Basic Principle of Temperament

I believe I said (correctly) in an earlier post that the three pairs of
consonances vary independently under temperament. In fact, to be more
precise, this is true for equal temperaments only; in unequal
temperaments of value one can arrange for (at most) two of the three
pairs to vary together, but never all three. In the 1/3 mesotonic for
example, the fifth and major third are diminished by 1/3 comma, while
the minor third is held just. In the 1/4 comma mesotonic the fifth and
minor third are diminished by 1/4 comma, while the major third is held
just. In unequal temperaments indeed one could arrange for the
consonances to vary together (except for the 'wolves') but the result
would be execrable octaves.

All this is a commonplace for the cognoscenti. I set it down here as a
help to those whose musical education ? in other respects perhaps quite
excellent ? has not much prepared them for tuning questions.


SMTPOriginator: tuning@eartha.mills.edu
From: Gregg Gibson
Subject: 19-tone Equal Tetrachords
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