source file: m1514.txt Date: Tue, 25 Aug 1998 07:31:55 -0500 Subject: Re: geometrical mean From: Gary Morrison > if X , Y are two tone frequencies, > how to tune the value Z=sqrt(X*Y) acousticaly I'm not completely certain what in particular you mean by "acoustically" in this particular case, but I suppose it's worth pointing out that, to our logarithmic tuning perception, a geometric mean sounds like an arithmetic mean. So, if by "acoustically" you mean "by ear", you can tune that intermediate pitch so that the melodic interval size from the 1:1 to the pitch in question sounds the same as the interval from the pitch in question to the 5:4.