9L 6s: Difference between revisions

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This MOS has three periods of 3L 2s and its generator is a chromatic 'whole tone' between 1/9edo (133.333) and 2/15edo (160 cents). Therefore, the period minus one generator represents a 23+-limit interval between 23/20 and 7/6.
{{Infobox MOS}}
{{MOS intro}}


{| class="wikitable"
The period (400{{c}}) minus one [[dark]] generator represents a 23+-[[limit]] interval between [[23/20]] and [[7/6]] (between ~242{{c}} to ~267{{c}}).
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| | 1/9
== Scale properties ==
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{{TAMNAMS use}}
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=== Intervals ===
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{{MOS intervals}}
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=== Generator chain ===
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{{MOS genchain}}
| | 133.333
 
|-
=== Modes ===
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{{MOS mode degrees}}
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== Scale tree ==
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{{MOS tuning spectrum}}
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{{stub}}
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|9/78
[[Category:Abstract MOS patterns]]
|138.4615
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|8/69
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|139.13
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|7/60
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|140
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| | 6/51
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| | 141.1765
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| | 5/42
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| | 142.857
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| | 14/117
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| | 143.59
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| | 9/75
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| | 144
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| | 145.004
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| | 4/33
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| | 145.4545
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| | 146.463
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| | 11/90
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| | 146.667
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| | 146.864
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| | 7/57
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| | 147.368
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| | 10/81
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| | 148.148
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| | 13/105
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| | 148.571
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| | 16/129
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| | 148.837
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| | 19/153
| | 149.02
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| | 3/24
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| | 150
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| | 11/87
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| | 151.724
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| | 151.862
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| | 8/63
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| | 152.381
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| | 152.786
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| | 13/102
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| | 152.941
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| | 153.197
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| | 5/39
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| | 153.769
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| | 12/93
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| | 154.839
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| | 7/54
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| | 154.444
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| | 9/69
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| | 156.522
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|11/84
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|157.143
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|13/99
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|157.576
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|15/114
|157.895
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| | 2/15
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| | 160
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Latest revision as of 14:06, 5 May 2025

↖ 8L 5s ↑ 9L 5s 10L 5s ↗
← 8L 6s 9L 6s 10L 6s →
↙ 8L 7s ↓ 9L 7s 10L 7s ↘
Scale structure
Step pattern LLsLsLLsLsLLsLs
sLsLLsLsLLsLsLL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 3\15 to 2\9 (240.0 ¢ to 266.7 ¢)
Dark 1\9 to 2\15 (133.3 ¢ to 160.0 ¢)
TAMNAMS information
Related to 6L 3s (hyrulic)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 6L 3s
Sister 6L 9s
Daughters 15L 9s, 9L 15s
Neutralized 3L 12s
2-Flought 24L 6s, 9L 21s
Equal tunings
Equalized (L:s = 1:1) 3\15 (240.0 ¢)
Supersoft (L:s = 4:3) 11\54 (244.4 ¢)
Soft (L:s = 3:2) 8\39 (246.2 ¢)
Semisoft (L:s = 5:3) 13\63 (247.6 ¢)
Basic (L:s = 2:1) 5\24 (250.0 ¢)
Semihard (L:s = 5:2) 12\57 (252.6 ¢)
Hard (L:s = 3:1) 7\33 (254.5 ¢)
Superhard (L:s = 4:1) 9\42 (257.1 ¢)
Collapsed (L:s = 1:0) 2\9 (266.7 ¢)
View • Talk • Edit

9L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 6 small steps, with a period of 3 large steps and 2 small steps that repeats every 400.0 ¢, or 3 times every octave. 9L 6s is a child scale of 6L 3s, expanding it by 6 tones. Generators that produce this scale range from 240 ¢ to 266.7 ¢, or from 133.3 ¢ to 160 ¢.

The period (400 ¢) minus one dark generator represents a 23+-limit interval between 23/20 and 7/6 (between ~242 ¢ to ~267 ¢).

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 interval regions.

Intervals

Intervals of 9L 6s
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 133.3 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 133.3 ¢ to 160.0 ¢
Augmented 2-mosstep A2ms 2L 160.0 ¢ to 266.7 ¢
3-mosstep Diminished 3-mosstep d3ms L + 2s 133.3 ¢ to 240.0 ¢
Perfect 3-mosstep P3ms 2L + s 240.0 ¢ to 266.7 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 266.7 ¢ to 320.0 ¢
Major 4-mosstep M4ms 3L + s 320.0 ¢ to 400.0 ¢
5-mosstep Perfect 5-mosstep P5ms 3L + 2s 400.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 400.0 ¢ to 480.0 ¢
Major 6-mosstep M6ms 4L + 2s 480.0 ¢ to 533.3 ¢
7-mosstep Perfect 7-mosstep P7ms 4L + 3s 533.3 ¢ to 560.0 ¢
Augmented 7-mosstep A7ms 5L + 2s 560.0 ¢ to 666.7 ¢
8-mosstep Diminished 8-mosstep d8ms 4L + 4s 533.3 ¢ to 640.0 ¢
Perfect 8-mosstep P8ms 5L + 3s 640.0 ¢ to 666.7 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 666.7 ¢ to 720.0 ¢
Major 9-mosstep M9ms 6L + 3s 720.0 ¢ to 800.0 ¢
10-mosstep Perfect 10-mosstep P10ms 6L + 4s 800.0 ¢
11-mosstep Minor 11-mosstep m11ms 6L + 5s 800.0 ¢ to 880.0 ¢
Major 11-mosstep M11ms 7L + 4s 880.0 ¢ to 933.3 ¢
12-mosstep Perfect 12-mosstep P12ms 7L + 5s 933.3 ¢ to 960.0 ¢
Augmented 12-mosstep A12ms 8L + 4s 960.0 ¢ to 1066.7 ¢
13-mosstep Diminished 13-mosstep d13ms 7L + 6s 933.3 ¢ to 1040.0 ¢
Perfect 13-mosstep P13ms 8L + 5s 1040.0 ¢ to 1066.7 ¢
14-mosstep Minor 14-mosstep m14ms 8L + 6s 1066.7 ¢ to 1120.0 ¢
Major 14-mosstep M14ms 9L + 5s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 9L + 6s 1200.0 ¢

Generator chain

Generator chain of 9L 6s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
7 Augmented 1-mosdegree A1md Augmented 6-mosdegree A6md Augmented 11-mosdegree A11md
6 Augmented 3-mosdegree A3md Augmented 8-mosdegree A8md Augmented 13-mosdegree A13md
5 Augmented 0-mosdegree A0md Augmented 5-mosdegree A5md Augmented 10-mosdegree A10md
4 Augmented 2-mosdegree A2md Augmented 7-mosdegree A7md Augmented 12-mosdegree A12md
3 Major 4-mosdegree M4md Major 9-mosdegree M9md Major 14-mosdegree M14md
2 Major 1-mosdegree M1md Major 6-mosdegree M6md Major 11-mosdegree M11md
1 Perfect 3-mosdegree P3md Perfect 8-mosdegree P8md Perfect 13-mosdegree P13md
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 2-mosdegree P2md Perfect 7-mosdegree P7md Perfect 12-mosdegree P12md
−2 Minor 4-mosdegree m4md Minor 9-mosdegree m9md Minor 14-mosdegree m14md
−3 Minor 1-mosdegree m1md Minor 6-mosdegree m6md Minor 11-mosdegree m11md
−4 Diminished 3-mosdegree d3md Diminished 8-mosdegree d8md Diminished 13-mosdegree d13md
−5 Diminished 5-mosdegree d5md Diminished 10-mosdegree d10md Diminished 15-mosdegree d15md
−6 Diminished 2-mosdegree d2md Diminished 7-mosdegree d7md Diminished 12-mosdegree d12md
−7 Diminished 4-mosdegree d4md Diminished 9-mosdegree d9md Diminished 14-mosdegree d14md

Modes

Scale degrees of the modes of 9L 6s
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 LLsLsLLsLsLLsLs Perf. Maj. Aug. Perf. Maj. Perf. Maj. Aug. Perf. Maj. Perf. Maj. Aug. Perf. Maj. Perf.
9|3(3) 4 LsLLsLsLLsLsLLs Perf. Maj. Perf. Perf. Maj. Perf. Maj. Perf. Perf. Maj. Perf. Maj. Perf. Perf. Maj. Perf.
6|6(3) 2 LsLsLLsLsLLsLsL Perf. Maj. Perf. Perf. Min. Perf. Maj. Perf. Perf. Min. Perf. Maj. Perf. Perf. Min. Perf.
3|9(3) 5 sLLsLsLLsLsLLsL Perf. Min. Perf. Perf. Min. Perf. Min. Perf. Perf. Min. Perf. Min. Perf. Perf. Min. Perf.
0|12(3) 3 sLsLLsLsLLsLsLL Perf. Min. Perf. Dim. Min. Perf. Min. Perf. Dim. Min. Perf. Min. Perf. Dim. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\15 240.000 160.000 1:1 1.000 Equalized 9L 6s
17\84 242.857 157.143 6:5 1.200
14\69 243.478 156.522 5:4 1.250
25\123 243.902 156.098 9:7 1.286
11\54 244.444 155.556 4:3 1.333 Supersoft 9L 6s
30\147 244.898 155.102 11:8 1.375
19\93 245.161 154.839 7:5 1.400
27\132 245.455 154.545 10:7 1.429
8\39 246.154 153.846 3:2 1.500 Soft 9L 6s
29\141 246.809 153.191 11:7 1.571
21\102 247.059 152.941 8:5 1.600
34\165 247.273 152.727 13:8 1.625
13\63 247.619 152.381 5:3 1.667 Semisoft 9L 6s
31\150 248.000 152.000 12:7 1.714
18\87 248.276 151.724 7:4 1.750
23\111 248.649 151.351 9:5 1.800
5\24 250.000 150.000 2:1 2.000 Basic 9L 6s
Scales with tunings softer than this are proper
22\105 251.429 148.571 9:4 2.250
17\81 251.852 148.148 7:3 2.333
29\138 252.174 147.826 12:5 2.400
12\57 252.632 147.368 5:2 2.500 Semihard 9L 6s
31\147 253.061 146.939 13:5 2.600
19\90 253.333 146.667 8:3 2.667
26\123 253.659 146.341 11:4 2.750
7\33 254.545 145.455 3:1 3.000 Hard 9L 6s
23\108 255.556 144.444 10:3 3.333
16\75 256.000 144.000 7:2 3.500
25\117 256.410 143.590 11:3 3.667
9\42 257.143 142.857 4:1 4.000 Superhard 9L 6s
20\93 258.065 141.935 9:2 4.500
11\51 258.824 141.176 5:1 5.000
13\60 260.000 140.000 6:1 6.000
2\9 266.667 133.333 1:0 → ∞ Collapsed 9L 6s
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