[CAUT] P-12ths was: Tuning a Steinway D and a Bosendorfer Imperial together

[Porritt, David]

Richard:

The difference between the 12th root of 2 and the 19th root of 3 is
6.297037897993807971388553887547e-5 or
0.00006297037897993807971388553887547.  I can't tune that precisely but
maybe you can.  :-)

dp


David M. Porritt, RPT
dporritt at smu.edu


-----Original Message-----
From: caut-bounces at ptg.org [mailto:caut-bounces at ptg.org] On Behalf Of
Richard Brekne
Sent: Monday, October 13, 2008 4:35 PM
To: caut at ptg.org
Subject: [CAUT] P-12ths was: Tuning a Steinway D and a Bosendorfer
Imperial together

Hi Kent

    I don't understand why anyone would assume that the mathematical
    model for 19 tone to the P12 equal temperament would be followed any
    more closely in practice than that of the 12 tone to the octave
    equal temperament.

I dont think I am assuming anything. Its just a fact that if you take 
the 19th root of 3 and split up the 19 tones of the  12th and compare it

to what you get if you split an octave in that same range up into 12 
equal parts using the 12th root of 2 then you will get slightly 
different frequencies for the 12 notes in the octave. Indeed... if there

was to be given any credence at all to the idea that a P-12th tuning 
could sound any better (read different) then some difference would have 
to be present.


    When we tune 12 tone to the octave ET we modify the tuning for
    aesthetic reasons and to deal with the change in inharmonicity
    across the scale and to
    tune the treble as sharp as we like to hear.

    Same thing with the P12th ET.

No arguement there... except one is using different tuning priorities...

which of course yield somewhat different effects. There is no magic to 
Stoppers programs.  He just bases his tuning on assuring   P12ths...... 
which I dont believe is exactly and strictly speaking an ET tuning..... 
but thats another matter.

Cheers
RicB