[CAUT] The Origins of P12ths tuning.

[Fred Sturm]

On Oct 21, 2008, at 4:32 PM, Richard Brekne wrote:

>  I think, stumbled onto another interesting coincident. The 6:3:1.   
> Immediately upon looking at that ratio one sees implied a 6:3 octave  
> that matches both a perfect 19th and a perfect 12th.

	Yes, absolutely.
	When I tuned aurally, I would use the m3 (down), M6, M10, M17 to  
check the 6:3 octave and the 3:1 12th and 6:1 19th above. (To add 8:1  
(and 8:4) to that mix requires the m6 down as well, but I could rarely  
hear it distinctly enough to find it all that useful). Essentially you  
are zeroing in on the upper note, making the corresponding partials of  
those lower notes coincide up there to the extent possible (making  
what compromises seem necessary in the individual circumstance). With  
ETD, it is that much simpler: set the ETD to the top note and play the  
notes an octave, 12th, double octave, and 19th (and triple octave)  
below and see what the display says. You have to start with a fairly  
wide stretch in the initial temperament to have this be successful. I  
suspect a 3:1 would fit the bill quite well (I never looked at it in  
those terms).
	My notion is that this style of tuning would amplify and enhance the  
upper notes, at the same time as it creates a cohesive sound. I always  
wanted to test it to see if it actually worked in a scientifically  
measurable way (under controlled conditions), but the logistics are  
too hard to come by (the right measuring equipment and the means to  
duplicate the blow perfectly, plus a way of timing the damper pedal  
precisely to the keystroke, in various alignments of time - and  
keeping the setup perfectly in place while re-tuning to test again  
with a different approach). This remains my basic "inner picture" that  
I base my personal tuning philosophy on. I like the results, but I  
make no claims.
	
Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu