Hi Richard: As I wrote on this list about a week or two ago, what you are proposing has already been done. The major problem is with the usefulness of it. We don't know what the beats should be until we have tuned a bit of the piano anyway. A better answer to what you are looking for can be found using any of the very accurate Electronic Tuning Devices which measure sounds to .1 cent. On can quickly select the coincident partials of a beating interval and with a computer program, compute the Hz difference from the Cents readings. I have done this many times and I wrote a conversion program in Qbasic which is a free program that comes with Windows 95 and I think 98. The program takes about 12 lines of code. The procedure is to first input the note no. where the partials meet, then, read and input the cents deviation of the upper note partial, then read and input the cents deviation of the lower note partial. The result is the beat rate between the two partial with accuracy to 3 decimals. The problem with all this is that it does not show you what the beat rate should be, it only shows you what it is. The newer ETDs can do a better job of locating each note with their smooth curving methods along with the control of the stretching of the octaves. Any tuning method which involves measuring individual beat rates leaves the possibility of accumulated errors. Our manual skills are not accurate enough to handle this problem even if we are using ETDs to guide us. The intelligent smooth curving methods of tuning are more accurate and they are here and now, not pie in the sky. Smooth curve methods of the ETDs do not permit accumulated errors. Our manual techniques limit us in our ability to tune within .1 cent accuracy, but at least we know where the curve is supposed to be. Jim Coleman, Sr. On Sun, 2 May 1999, Richard Brekne wrote:
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