meantone

[Richard Moody]

> Alas....This sort of extension of terminology misses the point about
> meantone. Just as there is only a single temperament that can truly be
> called "equal" there is only a single temperament that should be called
> meantone - i.e. 1/4 comma meantone. The name comes from the placement of
> D in the mean position between C and E i.e. both tone CD and DE are
> identically size intervals.
> Stephen

Perhaps it should be capitalized.  Actually the D just happens to be
the meantone, or the mean of the ratio of the pure third which is the
distinguishing characteristic of 1/4 comma MT.  When "meantone" started to
be used would be interesting to know.  Mersenne (1638) doesn't use the term.
(unless I missed it).
    Why it is called meantone is not really clear.  There are several
tunings and temperaments where D is the the meantone of  the 3rd C--E.   ET
for one, and Pythagorean for another.  Of course these thirds are not the
5/4 or pure third in MT.
     In fact whenever E is formed by four successive equal 5ths from C,   D
automatically is the mean between C and E. This means the ratios of C--D,
and D--E are equal.  The simplest example is Pythagorean where C--D  = 9/8
and D--E = 9/8.     When these two ratios are multiplied 81/64 results which
is the ratio of a Pythagorean 3rd, often called the ditone.   Now don't ask
me why the 'ditonic comma' is the excess of twelve pure 5ths over the
octave, and not the difference of the ditone (formed by four pure 5ths )
over the pure third.  ---ric