612edo: Difference between revisions

== Theory ==

612edo is a very strong [[5-limit]] system, a fact noted by [[Bosanquet]] and [[Barbour]]. It tempers out the sasktel comma, {{monzo| 485 -306 }}, in the 3-limit, and in the 5-limit {{monzo| -52 -17 34 }}, the [[septendecima]], {{monzo| 1 -27 18 }}, the [[ennealimma]], {{monzo| -53 10 16 }}, the kwazy comma, {{monzo| 54 -37 2 }}, the [[monzisma]], {{monzo| -107 47 14 }}, the fortune comma, and {{monzo| 161 -84 -12 }}, the [[atom]]. In the 7-limit it tempers out [[2401/2400]] and [[4375/4374]], so that it [[support]]s the [[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 kwazy comma. In the 11-limit, it tempers out [[3025/3024]] and [[9801/9800]], so that 612 supports the [[hemiennealimmal]] temperament. In the 13-limit, it tempers [[2200/2197]] and [[4096/4095]].

=== Prime harmonics ===

{{Harmonics in equal|612}}

== Regular temperament properties ==

| 4.68

|}