The acoustic version of P12ths is a little simpler than the electronic. To tune, say, A4 a P121 from D3, start off by playing that P12th using the L string of A4. Listen to the beat rate on that P12th, occurring as RicB points out, between the 3d partial of D3 and the 1st partial of A4. Reproduce that beat rate by mis-tuning the center string of A4 (up or down, as needed) against the L string. Now bring that L string into unison with the center string. Check again for drift, and correct again by shimming the unison. Want to preview how the amount by which A4 as determined by this P12th, may be stretched sharp of the octaves it is normally referenced to? (That is the 2:1 single octave with A3, and the double, 4:1 octave with A2.) Play the chord formed by A2/D3/A3. When A4 is a P12th from D3, the double octave beat rate between A4 and A2 will be equal to the 4ths beat rate between A2 and D3. The single (2:1) octave will likewise have a beat rate equivalent to the 3:2 5ths beat rate between D3 and A3. Also if the 6:4 beat rate in that same 5th is something other than a reasonable approximation of double the 3:2's beat rate, this is a clear indication of poor scaling. When this P12ths pattern is carried up an octave, say in the example, A5, there will be disagreements between A5's triple octave and it's double octave. Be ready with the fudge brush. Yep, I like P12ths. I've been tuning the top half of the piano that way for years. Or at least as high up as I can hear the 3rd partial in the lower, reference note, which is usually most of the way through the 5th octave. After that, the tuned note is at the bottom of the 7th and from there on up it's 2:1s. Bill Ballard RPT NH Chapter, P.T.G. "I go, two plus like, three is pretty much totally five. Whatever" ...........The new math +++++++++++++++++++++
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