source file: m1514.txt
Date: Tue, 25 Aug 1998 09:40:24 -0500 (CDT)

Subject: Re: geometrical mean

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Mon, 24 Aug 1998, Jan Haluska wrote:
> if  X , Y  are two tone frequencies, 
> how to tune the  value  Z=sqrt(X*Y)  acousticaly
> ( sqrt(X*Y)  denotes the geometrical mean of the tones  X  and  Y )? 
> Demonstrate the method on   X = 1,   Y =   5/4 .

In the general case, this is a Hard Problem.  Which is why widespread
experimentation with random ETs has had to wait until the computer
revolution.

In the specific case requested, that of determining the mean tone (used
in 1/4-comma meantone tuning), there are various methods.  If I were
tuning my virginal or something, I would probably do something like
this: tune up a (just) 3/2 and a 6/5 to get 9/5 above; tune down a 3/2
and then up a 4/3 (again just) to get 8/9 below, then tune the target
string (halfway between 10/9 and 9/8, we hope) to beat at the same rate
with each of those.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
   /\        "Churchill? Can he run a hundred balls?"
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