curious.
>F3 partial 2
> 1.32 1.35
> 1.33 1.18
> 1.19 1.31
> 1.46 1.35
> 1.81 1.37
> 1.59 1.22
> 2.50 1.57 ??
> 1.22 1.29
> 1.41 1.32
> 1.31 1.39
> ===== =====
> Average 1.514 1.335 difference = .179
Std.Dev .372 .100
Since all the other readings are so close together, it seems that the 7th
line might be a ringer. If you leave out both entries for line 7 you get a
difference of only .095 cents for the averages - much smaller, but still
significant.
What surprises me the most about your 8th partial results was the
uniformity:
>F3 partial 8
> 11.12 11.05
> 11.23 11.25
> 11.23 11.11
> 11.14 11.18
> 11.12 11.17
> 11.15 11.06
> 11.07 11.16
> 11.13 11.19
> 11.21 11.20
> 11.11 11.20
> ====== ======
> Average 11.151 11.157
I would have thought that the higher partials would be much less stable,
more subject to false beats, and harder to measure. That's a great
stringing job on that "L".
It is interesting to note that the SAT results on F3 partial 4 were in
the opposite direction as the RCT results. The RCT results showed
..020 cents more with the felt strip inserted. The SAT results showed
..160 cents less with the felt strip inserted.
I also find it interesting that the inharmonicity jumped up more than
2 cents just from a tuning adjustment. I assume that you did only a
small tuning adjustment. This result actually casts doubt on the
usefulness of inharmonicity readings to create tunings. If the
inharmonicity changes that much when you fine-tune, then the
assumptions upon which any stretch calculator (like the FAC) is
based are invalidated. You would have to go back and remeasure
inharmonicity after your fine-tuning in order to re-calculate the stretch
for yet another fine-tuning.
Looking at the difference between the prompt pitch and the end pitch, you
observed:
>F3 partial 3
> prompt end w/felt
> 0-2sec. 2-6sec. 0-4sec 4-7sec
>
> 4.9 4.0 5.0 4.2 In this test, it became obvious
> 4.8 3.8 4.9 4.2 that there was a good bit of
> 4.8 3.8 4.9 4.2 difference between the prompt
> 4.8 3.8 4.9 4.2 pitch and the end pitch, so two
> 4.8 3.8 4.9 4.2 readings were taken in each case.
> 4.8 3.8 4.9 4.2 This was not noticed in the higher
> 4.8 3.8 4.9 4.2 partials.
> 4.8 3.8 4.9 4.2
> 4.8 3.8 4.9 4.2
> 4.8 3.8 4.9 4.2
> ===== ===== ===== =====
> 4.81 3.82 4.91 4.2 The Averages of each test.
> 4.315 4.56 The average of the averages.
This raises an interesting question. What does it mean to say that
the inharmonicity of the 3rd partial of F3 is 4.8 cents in the prompt
and 3.8 in the end tone? Supposedly both the fundamental and the
third partial could be changing in frequency as the note decays. When
you measure inharmonicity, you are supposedly measuring the ratio
between the fundamental and the given partial. But here we have a
case where both the fundamental and the 3rd partial are changing
at once. I assume that you zeroed you instrument on the fundamental
first and then began measuring the 3rd partial. But did you zero your
instrument on the prompt tone of the fundamental or the end tone?
Or does the instrument measure both the fundamental and the partial
at once? I could see how the RCT might do this, but not the SAT.
In any case, your results seem to show that the super-soft voicing
had less pitch change as the note decays. Could that be because
the super-soft voicing was less efficient in trasferring energy from the
hammer into the string and as a result gave you a prompt tone that was
already half-way down the road to being an end tone?
I was also interested in your comments about methods of measuring
inharmonicity (automatic vs manual). From my experience in developing
the TuneLab program, I found the process of locking on to a pitch to be
quite difficult, especially where there are instabilities. It seems that
people who use the SAT develop there own subjective criteria for saying
when the lights are "stopped". It would be hard to embody these criteria
into an automatic locking function. That is confirmed by your observation
that with the extra digit and averaging capability and the automatic "listening
ear" function, the RCT results were no more reliable than those obtained with
an SAT used with intelligent human intervention in the pitch locking process.
Once again, thanks for a most complete answer to my question.
Bob Scott
Ann Arbor, Michigan
This PTG archive page provided courtesy of Moy Piano Service, LLC