Monzo's and Canright's diagrams

>In my design, which is similar to the
>rectangular form above, lengths are proportional
>to the prime's place in the prime series, and
>angles are representative of circular "octave"
>pitch deployment for each interval.

On Monzo's diagram, only the tones whose interval with 1/1 has a prime
number in the numerator and a power of two in the denominator have
angles representative of circular "octave" pitch. All other intervals,
including composites with a power of two in the denominator, will not
have the correct angle. Therefore, Monzo's diagrams have no real
advantage over standard rectangular lattices or any other projection
thereof. However, I feel strongly about the advantage of triangular over
rectangular lattices, and one could certainly use Monzo's angles in
constructing a triangular lattice (but why would one?).

One way of determining what angles to use that makes more sense that
Monzo's proposal is Canright's (in his web article Harmonic-Melodic
Diagrams or something -- John Starrett's page is down right now so I
can't tell you the address). Although Canright uses a rectangular-type
lattice, aditional connections can easily be drawn to make it into a
triangular lattice. Canright derives the lengths and angles to use in
his lattice so that the position of the tones along a certain direction
will correspond to the pitch of the tones. This works for all the tones,
not just the ones at certain special intervals from 1/1, while Monzo's
circular pitch is only correct for a few tones. So, given Monzo's
willingness to have arbitrary angles in his diagram, and desire to
depict pitch relationships, he would be better served by Canright's
approach.