Definitions

The responses to my �Historical Questions� indicate that, not
surprisingly, terms referring to tuning are defined in different ways by
different people. I would like to check that my usage and understanding
of them is not outside generally accepted bounds. Here they are, and I
would appreciate any comments and criticisms you may have:
1. Tempering initially referred to how one deviated about the system of
Pythagorean tuning (ascending|descending fifths|fourths with frequency
ratios of 3/2|4/3) in order to temper sour and howling intervals.
Nowadays, however, temperament and tuning seem to be synonymous.
2. The circle of fifths seems to have generally been started on middle
C. This at least is what is suggested by both von Helmholtz�s book and
the piano keyboard�s layout.
3. Mean Temperament has two general meanings. First it means a system of
tuning by fifths such that four ascending fifths and two descending
octaves make up a perfect third. It also means any one of many slight
variations about this basic system.
4. Bach�s WTC refers to a mean tempered clavichord; in particular,
well-tempered means mean tempered. Since the WTC starts in the key of C,
it seems that Bach�s thought of mean tempered in terms of ascending
fifths started on C.
Ed Remler

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