source file: m1514.txt Date: Tue, 25 Aug 1998 09:40:24 -0500 (CDT) Subject: Re: geometrical mean From: Paul Hahn 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 http://library.wustl.edu/~manynote O /\ "Churchill? Can he run a hundred balls?" -\-\-- o NOTE: dehyphenate node to remove spamblock. <*>