3L 2s (3/2-equivalent): Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,004 edits
Inthar (talk | contribs)
autopatrolled, emailconfirmed
15,004 edits
Line 21: Line 21:
[[Comma]] list: [[245/243]]
[[Comma]] list: [[245/243]]


Optimal "inharmonic TE" pure-3/2 generator: ~7/6 = 262.8529
Optimal "[[inharmonic TE]]" pure-3/2 generator: ~7/6 = 262.8529


Optimal "subgroup TE" pure-3/2 generator: ~7/6 = 262.1728
Optimal "[[subgroup TE]]" pure-3/2 generator: ~7/6 = 262.1728


[[Mapping]]: [{{val|1 1 3}}, {{val|0 1 -2}}]
[[Mapping]]: [{{val|1 1 3}}, {{val|0 1 -2}}]
Line 33: Line 33:
[[Comma]] list: [[245/243]], [[100/99]]
[[Comma]] list: [[245/243]], [[100/99]]


Optimal "inharmonic TE" pure-3/2 generator: ~7/6 = 264.3198
Optimal "[[inharmonic TE]]" pure-3/2 generator: ~7/6 = 264.3198


Optimal "subgroup TE" pure-3/2 generator: ~7/6 = 264.3771
Optimal "[[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}}]
Line 46: Line 46:
[[Comma]] list: [[245/243]], [[441/440]]
[[Comma]] list: [[245/243]], [[441/440]]


Optimal "inharmonic TE" pure-3/2 generator: ~7/6 = 261.8554
Optimal "[[inharmonic TE]]" pure-3/2 generator: ~7/6 = 261.8554


Optimal "subgroup TE" pure-3/2 generator: ~7/6 = 261.5939
Optimal "[[subgroup TE]]" pure-3/2 generator: ~7/6 = 261.5939


[[Mapping]]: [{{val|1 1 3 1}}, {{val|0 1 -2 4}}]
[[Mapping]]: [{{val|1 1 3 1}}, {{val|0 1 -2 4}}]

Revision as of 22:33, 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⟩ ↘ 
┌╥╥┬╥┬┐
│║║│║││
│││││││
└┴┴┴┴┴┘
Scale structure
Step pattern LLsLs
sLsLL
Equave 3/2 (702.0 ¢)
Period 3/2 (702.0 ¢)
Generator size(edf)
Bright 3\5 to 2\3 (421.2 ¢ to 468.0 ¢)
Dark 1\3 to 2\5 (234.0 ¢ to 280.8 ¢)
Related MOS scales
Parent 2L 1s⟨3/2⟩
Sister 2L 3s⟨3/2⟩
Daughters 5L 3s⟨3/2⟩, 3L 5s⟨3/2⟩
Neutralized 1L 4s⟨3/2⟩
2-Flought 8L 2s⟨3/2⟩, 3L 7s⟨3/2⟩
Equal tunings(edf)
Equalized (L:s = 1:1) 3\5 (421.2 ¢)
Supersoft (L:s = 4:3) 11\18 (429.0 ¢)
Soft (L:s = 3:2) 8\13 (432.0 ¢)
Semisoft (L:s = 5:3) 13\21 (434.5 ¢)
Basic (L:s = 2:1) 5\8 (438.7 ¢)
Semihard (L:s = 5:2) 12\19 (443.3 ¢)
Hard (L:s = 3:1) 7\11 (446.7 ¢)
Superhard (L:s = 4:1) 9\14 (451.3 ¢)
Collapsed (L:s = 1:0) 2\3 (468.0 ¢)

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

Comma list: 245/243

Optimal "inharmonic TE" pure-3/2 generator: ~7/6 = 262.8529

Optimal "subgroup TE" pure-3/2 generator: ~7/6 = 262.1728

Mapping: [⟨1 1 3], ⟨0 1 -2]]

Vals: Template:Val list

Semilupine

Subgroup: 3/2.7/4.5/2.11/4

Comma list: 245/243, 100/99

Optimal "inharmonic TE" pure-3/2 generator: ~7/6 = 264.3198

Optimal "subgroup TE" pure-3/2 generator: ~7/6 = 264.3771

Mapping: [⟨1 1 3 4], ⟨0 1 -2 -4]]

Vals: Template:Val list

Hemilycan

Subgroup: 3/2.7/4.5/2.11/4

Comma list: 245/243, 441/440

Optimal "inharmonic TE" pure-3/2 generator: ~7/6 = 261.8554

Optimal "subgroup TE" pure-3/2 generator: ~7/6 = 261.5939

Mapping: [⟨1 1 3 1], ⟨0 1 -2 4]]

Vals: Template:Val list

Retrieved from "https://en.xen.wiki/index.php?title=3L_2s_(3/2-equivalent)&oldid=69104"