source file: mills2.txt
Date: Thu, 12 Jun 1997 11:05:00 +0200

Subject: Re: where do the 5ths go?

From: mr88cet@texas.net (Gary Morrison)

>Those 5ths that we mathematically alter...we
>are not HEARING them in their proper place in the Universe. They are
>actually sounding at some frequency well beyond our hearing. So, just
>where are they, then?

   You should not be distracted by the fact that these systems are
generally described relative to an original tonic, and the fact that the
notes you create in a stack of fifths would become ultrasonic quickly.  The
point of using circles (spirals, whatever) of fifths to construct a tuning
is one of several means of lending consistency to a tuning system,
especially consistency across many keys.  The point that matters is that a
tuning like meantone that is based upon a stack of fifths will always have
a consistent-sized fifth, which makes where you start unimportant.

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