Making P12ths Acoustically

[Bill Ballard]

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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