Irrational-subgroup temperaments

This page is a list of temperaments which have an irrational subgroup that cannot be expressed in surds.

Polyraider

The temperament below can also be written with 34ed30 nominals and cent-deviation (1\1171) accidentals.

Subgroup: 2.3.5.11.f2.f3 where f2, f3 are the second and third modes of an ideal unsupported bar.

Comma list: 1771561/1771470, 1310730070806386550964611/1310720000000000000000000, [-8 6 -3 2 -1 0>, [-11 10 -7 4 0 -1>

Mapping: [⟨1 65 172 148 162 27], ⟨0 −111 −297 −253 −281 −43]]

mapping generators: ~2, ~10460353203/7040000000

Optimal tunings:

• WE: ~2 = 1199.999 ¢, ~10460353203/7040000000 = 685.567 ¢

error map: ⟨-0.001 -0.001 -0.002 -0.017 -0.024 0.122]

• CWE: ~2 = 1200.000 ¢, ~10460353203/7040000000 = 685.568 ¢

error map: ⟨0.000 0.000 -0.001 -0.014 -0.023 0.125]

Optimal ET sequence: 7, 1164, 1171, 1178, 1185, 2335, 2349, 3506, 3520, 3527, 4691

Badness (Sintel): 0.655