Hey, Aural Gurus ...

[Bernhard Stopper]

Hi William, Ric, Alan,

The main thing behind the pure 12 tuning is to take the pythagorean comma 
from the fifths/twelfths side to the octaves side. To divide a pure twelfth 
into 19 steps and to try to have an octave pure, (no matter in what partial 
pair) is the quadrature of a circle. Thus, for me in the pure twelfth tuning 
the octave must not be pure at no partial pair at all.(but so what if it 
falls sometimes on some pair) . To choose any partial pair coincident is 
highly arbitraily and does not ensure that the sum of the beats are minimal. 
On inharmonicity related instruments pure means for me that the sum of the 
beats are minimal. Octave is an octave and in pure twelfth tuning there are 
hevy reasons, why it should not be pure in no way. See my post about the 
OnlyPure tuning method why not.

regards,

Bernhard

----- Original Message ----- 
From: "William Ballard"
To: "Pianotech"
Sent: Friday, April 08, 2005 6:35 AM
Subject: RE: Hey, Aural Gurus ...


> At 10:39 PM -0500 4/5/05, Alan wrote:
>>I'm still curious about the P12th D3-A4 bit, though. Is the logic correct 
>>or
>>would different pianos require a, shall we say, less-than-perfect 12th?
>
> Just kind of poking my head through the window here and admittedly not 
> reading all of the posts in this thread, but.....
>
> Are you asking for an aural temperament in which the octaves have been 
> stretched sufficiently that 12ths occurring within the temperament compass 
> (yes a two-octave compass) will be pure. That's how Ric and the 
> other-'cross-the-ponder-er were laying out octaves in general, Ric using 
> an ETD and t'other stating that the mathematical principle was there. That 
> was back in September.