Bram's Diamond

Bram wrote,

>You're probably right about a higher-limit diamond being preferable. If
>I'm not mistaken, the 11-limit diamond only has 20 notes in it and the
>13-limit one only has 30, so using them might be pretty reasonable.

The 11-limit tonality diamond has 29 notes per octave, and the 13-limit
diamond has 41. Partchian tonality diamonds consist of all the ratios
where the numerator and denominator have no odd factors higher than the
limit. The 3-limit t.d. has 3 notes; the 5-limit t.d. has 7 notes;
7-limit, 13 notes; and 9-limit, 19 notes.