On Apr 21, 2010, at 8:19 PM, Ed Sutton wrote: > 1) Does Ellis note whether he is measuring single strings or > unisons? If unisons, the slipped note argument is impossible to > support. Unfortunately, he is silent on that detail - or at least I haven't happened across a description that is sufficiently detailed. One would assume he might average the two or three strings if the unison were imperfect, but one can only speculate. Some details he does give: He measured notes from C3 to C4, and his commentary seems to say that pitches higher than that would be too difficult by his method (he does note that the tuners all did F3 to F4 temperaments, by alternating 5ths up and 4ths down). He relied on listening to beats over long periods of time, 40 seconds being the norm both when he was actually tuning the forks, and for taking measurements of pitches. He would measure (count number of beats) against the fork just lower in pitch, then against the one just higher. And then check himself by calculating that the number of beats of both put together was the same as the number the two forks would produce against one another (at 4 Hz apart, that would be 160 beats in 40 seconds). He seems to have been pretty careful about temperature. > > 2) Ellis knew nothing of inharmonicity, and was measuring > fundamentals. We know now that the "sound of equal temperament" is > produced by the inharmonic coincident partials. Without some > knowledge of the scales of the pianos he measured, how much can be > deduced from the data? > Yes, one wonders if his own piano, for instance, was a square, as would be likely. And where was the break? within the octave measured? He was measuring fundamentals, I suppose, but the second partials can enter into what you hear (with a fork), and that beat can confuse the ear. There are many practical questions that would need to be investigated to determine just how precise his method could have been. I don't think I'll be the one to do it though <G>. Regards, Fred Sturm University of New Mexico fssturm at unm.edu -------------- next part -------------- An HTML attachment was scrubbed... URL: <http://ptg.org/pipermail/caut.php/attachments/20100421/2c132357/attachment.htm>
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