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

[Richard Brekne]

David... Google has it different.

The 12th root of 2 is 1.05946309
The 19th root of 3 is 1.05952606

Which I think you will find are the correct figures.  If you take even a 
low number like  220hz and multiply that out over an octave range by 
each value... you'll end up with a 3rd of a bps difference at 440.  Add 
in all the intervals we need to take consideration to its clear that 
imposing a P 12th system will yield a significantly different, that is 
to say discernible to the ear should one take the time to notice, 
result.  That said... given the famous temperament tests of a decade or 
more ago... I'll go along ways down any road with you that implies it 
doesnt make all that much difference.  At least not to most people and 
not all that consciously to most of those who on some level or another 
do "notice"

Fred... excellent post... I have to read it a couple times on the morrow 
and reply.   But off hand I'd agree that we are very much more on the 
same page then not. Tho to be sure, and as is my wont, I differ here and 
there :)  Late here... I'm 56 today... and off to bed

Cheers !
RicB


    Fred:

    The 12th root of 2.0012 is the equivalent of the 19th root of 3 to 4
    decimal places (1.059516053 rather than 1.059526065).

    dp