2.3.5.13 subgroup: Difference between revisions
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=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
[[Cata]] provides a fairly low complexity approximation to the subgroup, using ~6/5 as a generator, finding ~5/4 at + | [[Cata]] provides a fairly low complexity approximation to the subgroup, using ~6/5 as a generator, finding ~5/4 at +5 gens, ~3/2 at +6 gens, and ~13/8 at +14 gens. | ||
[[Pythagorean tuning]] also works surprisingly well, where the diminished fourth (-8 fifths) [[8192/6561]] and the triple augmented fourth (+20 fifths) 3486784401/2147483648 sound extremely close to 5/4 and 13/8 respectively, wherein tempering the [[schisma]] and [[tridecapyth comma]] provide a fairly more complex but 3/2-[[Telicity|telic]] microtemperament, of which 53edo offers an almost perfect approximation. Pure fifths and octaves on the other hand, offer 5 and 13 with -1.954c and +1.428c of error. | [[Pythagorean tuning]] also works surprisingly well, where the diminished fourth (-8 fifths) [[8192/6561]] and the triple augmented fourth (+20 fifths) 3486784401/2147483648 sound extremely close to 5/4 and 13/8 respectively, wherein tempering the [[schisma]] and [[tridecapyth comma]] provide a fairly more complex but 3/2-[[Telicity|telic]] microtemperament, of which 53edo offers an almost perfect approximation. Pure fifths and octaves on the other hand, offer 5 and 13 with -1.954c and +1.428c of error. | ||