---------------------- multipart/alternative attachment Michael G sez: > Yes, I agree. There is no likelihood of the exact science of sound and its > harmonics being produced text-book fashion in the piano. The principle > applies though - and I doubt it's far removed from the "text book" version. What > say you? Depends upon what you call far removed, but it's precisely that difference that is important to piano tuners. You're right that the principle of coincident partials explains where beats come from, but it's the _departure_ from the principle which explains the compromises necessitated by inharmonic mismatches, and that is so vital to refined tuning. It's still in the textbook; it's just on a different page. The other day I mentioned some phony figures to help illustrate this point. You have a Steinway A, so here are some real measurements, from the temperament area of a Steinway A. If A4 is tuned to 440 Hz., its 2nd partial vibrates at 880.92 its 4th partial is 1766.4 instead of 1760 (and its 8th partial is 3609.36, instead of 3520) If A3 is tuned to 220 Hz., its 2nd partial vibrates @ 440.48 instead of 440 its 4th partial is 882.6, instead of 880 its 8th partial is 1774.8, instead of 1760 This creates significant beating, even though the fundamental of the upper note is twice that of the lower. You can see that at the 4:2 level, you've got 880.92 versus 882.6, (over a beat and a half per second). At the 8:4, it's even worse. If A3 is then retuned so that its 2nd partial is also 440, its fundamental will be at 219.76, but the other coincident partials will come a little closer to matching. Fortunately, we do some of this automatically by ear, but it's still important to know when to go for smooth and when we are likely to have to squeeze it a little to get better results elsewhere in the piano. Bob Davis Stockton, California ---------------------- multipart/alternative attachment An HTML attachment was scrubbed... URL: https://www.moypiano.com/ptg/pianotech.php/attachments/3f/45/e1/bb/attachment.htm ---------------------- multipart/alternative attachment--
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