source file: m1373.txt
Date: Fri, 3 Apr 1998 08:53:21 -0600 (CST)

Subject: Re: comma/error

From: mr88cet@texas.net (Gary Morrison)

>As most theorists have done, he called this comma an "error"
>(I've also seen it called an "anomaly"). However, I don't think "error"
>is an appropriate name for this occurance, since it is a natural feature
>of the spiral of 5ths...

   I can see Neil's concern here.

   Calling a comma an "error" is, more or less, using the mathematical
usage of the word, which doesn't suggest anything like a mistake.

   The entire point of a comma is that there is a conceptual framework -
often 12-tone-per-octave scales - wherein we'd like two different pitches
to have turned out the same, but they didn't.  For example in the case of
the pythagorean comma, the 12-toned conceptual framework suggest that a
stack of 12 3:2 should be the same as 7 2:1s.  And indeed they fail to
coincide because they DO obey the laws of nature (or mathematics at least),
and NOT our simplified conceptualizations.

   So perhaps the concern here boils down to me, and others, failing to
make clear which of the two is "in error".  To the degree that this usage
of "error" can be thought of as a mistake or inadequacy or such, the
12-toned conceputal framework is what's inadequate, not the meaningfulness
of 3:2 or 2:1.