3L 2s (3/2-equivalent): Difference between revisions
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"Subgroup TE" pure-3/2 generator: ~7/6 = 264.3771 | "Subgroup TE" pure-3/2 generator: ~7/6 = 264.3771 | ||
[[Mapping]]: [{{val|1 1 3 4}}, {{val|0 1 -2 -4}}] | [[Mapping]]: [{{val|1 1 3 4}}, {{val|0 1 -2 -4}}] | ||
[[Vals]]: {{val list|8edf, 13edf}} | [[Vals]]: {{val list|8edf, 13edf}} | ||
==== Hemilycan ==== | ==== Hemilycan ==== | ||
[[Subgroup]]: 3/2.7/4.5/2.11/4 | [[Subgroup]]: 3/2.7/4.5/2.11/4 | ||
Revision as of 19:48, 1 May 2021
| ↖ 2L 1s⟨3/2⟩ | ↑ 3L 1s⟨3/2⟩ | 4L 1s⟨3/2⟩ ↗ |
| ← 2L 2s⟨3/2⟩ | 3L 2s (3/2-equivalent) | 4L 2s⟨3/2⟩ → |
| ↙ 2L 3s⟨3/2⟩ | ↓ 3L 3s⟨3/2⟩ | 4L 3s⟨3/2⟩ ↘ |
┌╥╥┬╥┬┐ │║║│║││ │││││││ └┴┴┴┴┴┘
sLsLL
3L 2s<3/2> (sometimes called uranian), is a fifth-repeating MOS scale. The notation "<3/2>" means the period of the MOS is 3/2, disambiguating it from octave-repeating 3L 2s.
Because uranian is a fifth-repeating scale, each tone has a 3/2 perfect fifth above it. The scale has three major chords and two minor chords, all voiced so that the third of the triad is an octave higher, a tenth. Uranian also has two harmonic 7th chords.
Basic uranian is in 8edf, which is a very good fifth-based equal tuning similar to 88cET.
Temperaments
The most basic rank-2 temperament interpretation of uranian is semiwolf, which has 4:7:10 chords spelled root-(p+1g)-(3p-2g) (p = 3/2, g = the approximate 7/6). The name "semiwolf" comes from two 7/6 generators approximating a 27/20 wolf fourth.
Semiwolf
Subgroup: 3/2.7/4.5/2
"Inharmonic TE" pure-3/2 generator: ~7/6 = 262.8529
"Subgroup TE" pure-3/2 generator: ~7/6 = 262.1728
Mapping: [⟨1 1 3], ⟨0 1 -2]]
Semilupine
Subgroup: 3/2.7/4.5/2.11/4
"Inharmonic TE" pure-3/2 generator: ~7/6 = 264.3198
"Subgroup TE" pure-3/2 generator: ~7/6 = 264.3771
Mapping: [⟨1 1 3 4], ⟨0 1 -2 -4]]
Hemilycan
Subgroup: 3/2.7/4.5/2.11/4
"Inharmonic TE" pure-3/2 generator: ~7/6 = 261.8554
"Subgroup TE" pure-3/2 generator: ~7/6 = 261.5939
Mapping: [⟨1 1 3 1], ⟨0 1 -2 4]]