meantone

[Joe & Penny Goss]

MEAN= adj. occupying a middle position ( as in space, order, or time )
Joe Goss

----- Original Message -----
From: Richard Moody <remoody@midstatesd.net>
To: piano tech <pianotech@ptg.org>
Sent: Wednesday, June 21, 2000 11:44 PM
Subject: Re: meantone


>
>
> > 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
>
>
>
>