612edo

The 612 equal division divides the octave into 612 equal parts of 1.961 cents each, 1/12 of a Pythagorean comma or 1/11 of a syntonic comma. It is a very strong 5-limit system, a fact noted by Bosanquet and Barbour. It tempers out the sasktel comma, |485 -306>, in the 3-limit and in the 5-limit |-52 -17 34>, the septendecima, |1 -27 18>, the ennealimma, |-53 10 16>, the kwazy comma, |54 -37 2>, the monzisma, |-107 47 14>, the fortune comma, and |161 -84 -12>, the atom. In the 7-limit it tempers out 2401/2400 and 4375/4374, so that it supports ennealimmal temperament, and in fact provides the optimal patent val for ennealimmal. The 7-limit val for 612 can be characterized as the ennealimmal commas plus the kwasy comma. In the 11-limit, it tempers out 3025/3024 and 9801/9800, so that 612 supports hemiennealimmal temperament.

The 612 division has been proposed as the logarithmic interval size measure Skisma (or sk), since one step is nearly the same size as the schisma (32805/32768). Since 612 is divisible by 2, 3, 4, 6, 9, 12, 17, 18, 34, 36, 51, 68, 102, 153, 204 and 306, it can readily express the step sizes of the 12, 17, 34, 68 and 72 divisions. A table of intervals approximated by 612 can be found under Table of 612edo intervals.