source file: m1606.txt
Date: Fri, 11 Dec 1998 15:52:04 -0500

Subject: RE: Hypertones, counterset & other weird microanimals (fwd)

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

I forgot to point out that Medieval Western practice ("Gothic?") also
fails the three-chord-covering property. The consonant chords were
3-limit dyads, but three of those would cover at most 6 notes, while the
diatonic scale has 7. The diatonic scale with 3-limit harmony is another
system which I wanted to leave out of my paper for brevity, but clearly
cannot be dismissed altogether, as it was a language in which great
musical works were produced for a few centuries.