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
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