720edo
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
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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.
In just intonation, 720edo patent val is good at the 2.3.17.23.31.43 subgroup, in which it supports the 195 & 720 temperament, period 15.
Using the 720bbcccdde val, [720 1140 1670 2020 2490⟩ in the 13-limit makes use of 72edo with 13/8 from 10edo. Mixing this with the 72edo replica provides temperaments like infraorwell, mintone, secant.