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

[Fred Sturm]

On Oct 14, 2008, at 12:19 PM, Porritt, David wrote:

> 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
>
> David M. Porritt, RPT
> dporritt at smu.edu

Thanks, Dave! Considerably closer than I thought. Multiplied out over  
the full range of a piano, these differences matter, but not as much  
as inharmonicity produces. It's interesting to remember that stacking  
12 "just, theoretical" 5ths, from A0 to A7, produces a theoretical  
excess of 24 cents over a "just, theoretical" seven octaves. Quite a  
bit less than standard tuning "stretch" of even the most conservative  
among us.

Regards,
Fred Sturm
University of New Mexico
fssturm at unm.edu

PS to Ric: re-read what Dave wrote. He's coming up with an increase of  
2 ( to 2.0012) where the 12th root is quite close to the 19th root of  
3. Obviously one can carry this process out as many decimal places as  
one wants, and one will come to practical convergence at some point.
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