source file: m1364.txt
Date: Tue, 24 Mar 1998 15:46:41 -0500

Subject: RE: Well temperaments, just diminished

From: "Paul H. Erlich" <PErlich@Acadian-Asset.com>

>}On another subject, some of the music I play contains "diminished 7th"
>}chords (stacked minor thirds).  Is this chord a modern invention?  It seems
>}to me that such a thing is impossible in anything but equal temperament.
>
>Please note that Just Intonation is really a "modern invention" as well. The
>only tunings that had real significance in the West since the earliest
>notated music have been Pythagorean, Meantone, and varieties of
>Well-Temperament including Equal Temperament.
>
>}I'm having a hard time getting acceptable diminished chords out of my E9
>}pedal steel using the standard JI tuned pedals.  I know I could tune a pedal
>}specifically for these chords, but that's really an awkward solution.
>}Comments?
>
>Well, in meantone tuning, the diminished seventh chord sounds pretty good,
>since the intervals are very close to 6/5, 6/5, 6/5, 7/6. But equal
>temperament may maximize the consonance of the chords, since all intervals
>are then kinda close to 6/5, which is more consonant that 7/6, even when the
>former is a little out-of-tune and the latter is tuned justly.