6L 10s

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↖ 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 ¢)

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 ¢).

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

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 ¢

Generator chain

Generator chain of 6L 10s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
10 Augmented 2-mosdegree A2md Augmented 10-mosdegree A10md
9 Augmented 5-mosdegree A5md Augmented 13-mosdegree A13md
8 Augmented 0-mosdegree A0md Augmented 8-mosdegree A8md
7 Augmented 3-mosdegree A3md Augmented 11-mosdegree A11md
6 Major 6-mosdegree M6md Major 14-mosdegree M14md
5 Major 1-mosdegree M1md Major 9-mosdegree M9md
4 Major 4-mosdegree M4md Major 12-mosdegree M12md
3 Major 7-mosdegree M7md Major 15-mosdegree M15md
2 Major 2-mosdegree M2md Major 10-mosdegree M10md
1 Perfect 5-mosdegree P5md Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 8-mosdegree		 P0md
P8md		 Perfect 8-mosdegree
Perfect 16-mosdegree		 P8md
P16md
−1 Perfect 3-mosdegree P3md Perfect 11-mosdegree P11md
−2 Minor 6-mosdegree m6md Minor 14-mosdegree m14md
−3 Minor 1-mosdegree m1md Minor 9-mosdegree m9md
−4 Minor 4-mosdegree m4md Minor 12-mosdegree m12md
−5 Minor 7-mosdegree m7md Minor 15-mosdegree m15md
−6 Minor 2-mosdegree m2md Minor 10-mosdegree m10md
−7 Diminished 5-mosdegree d5md Diminished 13-mosdegree d13md
−8 Diminished 8-mosdegree d8md Diminished 16-mosdegree d16md
−9 Diminished 3-mosdegree d3md Diminished 11-mosdegree d11md
−10 Diminished 6-mosdegree d6md Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 6L 10s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16
14|0(2) 1 LsLssLssLsLssLss Perf. Maj. Maj. Aug. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Aug. Maj. Perf. Maj. Maj. Perf.
12|2(2) 6 LssLsLssLssLsLss Perf. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Perf. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Perf.
10|4(2) 3 LssLssLsLssLssLs Perf. Maj. Maj. Perf. Maj. Perf. Min. Maj. Perf. Maj. Maj. Perf. Maj. Perf. Min. Maj. Perf.
8|6(2) 8 sLsLssLssLsLssLs Perf. Min. Maj. Perf. Maj. Perf. Min. Maj. Perf. Min. Maj. Perf. Maj. Perf. Min. Maj. Perf.
6|8(2) 5 sLssLsLssLssLsLs Perf. Min. Maj. Perf. Min. Perf. Min. Maj. Perf. Min. Maj. Perf. Min. Perf. Min. Maj. Perf.
4|10(2) 2 sLssLssLsLssLssL Perf. Min. Maj. Perf. Min. Perf. Min. Min. Perf. Min. Maj. Perf. Min. Perf. Min. Min. Perf.
2|12(2) 7 ssLsLssLssLsLssL Perf. Min. Min. Perf. Min. Perf. Min. Min. Perf. Min. Min. Perf. Min. Perf. Min. Min. Perf.
0|14(2) 4 ssLssLsLssLssLsL Perf. Min. Min. Perf. Min. Dim. Min. Min. Perf. Min. Min. Perf. Min. Dim. Min. Min. Perf.

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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