6L 10s

Revision as of 10:26, 11 February 2024 by BudjarnLambeth (talk | contribs) (Slightly modified wording to flow better from the intro)

6L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 10 small steps, with a period of 3 large steps and 5 small steps that repeats every 600.0 ¢, or twice every octave. 6L 10s is a child scale of 6L 4s, expanding it by 6 tones. Generators that produce this scale range from 375 ¢ to 400 ¢, or from 200 ¢ to 225 ¢. Being a small major third scale with a half octave period, this makes it the same scale as Magic/Würschmidt[16] enforcing the half octaves as diatonic notes to the scale. With a half octave period, the generator inverts to 1/6edo (200) to 3/16edo (225 cents).

↖ 5L 9s ↑ 6L 9s 7L 9s ↗
← 5L 10s 6L 10s 7L 10s →
↙ 5L 11s ↓ 6L 11s 7L 11s ↘
Scale structure
Step pattern LsLssLssLsLssLss
ssLssLsLssLssLsL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 5\16 to 2\6 (375.0 ¢ to 400.0 ¢)
Dark 1\6 to 3\16 (200.0 ¢ to 225.0 ¢)
TAMNAMS information
Related to 6L 4s (lemon)
With tunings 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 6L 4s
Sister 10L 6s
Daughters 16L 6s, 6L 16s
Neutralized 12L 4s
2-Flought 22L 10s, 6L 26s
Equal tunings
Equalized (L:s = 1:1) 5\16 (375.0 ¢)
Supersoft (L:s = 4:3) 17\54 (377.8 ¢)
Soft (L:s = 3:2) 12\38 (378.9 ¢)
Semisoft (L:s = 5:3) 19\60 (380.0 ¢)
Basic (L:s = 2:1) 7\22 (381.8 ¢)
Semihard (L:s = 5:2) 16\50 (384.0 ¢)
Hard (L:s = 3:1) 9\28 (385.7 ¢)
Superhard (L:s = 4:1) 11\34 (388.2 ¢)
Collapsed (L:s = 1:0) 2\6 (400.0 ¢)
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Modes

Modes of 6L 10s
UDP Cyclic
order
Step
pattern
14|0(2) 1 LsLssLssLsLssLss
12|2(2) 6 LssLsLssLssLsLss
10|4(2) 3 LssLssLsLssLssLs
8|6(2) 8 sLsLssLssLsLssLs
6|8(2) 5 sLssLsLssLssLsLs
4|10(2) 2 sLssLssLsLssLssL
2|12(2) 7 ssLsLssLssLsLssL
0|14(2) 4 ssLssLsLssLssLsL

Scale tree

1/6 200
7/40 210
6/34 211.765
11/62 212.903
213.865
5/28 214.286
215.2035
14/78 215.385
215.559
9/50 216
13/72 216.667
4/22 218.182
15/82 219.512
219.615
11/60 220
220.296
18/98 220.408
220.592
7/38 221.053
17/92 221.739
10/54 222.222
13/70 222.667-
3/16 225