8L 3s

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↖ 7L 2s ↑ 8L 2s 9L 2s ↗
← 7L 3s 8L 3s 9L 3s →
↙ 7L 4s ↓ 8L 4s 9L 4s ↘ 
┌╥╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║║│║║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLs
sLLsLLLsLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 4\11 to 3\8 (436.4 ¢ to 450.0 ¢)
Dark 5\8 to 7\11 (750.0 ¢ to 763.6 ¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Ancestor's step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 3L 5s
Sister 3L 8s
Daughters 11L 8s, 8L 11s
Neutralized 5L 6s
2-Flought 19L 3s, 8L 14s
Equal tunings
Equalized (L:s = 1:1) 4\11 (436.4 ¢)
Supersoft (L:s = 4:3) 15\41 (439.0 ¢)
Soft (L:s = 3:2) 11\30 (440.0 ¢)
Semisoft (L:s = 5:3) 18\49 (440.8 ¢)
Basic (L:s = 2:1) 7\19 (442.1 ¢)
Semihard (L:s = 5:2) 17\46 (443.5 ¢)
Hard (L:s = 3:1) 10\27 (444.4 ¢)
Superhard (L:s = 4:1) 13\35 (445.7 ¢)
Collapsed (L:s = 1:0) 3\8 (450.0 ¢)

8L 3s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 3 small steps, repeating every octave. 8L 3s is a child scale of 3L 5s, expanding it by 3 tones. Generators that produce this scale range from 436.4 ¢ to 450 ¢, or from 750 ¢ to 763.6 ¢.

The only significant harmonic entropy minimum with this mos pattern is sensi, in which the generator is 9/7 and two of them make a 5/3.

Scale properties

Intervals

Intervals of 8L 3s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 109.1 ¢
Major 1-mosstep M1ms L 109.1 ¢ to 150.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 150.0 ¢ to 218.2 ¢
Major 2-mosstep M2ms 2L 218.2 ¢ to 300.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 300.0 ¢ to 327.3 ¢
Major 3-mosstep M3ms 3L 327.3 ¢ to 450.0 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 300.0 ¢ to 436.4 ¢
Perfect 4-mosstep P4ms 3L + s 436.4 ¢ to 450.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 450.0 ¢ to 545.5 ¢
Major 5-mosstep M5ms 4L + s 545.5 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 600.0 ¢ to 654.5 ¢
Major 6-mosstep M6ms 5L + s 654.5 ¢ to 750.0 ¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 750.0 ¢ to 763.6 ¢
Augmented 7-mosstep A7ms 6L + s 763.6 ¢ to 900.0 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 750.0 ¢ to 872.7 ¢
Major 8-mosstep M8ms 6L + 2s 872.7 ¢ to 900.0 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 900.0 ¢ to 981.8 ¢
Major 9-mosstep M9ms 7L + 2s 981.8 ¢ to 1050.0 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 1050.0 ¢ to 1090.9 ¢
Major 10-mosstep M10ms 8L + 2s 1090.9 ¢ to 1200.0 ¢
11-mosstep Perfect 11-mosstep P11ms 8L + 3s 1200.0 ¢

Generator chain

Generator chain of 8L 3s
Bright gens Scale degree Abbrev.
18 Augmented 6-mosdegree A6md
17 Augmented 2-mosdegree A2md
16 Augmented 9-mosdegree A9md
15 Augmented 5-mosdegree A5md
14 Augmented 1-mosdegree A1md
13 Augmented 8-mosdegree A8md
12 Augmented 4-mosdegree A4md
11 Augmented 0-mosdegree A0md
10 Augmented 7-mosdegree A7md
9 Major 3-mosdegree M3md
8 Major 10-mosdegree M10md
7 Major 6-mosdegree M6md
6 Major 2-mosdegree M2md
5 Major 9-mosdegree M9md
4 Major 5-mosdegree M5md
3 Major 1-mosdegree M1md
2 Major 8-mosdegree M8md
1 Perfect 4-mosdegree P4md
0 Perfect 0-mosdegree
Perfect 11-mosdegree		 P0md
P11md
−1 Perfect 7-mosdegree P7md
−2 Minor 3-mosdegree m3md
−3 Minor 10-mosdegree m10md
−4 Minor 6-mosdegree m6md
−5 Minor 2-mosdegree m2md
−6 Minor 9-mosdegree m9md
−7 Minor 5-mosdegree m5md
−8 Minor 1-mosdegree m1md
−9 Minor 8-mosdegree m8md
−10 Diminished 4-mosdegree d4md
−11 Diminished 11-mosdegree d11md
−12 Diminished 7-mosdegree d7md
−13 Diminished 3-mosdegree d3md
−14 Diminished 10-mosdegree d10md
−15 Diminished 6-mosdegree d6md
−16 Diminished 2-mosdegree d2md
−17 Diminished 9-mosdegree d9md
−18 Diminished 5-mosdegree d5md

Modes

Scale degrees of the modes of 8L 3s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11
10|0 1 LLLsLLLsLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Aug. Maj. Maj. Maj. Perf.
9|1 5 LLLsLLsLLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
8|2 9 LLsLLLsLLLs Perf. Maj. Maj. Min. Perf. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
7|3 2 LLsLLLsLLsL Perf. Maj. Maj. Min. Perf. Maj. Maj. Perf. Maj. Maj. Min. Perf.
6|4 6 LLsLLsLLLsL Perf. Maj. Maj. Min. Perf. Maj. Min. Perf. Maj. Maj. Min. Perf.
5|5 10 LsLLLsLLLsL Perf. Maj. Min. Min. Perf. Maj. Min. Perf. Maj. Maj. Min. Perf.
4|6 3 LsLLLsLLsLL Perf. Maj. Min. Min. Perf. Maj. Min. Perf. Maj. Min. Min. Perf.
3|7 7 LsLLsLLLsLL Perf. Maj. Min. Min. Perf. Min. Min. Perf. Maj. Min. Min. Perf.
2|8 11 sLLLsLLLsLL Perf. Min. Min. Min. Perf. Min. Min. Perf. Maj. Min. Min. Perf.
1|9 4 sLLLsLLsLLL Perf. Min. Min. Min. Perf. Min. Min. Perf. Min. Min. Min. Perf.
0|10 8 sLLsLLLsLLL Perf. Min. Min. Min. Dim. Min. Min. Perf. Min. Min. Min. Perf.

Proposed mode names

R-4981 has proposed names based on shogi pieces.

Modes of 8L 3s
UDP Cyclic
order		 Step
pattern		 Shogi-based names[proposed]
10|0 1 LLLsLLLsLLs Ōshō (王将)
9|1 5 LLLsLLsLLLs Ryūō (竜王)
8|2 9 LLsLLLsLLLs Ryūma (竜馬)
7|3 2 LLsLLLsLLsL Hisha (飛車)
6|4 6 LLsLLsLLLsL Kaku (角)
5|5 10 LsLLLsLLLsL Kin (金)
4|6 3 LsLLLsLLsLL Gin (銀)
3|7 7 LsLLsLLLsLL Keima (桂馬)
2|8 11 sLLLsLLLsLL Kyo (香)
1|9 4 sLLLsLLsLLL Tokin (と金)
0|10 8 sLLsLLLsLLL Fuhyo (歩兵)

Scale tree

Scale tree and tuning spectrum of 8L 3s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\11 436.364 763.636 1:1 1.000 Equalized 8L 3s
23\63 438.095 761.905 6:5 1.200
19\52 438.462 761.538 5:4 1.250
34\93 438.710 761.290 9:7 1.286
15\41 439.024 760.976 4:3 1.333 Supersoft 8L 3s
41\112 439.286 760.714 11:8 1.375
26\71 439.437 760.563 7:5 1.400
37\101 439.604 760.396 10:7 1.429
11\30 440.000 760.000 3:2 1.500 Soft 8L 3s
40\109 440.367 759.633 11:7 1.571
29\79 440.506 759.494 8:5 1.600
47\128 440.625 759.375 13:8 1.625 Golden sentry (440.5922 ¢)
18\49 440.816 759.184 5:3 1.667 Semisoft 8L 3s
43\117 441.026 758.974 12:7 1.714
25\68 441.176 758.824 7:4 1.750
32\87 441.379 758.621 9:5 1.800 Clyde
7\19 442.105 757.895 2:1 2.000 Basic 8L 3s
Scales with tunings softer than this are proper
31\84 442.857 757.143 9:4 2.250 Sensei
24\65 443.077 756.923 7:3 2.333
41\111 443.243 756.757 12:5 2.400 Warrior
17\46 443.478 756.522 5:2 2.500 Semihard 8L 3s
Sensi (optimal around here)
44\119 443.697 756.303 13:5 2.600 Golden sensi
27\73 443.836 756.164 8:3 2.667
37\100 444.000 756.000 11:4 2.750
10\27 444.444 755.556 3:1 3.000 Hard 8L 3s
33\89 444.944 755.056 10:3 3.333
23\62 445.161 754.839 7:2 3.500
36\97 445.361 754.639 11:3 3.667
13\35 445.714 754.286 4:1 4.000 Superhard 8L 3s
29\78 446.154 753.846 9:2 4.500
16\43 446.512 753.488 5:1 5.000
19\51 447.059 752.941 6:1 6.000
3\8 450.000 750.000 1:0 → ∞ Collapsed 8L 3s


Icon-Todo.png Todo: review

Make pentachordal analysis its own section (see history of this section)?

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