4L 3s/Temperaments

Kleismic

Subgroup: 2.3.5

Comma list: 15625/15552

Mapping: [⟨1 0 1], ⟨0 6 5]]

POTE generator: ~6/5 = 317.007

Tuning ranges:

• valid range: [300.000, 327.273] (4 to 11b)
• nice range: [315.641, 317.263]
• strict range: [315.641, 317.263]

Orgone (15&11, 2.7.11)

Main article: Orgone

Commas:65536/65219

Subgroup: 2.7.11

POTE generator: ~77/64 = 323.372

Sval map: [<1 2 4|, <0 3 -2|]

EDOs: 7, 11, 15, 26, 37, 63, 89, 115, 141, 167, 308, 475bc, 783bc

Sixix (18&25)

Sixix can be viewed as a dual-fifth temperament, i.e. a temperament on the 2.3+.3-.5 "subgroup" (3+ = sharp 3, 3- = flat 3):

• It has both a sharp fifth and a flat fifth but no near-just 3/2.
• Combining the sharp fifth and the flat fifth yields a good approximation of 9/8; two 9/8's make a 5/4, so it tempers out 81/80 in the underlying 2.9.5 subgroup.
• The chroma of sixix[7] is the difference between the sharp fifth and the flat fifth, and functions much like a(n untempered) comma in sixix harmony, giving two slightly different flavors of fifths, minor thirds, major thirds, etc, much like in porcupine harmony. Tempering out this comma leads to 7edo.