8L 1s (3/1-equivalent): Difference between revisions

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Revision as of 04:00, 14 October 2024

← 7L 1s⟨3/1⟩ 8L 1s (3/1-equivalent) 9L 1s⟨3/1⟩ →
↙ 7L 2s⟨3/1⟩ ↓ 8L 2s⟨3/1⟩ 9L 2s⟨3/1⟩ ↘ 
┌╥╥╥╥╥╥╥╥┬┐
│║║║║║║║║││
│││││││││││
└┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLLLLLs
sLLLLLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 1\9 to 1\8 (211.3 ¢ to 237.7 ¢)
Dark 7\8 to 8\9 (1664.2 ¢ to 1690.6 ¢)
Related MOS scales
Parent 1L 7s⟨3/1⟩
Sister 1L 8s⟨3/1⟩
Daughters 9L 8s⟨3/1⟩, 8L 9s⟨3/1⟩
Neutralized 7L 2s⟨3/1⟩
2-Flought 17L 1s⟨3/1⟩, 8L 10s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 1\9 (211.3 ¢)
Supersoft (L:s = 4:3) 4\35 (217.4 ¢)
Soft (L:s = 3:2) 3\26 (219.5 ¢)
Semisoft (L:s = 5:3) 5\43 (221.2 ¢)
Basic (L:s = 2:1) 2\17 (223.8 ¢)
Semihard (L:s = 5:2) 5\42 (226.4 ¢)
Hard (L:s = 3:1) 3\25 (228.2 ¢)
Superhard (L:s = 4:1) 4\33 (230.5 ¢)
Collapsed (L:s = 1:0) 1\8 (237.7 ¢)

8L 1s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 8 large steps and 1 small step, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 211.3 ¢ to 237.7 ¢, or from 1664.2 ¢ to 1690.6 ¢. Scales of this form are always proper because there is only one small step.

Theory

Temperament interpretations

Modes

Modes of 8L 1s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
8|0 1 LLLLLLLLs
7|1 2 LLLLLLLsL
6|2 3 LLLLLLsLL
5|3 4 LLLLLsLLL
4|4 5 LLLLsLLLL
3|5 6 LLLsLLLLL
2|6 7 LLsLLLLLL
1|7 8 LsLLLLLLL
0|8 9 sLLLLLLLL

Scale degrees

Scale degrees of the modes of 8L 1s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLLLLLLLs Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Perf.
7|1 2 LLLLLLLsL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Perf.
6|2 3 LLLLLLsLL Perf. Perf. Maj. Maj. Maj. Maj. Maj. Min. Perf. Perf.
5|3 4 LLLLLsLLL Perf. Perf. Maj. Maj. Maj. Maj. Min. Min. Perf. Perf.
4|4 5 LLLLsLLLL Perf. Perf. Maj. Maj. Maj. Min. Min. Min. Perf. Perf.
3|5 6 LLLsLLLLL Perf. Perf. Maj. Maj. Min. Min. Min. Min. Perf. Perf.
2|6 7 LLsLLLLLL Perf. Perf. Maj. Min. Min. Min. Min. Min. Perf. Perf.
1|7 8 LsLLLLLLL Perf. Perf. Min. Min. Min. Min. Min. Min. Perf. Perf.
0|8 9 sLLLLLLLL Perf. Dim. Min. Min. Min. Min. Min. Min. Perf. Perf.

Scale tree

Template:Scale tree

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