Harmonic waste

>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."

On Thu, 12 Nov 1998, Paul H. Erlich wrote:
> I realize that with 12 notes, 2/7-comma meantone would lead to a wolf
> fifth larger than just but I was thinking either an infinite number of
> notes or, perhaps, 19 notes, where the wolf fifth would be 675.4 cents.

Oh. I think the term has generally been used in the context of 12-tone
circulating temperaments.

--pH http://library.wustl.edu/~manynote
O
/\ "Do you like to gamble, Eddie?
-\-\-- o Gamble money on pool games?"

NOTE: dehyphenate node to remove spamblock. <*>

On Thu, 12 Nov 1998, Paul Hahn wrote:
> On Thu, 12 Nov 1998, Paul H. Erlich wrote:
>> I realize that with 12 notes, 2/7-comma meantone would lead to a wolf
>> fifth larger than just but I was thinking either an infinite number of
>> notes or, perhaps, 19 notes, where the wolf fifth would be 675.4 cents.
>
> Oh. I think the term has generally been used in the context of 12-tone
> circulating temperaments.

You could certainly generalize it, to other closed temperaments at
least, but the criteria would vary from temperament to temperament. For
19TET the analogous criteria would be no minor thirds narrower than
just, or major thirds wider than just.

For an open (meantone) temperament, hmm. You can't total an infinite
number of intervals--but if you assume that the temperament is uniform
and extends infinitely in both directions, you can just sum the errors
of a single fifth, major third, and minor third to get a sort of
"instantaneous" or "average" value. The result would be that any
deviation from 1/4-comma meantone causes harmonic waste.

--pH http://library.wustl.edu/~manynote
O
/\ "Do you like to gamble, Eddie?
-\-\-- o Gamble money on pool games?"

NOTE: dehyphenate node to remove spamblock. <*>