pretty picture

If you want to see something pretty, go to
http://www.egroups.com/files/tuning/perlich/triads36.jpg.

It's a triangular (like Chalmers' tetrachordal graphs) plot of triads with
integer limit 36. There are six identical sextants, each one the mirror
image of the two next to it (as in a kaleidoscope with the mirrors at 60°).
Each sextant contains a large equilateral triangle, which represents the
triads within one octave (like Chalmers' graph represents the triads within
a fourth). The sextants represent every possible sign assignment to the
three intervals in the chord so that they sum to zero. In other words, there
are six sextants because any chord can be expressed in six ways:

x:y:z
y:x:z
z:x:y
x:z:y
y:z:x
z:y:x

The point in the center is 1:1:1, and the six lines emanating from the
center consist of triads of the form

a:a:b
a:b:b
a:b:a
b:b:a
b:a:a
b:a:b

In three of the sextants, I've marked the three inversions of the JI major
triad in red, and of the JI minor triad in blue. You can see that the major
triads have a lot more "room" around them than the minor triads.

The points get sparser as one moves away from the center because I'm using a
maximum limit (36) rather than a product (i.e. geometric mean) limit.

Further discussion should take place at harmonic_entropy@egroups.com.