6L 10s

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↖ 5L 9s ↑ 6L 9s 7L 9s ↗
← 5L 10s 6L 10s 7L 10s →
↙ 5L 11s ↓ 6L 11s 7L 11s ↘ 
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│║│║││║││║│║││║│││
││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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
Descends from 6L 4s
Ancestor's step ratio range 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¢)

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).

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

Intervals

Intervals of 6L 10s
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 75.0 ¢
Major 1-mosstep M1ms L 75.0 ¢ to 200.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 150.0 ¢
Major 2-mosstep M2ms L + s 150.0 ¢ to 200.0 ¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 200.0 ¢ to 225.0 ¢
Augmented 3-mosstep A3ms 2L + s 225.0 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 200.0 ¢ to 300.0 ¢
Major 4-mosstep M4ms 2L + 2s 300.0 ¢ to 400.0 ¢
5-mosstep Diminished 5-mosstep d5ms L + 4s 200.0 ¢ to 375.0 ¢
Perfect 5-mosstep P5ms 2L + 3s 375.0 ¢ to 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 400.0 ¢ to 450.0 ¢
Major 6-mosstep M6ms 3L + 3s 450.0 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 400.0 ¢ to 525.0 ¢
Major 7-mosstep M7ms 3L + 4s 525.0 ¢ to 600.0 ¢
8-mosstep Perfect 8-mosstep P8ms 3L + 5s 600.0¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 600.0 ¢ to 675.0 ¢
Major 9-mosstep M9ms 4L + 5s 675.0 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms 3L + 7s 600.0 ¢ to 750.0 ¢
Major 10-mosstep M10ms 4L + 6s 750.0 ¢ to 800.0 ¢
11-mosstep Perfect 11-mosstep P11ms 4L + 7s 800.0 ¢ to 825.0 ¢
Augmented 11-mosstep A11ms 5L + 6s 825.0 ¢ to 1000.0 ¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 800.0 ¢ to 900.0 ¢
Major 12-mosstep M12ms 5L + 7s 900.0 ¢ to 1000.0 ¢
13-mosstep Diminished 13-mosstep d13ms 4L + 9s 800.0 ¢ to 975.0 ¢
Perfect 13-mosstep P13ms 5L + 8s 975.0 ¢ to 1000.0 ¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 1000.0 ¢ to 1050.0 ¢
Major 14-mosstep M14ms 6L + 8s 1050.0 ¢ to 1200.0 ¢
15-mosstep Minor 15-mosstep m15ms 5L + 10s 1000.0 ¢ to 1125.0 ¢
Major 15-mosstep M15ms 6L + 9s 1125.0 ¢ to 1200.0 ¢
16-mosstep Perfect 16-mosstep P16ms 6L + 10s 1200.0¢

Scale tree

Scale tree and tuning spectrum of 6L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
5\16 375.000 225.000 1:1 1.000 Equalized 6L 10s
27\86 376.744 223.256 6:5 1.200
22\70 377.143 222.857 5:4 1.250
39\124 377.419 222.581 9:7 1.286
17\54 377.778 222.222 4:3 1.333 Supersoft 6L 10s
46\146 378.082 221.918 11:8 1.375
29\92 378.261 221.739 7:5 1.400
41\130 378.462 221.538 10:7 1.429
12\38 378.947 221.053 3:2 1.500 Soft 6L 10s
43\136 379.412 220.588 11:7 1.571
31\98 379.592 220.408 8:5 1.600
50\158 379.747 220.253 13:8 1.625
19\60 380.000 220.000 5:3 1.667 Semisoft 6L 10s
45\142 380.282 219.718 12:7 1.714
26\82 380.488 219.512 7:4 1.750
33\104 380.769 219.231 9:5 1.800
7\22 381.818 218.182 2:1 2.000 Basic 6L 10s
Scales with tunings softer than this are proper
30\94 382.979 217.021 9:4 2.250
23\72 383.333 216.667 7:3 2.333
39\122 383.607 216.393 12:5 2.400
16\50 384.000 216.000 5:2 2.500 Semihard 6L 10s
41\128 384.375 215.625 13:5 2.600
25\78 384.615 215.385 8:3 2.667
34\106 384.906 215.094 11:4 2.750
9\28 385.714 214.286 3:1 3.000 Hard 6L 10s
29\90 386.667 213.333 10:3 3.333
20\62 387.097 212.903 7:2 3.500
31\96 387.500 212.500 11:3 3.667
11\34 388.235 211.765 4:1 4.000 Superhard 6L 10s
24\74 389.189 210.811 9:2 4.500
13\40 390.000 210.000 5:1 5.000
15\46 391.304 208.696 6:1 6.000
2\6 400.000 200.000 1:0 → ∞ Collapsed 6L 10s
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