source file: m1602.txt Date: Fri, 4 Dec 1998 15:57:38 -0500 Subject: Monzo's and Canright's diagrams From: "Paul H. Erlich" >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.