12edo: Difference between revisions
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12edo is the largest equal division of the octave which uniquely patently alternates with an *ed(9/8) in a [[Well tempered nonet|wtn]]{{clarify}}, and it also contains [[2edo]], [[3edo]], [[4edo]] and [[6edo]] as subsets. 12edo is the 5th [[highly melodic EDO]], 12 being both a superabundant and a highly composte number. As of right now, it is the only known EDO that is both highly melodic and zeta, and the only one with a step size larger than the just noticeable difference (~3-4 cents). | 12edo is the largest equal division of the octave which uniquely patently alternates with an *ed(9/8) in a [[Well tempered nonet|wtn]]{{clarify}}, and it also contains [[2edo]], [[3edo]], [[4edo]] and [[6edo]] as subsets. 12edo is the 5th [[highly melodic EDO]], 12 being both a superabundant and a highly composte number. As of right now, it is the only known EDO that is both highly melodic and zeta, and the only one with a step size larger than the just noticeable difference (~3-4 cents). | ||
12edo offers very good approximations to intervals in the 2.3.17.19 subgroup. This indicates one way to use 12edo that deviates from common-practice harmony | 12edo offers very good approximations to intervals in the 2.3.17.19 subgroup. This indicates one way to use 12edo that deviates from common-practice harmony; for instance the cluster chord 8:17:36:76 is well represented. | ||
=== Prime harmonics === | === Prime harmonics === | ||