720edo

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720edo divides the octave into steps of 1.666 cents each.

720edo is the 14th superabundant EDO, and also the 6th factorial EDO (720 = 1*2*3*4*5*6 = 6!), which means it contains a massive amount of sub-EDOs, limited modes of transposition, and fraction-octave MOSses.

Theory

Approximation of prime intervals in 720 EDO
Prime number 2 3 5 7 11 13 17 19 23 29 31 37 41 43
Error absolute (¢) +0.000 -0.288 +0.353 -0.493 +0.349 -0.528 +0.045 +0.820 +0.059 +0.423 -0.036 +0.323 -0.729 +0.149
relative (%) +0 -17 +21 -30 +21 -32 +3 +49 +4 +25 -2 +19 -44 +9
Steps (reduced) 720 (0) 1141 (421) 1672 (232) 2021 (581) 2491 (331) 2664 (504) 2943 (63) 3059 (179) 3257 (377) 3498 (618) 3567 (687) 3751 (151) 3857 (257) 3907 (307)

As with most composite EDOs, it's better to use various vals mimicking smaller EDOs instead of the patent val, because it sounds as if the patent val is creating commas, not tempering them out. Nonetheless, 720edo patent val is good at the 2.3.17.23.31.43 subgroup.

Using the 720bbcccdde val, [720 1140 1670 2020 2490⟩ 720edo is effectively a replica of 72edo and therefore is contorted order 10. Some of the harmonics that still stay patent are 13/8 from 10edo. Mixing this with the 72edo replica provides temperaments like infraorwell, mintone, secant.