source file: m1580.txt
Date: Thu, 12 Nov 1998 15:02:12 -0600 (CST)

Subject: Re: Harmonic waste

From: Paul Hahn <Paul-Hahn@library.wustl.edu>

On Thu, 12 Nov 1998, Paul H. Erlich wrote:
>> the definition of
>> harmonic waste [is] any thirds narrower or fifths wider than just.
> 
> Presumably, this means major thirds, but shouldn't the criterion be
> minor thirds? Is 2/7-comma meantone harmonically wasteful? I think the
> criterion about thirds should be changed to "any minor thirds wider than
> just."

Well, it's defined the way it is because if you add up the total amount
of tempering in all of the fifths, major thirds, and minor thirds (i.e.
the consonant intervals) in any temperament, that total will be constant
as long as no harmonic waste exists.  If we change the definition to
Paul E.'s proposed one this is no longer true.

--pH <manynote@lib-rary.wustl.edu> http://library.wustl.edu/~manynote
    O
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