6L 9s

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↖ 5L 8s ↑ 6L 8s 7L 8s ↗
← 5L 9s 6L 9s 7L 9s →
↙ 5L 10s ↓ 6L 10s 7L 10s ↘ 
┌╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐
│║│║││║│║││║│║│││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLssLsLssLsLss
ssLsLssLsLssLsL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 2\15 to 1\6 (160.0 ¢ to 200.0 ¢)
Dark 1\6 to 3\15 (200.0 ¢ to 240.0 ¢)
TAMNAMS information
Descends from 6L 3s (hyrulic)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 6L 3s
Sister 9L 6s
Daughters 15L 6s, 6L 15s
Neutralized 12L 3s
2-Flought 21L 9s, 6L 24s
Equal tunings
Equalized (L:s = 1:1) 2\15 (160.0 ¢)
Supersoft (L:s = 4:3) 7\51 (164.7 ¢)
Soft (L:s = 3:2) 5\36 (166.7 ¢)
Semisoft (L:s = 5:3) 8\57 (168.4 ¢)
Basic (L:s = 2:1) 3\21 (171.4 ¢)
Semihard (L:s = 5:2) 7\48 (175.0 ¢)
Hard (L:s = 3:1) 4\27 (177.8 ¢)
Superhard (L:s = 4:1) 5\33 (181.8 ¢)
Collapsed (L:s = 1:0) 1\6 (200.0 ¢)

6L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 9 small steps, with a period of 2 large steps and 3 small steps that repeats every 400.0 ¢, or 3 times every octave. 6L 9s is a child scale of 6L 3s, expanding it by 6 tones. Generators that produce this scale range from 160 ¢ to 200 ¢, or from 200 ¢ to 240 ¢.

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 9s
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 80.0 ¢
Major 1-mosstep M1ms L 80.0 ¢ to 200.0 ¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0 ¢ to 160.0 ¢
Perfect 2-mosstep P2ms L + s 160.0 ¢ to 200.0 ¢
3-mosstep Perfect 3-mosstep P3ms L + 2s 200.0 ¢ to 240.0 ¢
Augmented 3-mosstep A3ms 2L + s 240.0 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms L + 3s 200.0 ¢ to 320.0 ¢
Major 4-mosstep M4ms 2L + 2s 320.0 ¢ to 400.0 ¢
5-mosstep Perfect 5-mosstep P5ms 2L + 3s 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 400.0 ¢ to 480.0 ¢
Major 6-mosstep M6ms 3L + 3s 480.0 ¢ to 600.0 ¢
7-mosstep Diminished 7-mosstep d7ms 2L + 5s 400.0 ¢ to 560.0 ¢
Perfect 7-mosstep P7ms 3L + 4s 560.0 ¢ to 600.0 ¢
8-mosstep Perfect 8-mosstep P8ms 3L + 5s 600.0 ¢ to 640.0 ¢
Augmented 8-mosstep A8ms 4L + 4s 640.0 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 600.0 ¢ to 720.0 ¢
Major 9-mosstep M9ms 4L + 5s 720.0 ¢ to 800.0 ¢
10-mosstep Perfect 10-mosstep P10ms 4L + 6s 800.0 ¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 800.0 ¢ to 880.0 ¢
Major 11-mosstep M11ms 5L + 6s 880.0 ¢ to 1000.0 ¢
12-mosstep Diminished 12-mosstep d12ms 4L + 8s 800.0 ¢ to 960.0 ¢
Perfect 12-mosstep P12ms 5L + 7s 960.0 ¢ to 1000.0 ¢
13-mosstep Perfect 13-mosstep P13ms 5L + 8s 1000.0 ¢ to 1040.0 ¢
Augmented 13-mosstep A13ms 6L + 7s 1040.0 ¢ to 1200.0 ¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 1000.0 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 6L + 8s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 6L + 9s 1200.0 ¢

Generator chain

Generator chain of 6L 9s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
6 Augmented 2-mosdegree A2md Augmented 7-mosdegree A7md Augmented 12-mosdegree A12md
5 Augmented 0-mosdegree A0md Augmented 5-mosdegree A5md Augmented 10-mosdegree A10md
4 Augmented 3-mosdegree A3md Augmented 8-mosdegree A8md Augmented 13-mosdegree A13md
3 Major 1-mosdegree M1md Major 6-mosdegree M6md Major 11-mosdegree M11md
2 Major 4-mosdegree M4md Major 9-mosdegree M9md Major 14-mosdegree M14md
1 Perfect 2-mosdegree P2md Perfect 7-mosdegree P7md Perfect 12-mosdegree P12md
0 Perfect 0-mosdegree
Perfect 5-mosdegree		 P0md
P5md		 Perfect 5-mosdegree
Perfect 10-mosdegree		 P5md
P10md		 Perfect 10-mosdegree
Perfect 15-mosdegree		 P10md
P15md
−1 Perfect 3-mosdegree P3md Perfect 8-mosdegree P8md Perfect 13-mosdegree P13md
−2 Minor 1-mosdegree m1md Minor 6-mosdegree m6md Minor 11-mosdegree m11md
−3 Minor 4-mosdegree m4md Minor 9-mosdegree m9md Minor 14-mosdegree m14md
−4 Diminished 2-mosdegree d2md Diminished 7-mosdegree d7md Diminished 12-mosdegree d12md
−5 Diminished 5-mosdegree d5md Diminished 10-mosdegree d10md Diminished 15-mosdegree d15md
−6 Diminished 3-mosdegree d3md Diminished 8-mosdegree d8md Diminished 13-mosdegree d13md

Modes

Scale degrees of the modes of 6L 9s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
12|0(3) 1 LsLssLsLssLsLss Perf. Maj. Perf. Aug. Maj. Perf. Maj. Perf. Aug. Maj. Perf. Maj. Perf. Aug. Maj. Perf.
9|3(3) 3 LssLsLssLsLssLs Perf. Maj. Perf. Perf. Maj. Perf. Maj. Perf. Perf. Maj. Perf. Maj. Perf. Perf. Maj. Perf.
6|6(3) 5 sLsLssLsLssLsLs Perf. Min. Perf. Perf. Maj. Perf. Min. Perf. Perf. Maj. Perf. Min. Perf. Perf. Maj. Perf.
3|9(3) 2 sLssLsLssLsLssL Perf. Min. Perf. Perf. Min. Perf. Min. Perf. Perf. Min. Perf. Min. Perf. Perf. Min. Perf.
0|12(3) 4 ssLsLssLsLssLsL Perf. Min. Dim. Perf. Min. Perf. Min. Dim. Perf. Min. Perf. Min. Dim. Perf. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 9s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\15 160.000 240.000 1:1 1.000 Equalized 6L 9s
11\81 162.963 237.037 6:5 1.200
9\66 163.636 236.364 5:4 1.250
16\117 164.103 235.897 9:7 1.286
7\51 164.706 235.294 4:3 1.333 Supersoft 6L 9s
19\138 165.217 234.783 11:8 1.375
12\87 165.517 234.483 7:5 1.400
17\123 165.854 234.146 10:7 1.429
5\36 166.667 233.333 3:2 1.500 Soft 6L 9s
18\129 167.442 232.558 11:7 1.571
13\93 167.742 232.258 8:5 1.600
21\150 168.000 232.000 13:8 1.625
8\57 168.421 231.579 5:3 1.667 Semisoft 6L 9s
Ternary is around here
19\135 168.889 231.111 12:7 1.714
11\78 169.231 230.769 7:4 1.750
14\99 169.697 230.303 9:5 1.800
3\21 171.429 228.571 2:1 2.000 Basic 6L 9s
Scales with tunings softer than this are proper
13\90 173.333 226.667 9:4 2.250
10\69 173.913 226.087 7:3 2.333 Oodako is around here
17\117 174.359 225.641 12:5 2.400
7\48 175.000 225.000 5:2 2.500 Semihard 6L 9s
18\123 175.610 224.390 13:5 2.600
11\75 176.000 224.000 8:3 2.667
15\102 176.471 223.529 11:4 2.750
4\27 177.778 222.222 3:1 3.000 Hard 6L 9s
13\87 179.310 220.690 10:3 3.333
9\60 180.000 220.000 7:2 3.500
14\93 180.645 219.355 11:3 3.667
5\33 181.818 218.182 4:1 4.000 Superhard 6L 9s
Terrain is around here
11\72 183.333 216.667 9:2 4.500 Mirkat is around here
6\39 184.615 215.385 5:1 5.000
7\45 186.667 213.333 6:1 6.000
1\6 200.000 200.000 1:0 → ∞ Collapsed 6L 9s
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