Hi Bob:
You mentioned that no one has given you data on measurements of inharmon-
icity changes due to voicing. Here is some.
In your last post regarding voicing having no effect on inharmonicity,
I decided to do some tests. First I'll describe some of the setup
which I used. Knowing that frequency is affected by amplitude, I
devised a key striking system to give rather even strokes to the key.
This is a 6" long dampp chaser tube with about 1 1/2" buckshot fill in
bottom half covered with a disk made from a ground down dime. On top
of that was a cushion of balance rail punchings about 1 1/2" tall,
covered with another dime. The remaining cylinder was filled with buck-
shot and capped with the endcap of a dampp-chaser rod. The caps were
secured on both ends with duct tape. All of this was devised to help
eliminate the weight from bouncing when dropped from a prescribed height.
A peice of piano wire 8" long was hooked thru the top cap for the
purpose
of lifting and dropping the weight on a selected key. For a poor man's
guidance system, the core of a paper towel roll was relieved on the
bottom end to depress the keys on either side of the one being tested.
It was found that a 1" striking height would be adequate for most key
strokes. With the prepared weight inside the core tube a matrix of piano
wires was placed across and thru the tube to limit the height the weight
could be raised while being lifted by the 8" long piano wire hook.
This first test is limited to note F3 on my Steinway L. Other tests may
be done later to see what effects can be noticed in other areas of the
piano.
In order to avoid damaging the hammer, a strip of thin nameboard felt
was passed down between the strings of G#3 and A3 and then brought up
between the strings of D3 and D#3. This strip could easily be slid back
under the strike point of the F3 when testing for the modified voicing
of F3. I realize that this only represents surface voicing effects.
More dramatic effects may be realized by deep needling, but as I said,
I did not want to damage my hammers.
The measurements were taken using the RCT tuning unit utilizing the
listening ear which listens to a tone for a prescribed amount of time
and averages the readout for that time. This test was not done in an
anechoic chamber so there is some variation in readings. Ten readings
were taken in each test and then averaged for comparison.
The first column shows readings for the unmodulated tone. The second col.
shows the tone with the felt placed between the hammer and string at the
strike point.
F3 partial 4
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 3.864
F3 partial 3
4.83 5.07
4.92 4.76
5.10 5.02
4.84 4.88
4.85 4.96
4.79 5.03
4.98 5.29
4.97 4.79
4.73 4.95
5.01 5.13
===== =====
Average 4.902 4.988
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
The following test was done on F3 listening to the 8th partial. It
was necessary to use a much harder blow to excite the 8th partial. I was
forced to use heavy finger blows which blows away some possible
objectivity
but the results were still quite reasonable.
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
As you can see from the above, the voicing change initiated by placing a
felt strip between the strings and the hammer does not cause much
change in
the higher partials, but does produce some change in the lower partials.
This BTW goes along with other observed variations in the lower partials
which are caused by what we think are variations in soundboard impedance,
bridge impedance and perhaps soundboard clamping (too near the edge of the
board) and perhaps other unknown to me causes which alter the reading of
lower partials more than higher partials. I first discovered these
types of
variations as far back as 1967. Dean Reyburn has termed this effect as
para-inharmonicity.
I did some additional testing using the SAT only.
F3 partial 4 w/felt
1.4 1.3
1.5 1.3
1.5 1.3
1.5 1.3
1.5 1.3
1.5 1.3
1.5 1.3
1.4 1.4
1.4 1.4
1.5 1.3
==== ====
1.48 1.32
After a change in tuning the following measurements were taken.
F3 partial 4 w/felt
3.7 3.7
3.8 3.6
3.7 3.7
3.7 3.7
3.7 3.7
3.7 3.7
3.7 3.7
3.7 3.7
3.7 3.7
3.8 3.7
===== =====
Average 3.72 3.69
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.
F3 partial 2 w/felt
0-3sec. 3-6sec no change
2.2 1.6 1.6 In this test there was less difference
2.2 1.6 1.6 between the prompt sound and the end
2.2 1.6 1.6 sound during the normal voicing. When
2.2 1.6 1.6 felt was inserted between the hammer
2.2 1.6 1.6 and the string, the softer sound was
2.2 1.6 1.6 the same as the end sound of the full
2.2 1.6 1.6 tone.
2.2 1.6 1.6
2.2 1.6 1.6
2.2 1.6 1.6
===== ===== =====
2.2 1.6 1.6 The average of each test
1.9 1.6 The average of the averages
Something new was learned in the above tests. Voicing does influence
inharmonicity, but mainly inasmuch as the amplitude of the partial is
concerned and the part of the tone which is listened to. Up to now I
have not considered the latter part of tones, but made estimates as to
what the highest pitch at the start of the tone was and made that my
reading. This explains why I always felt that voicing affected the pitch
or inharmonicity. Well it does, but mostly as a function of amplitude of
the particular partial.
Jim Coleman, Sr.
PS It was hoped that the listening ear with its 2 decimal readings and
averaging capability would give us more definitive readings, however, it
was discovered that the SAT readings were more dependable. The RCT
readings taken by the spinner of the CyberEar were comparable to the SAT,
but were slower to arrive at, hence the use of the SAT in the later tests.
JWC
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