159th-octave temperaments
159edo is a notable 17-limit system. It first contains 53edo, tempering out Mercator's comma.
159edo has attracted a lot of attention from prominent microtonalists like Ozan Yarman, Dawson Berry (also known as Aura), Gene Ward Smith. In addition, some of its multiples have large consistency limits as well, and this naturally commends itself to 159th-octave temperaments.
This page collects temperaments that are of theoretical interest specific to 159edo, beyond just 53edo.
Temperaments discussed elsewhere include auric and aemillic.
Aemic (rank-3)
Aemic, a shortening of aemilic (see below) tempers out the frameshift comma and the nexus comma. Aemic is alternately defined by setting the 2.3.11 mapping to that of 159edo and the rest being independent generators. On the patent val it is supported by first 10 multiples of 159edo.
Subgroup: 2.3.5.7.11
Comma list: 1771561/1769472, 22876792454961/22866405883904
Mapping: [⟨159 252 0 0 550], ⟨0 0 1 0 0], ⟨0 0 0 1 0]]
- mapping generators: ~243/242 = 1\159, ~5, ~7
Supporting ETs: 159, 318, 477, 636, 795, 954, 1113, 1272, 1431, 1590