source file: m1588.txt
Date: Fri, 20 Nov 1998 21:42:44 -0800

Subject: diatonicity in a nutshell

From: Carl Lumma <clumma@nni.com>

[Erlich]
>a given consonant interval is always approximated by the same number of
scale >steps. 

[me]
I think agree...

Okay.  I have thought it over.  I still agree that this may be responsible
for an important effect, but it is not the rule I'd give if I had to give
only one rule telling where the goodness of diatonicity comes from.

That rule is almost the reverse: that a given number of scale steps be able
to represent different consonances.

For example, 12tET, used like a diatonic scale, gives a complete tetrad on
every scale degree.  It is strictly proper, maximally even, and a MOS
between the two most fundamental intervals known.  And it is a very
resourceful scale!  But it lacks the ability to produce different harmonies
using the same number of scale degrees.  And this is the thing that gives
(7 tone) diatonic music much of its punch.  Changes to the relative minor
and so forth.

Carl