source file: m1606.txt
Date: Fri, 11 Dec 1998 15:37:02 -0500

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

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

Stephen brings up two important properties of the diatonic scale that
are not shared by my scale (a set of 10 in 22-tET). One is motivated
(perhaps) my a property I demand in my paper, that the scale be
completely covererable by three consonant chords. Stephen aptly points
out that in the diatonic case, this is often done using the I, IV, and V
chords. Another important example is I, II, and V; also I, IV, and VII
is often found in dorian or mixolydian rock music. All of these are
examples of three consecutive chords in a chain of fifths. Many rock
tunes, however, are based on three consecutive chords in the scale, such
as VI, VII, I in minor. So I don't view it as a great disadvantage that
my scale isn't covered by the tonic, subdominant, and dominant chords.
In fact, I recently stated on the List (with regard to my contest to
find another diatonic-like scale) that the property of coverability by
three consonant chords was not very important to me. In fact, I only
included it in my paper as a way of ruling out overly "complicated"
scales, such as 14 out of 26-tET, which I would otherwise have to
consider. I am now very happy to consider it, even though the (lack of)
clarity with which 4 or 5 chords might project a set of 14 notes clearly
presents a formidable compositional challenge.

Another property is that in the diatonic scale, any two triads can be
linked using only common tones and single-step-motion voice leading
(this was pointed out by Agmon). This is not true for the tetrads in the
decatonic scale. However, common practice music does not always progress
in this simple way -- passing tones and leaps are quite common, and
without them, one would have very little freedom in realizing a chord
progression or harmonizing a melody. So again, my scale posesses no
great disadvantage -- certain chord progressions will necessitate
passing tones or leaps. Decatonic melody will therefore be more active
than diatonic melody, in line with the greater number of tones that need
to be kept fresh in the mind of the listener.

As for "hypertones", I'm sure some very interesting music could be made
using this principle, particularly if each hypertone is associated with
a particluar timbre. But I would still want to make sure that the
ordinary "tones" making up the hypertones were forming good melodies, or
at least not forming awkward ones, since we are in some sense wired up
for speech recognition, and the human voice can only produce tones (i.e.
a fundamental and its harmonics, plus noise), not hypertones.