In a message dated 6/13/98 10:47:09 AM Central Daylight Time, pianotoo@IMAP2.ASU.EDU writes: << Thanks for triggering me on this subject. I haven't written about this since I wrote about it to Virgil Smith several years ago. this incidentally forms some of the basis for his theory about listening to the fundamentals only when tuning, or more correctly, listening to the whole tone. Jim Coleman, Sr. >> Thank you for these remarks. However, I don't think we are talking about the same thing. In order to hear beats, you have to hear them between coincident partials which are mismatched. If you had 2 pure tones (with no harmonics/partials) and one was slightly sharper than the other, you would hear a beat between them. However, if one were at a pitch which would form a tempered 3rd, 4th or 5th or a stretched octave, I don't think you could hear a beat in that case. Am I right or wrong about that? The example I think of is how you can clearly hear a beat in a tempered Octave and 5th (12th). The 3rd partial of the lower note is coincident with the fundamental of the upper one. You cannot however hear a beat in an octave and a 4th because there are no coincident partials. You could mistune the upper note flat or sharp all you want and there will be no beat. Bill Bremmer RPT Madison, Wisconsin
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