[CAUT] The Origins of P12ths tuning.

[Richard Brekne]

Hi Again Fred
You hit I think the thing on its proverbial nose rather exactly. The 
wide stretch in the initial temperament is needed and again governed by 
the fact that you impose as a starting precept a perfect 12th as that 
spread... I use D3-A4. In the treble the stretch starts to develop a bit 
steeper then traditional octave priority approaches... but the top 
octave ends up quite moderately stretched.  I rarely see C8 over 36 
cents... depends on the pianos built in inharmonicity.

Any you are correct in that an absolute imposition of the P-12ths scheme 
ends up being  unworkable as well.... tho we end up talking about  very 
small fudge factors, nearly negligible in most cases.

One can easily enough measure all the resulting partials from any tuning 
scheme with modern ETD's... but it is a bit time consuming.

One other point... para - inharmonicity. No matter what you do one is 
always forced to fudge big time when para shows its ugly face. The bane 
of ETD tuning really. If one simply follows the dial one can easily get 
into trouble when notes that simply have wild partial ladders.

Cheers
RicB


    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.

    Fred