9L 5s

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Verify temperaments that correspond with 9L 5s

↖ 8L 4s ↑ 9L 4s 10L 4s ↗
← 8L 5s 9L 5s 10L 5s →
↙ 8L 6s ↓ 9L 6s 10L 6s ↘ 
┌╥╥┬╥╥┬╥╥┬╥╥┬╥┬┐
│║║│║║│║║│║║│║││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLLsLLsLLsLs
sLsLLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 3\14 to 2\9 (257.1 ¢ to 266.7 ¢)
Dark 7\9 to 11\14 (933.3 ¢ to 942.9 ¢)
TAMNAMS information
Descends from 5L 4s (semiquartal)
Ancestor's step ratio range 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 4s
Sister 5L 9s
Daughters 14L 9s, 9L 14s
Neutralized 4L 10s
2-Flought 23L 5s, 9L 19s
Equal tunings
Equalized (L:s = 1:1) 3\14 (257.1 ¢)
Supersoft (L:s = 4:3) 11\51 (258.8 ¢)
Soft (L:s = 3:2) 8\37 (259.5 ¢)
Semisoft (L:s = 5:3) 13\60 (260.0 ¢)
Basic (L:s = 2:1) 5\23 (260.9 ¢)
Semihard (L:s = 5:2) 12\55 (261.8 ¢)
Hard (L:s = 3:1) 7\32 (262.5 ¢)
Superhard (L:s = 4:1) 9\41 (263.4 ¢)
Collapsed (L:s = 1:0) 2\9 (266.7 ¢)

9L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 5 small steps, repeating every octave. 9L 5s is a child scale of 5L 4s, expanding it by 5 tones. Generators that produce this scale range from 257.1 ¢ to 266.7 ¢, or from 933.3 ¢ to 942.9 ¢.

The generator can be said to approximate 7/6, but just 7/6 is larger than 2\9edo, so it cannot be used as a generator. The simplest just interval that works as a generator is 36/31. Two generators are said to create a fourth like Godzilla, but in reality it is closer to 27/20, if that is considered a consonance. 9L 5s is third smallest MOS of Semiphore.

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 9L 5s
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 85.7 ¢
Major 1-mosstep M1ms L 85.7 ¢ to 133.3 ¢
2-mosstep Minor 2-mosstep m2ms L + s 133.3 ¢ to 171.4 ¢
Major 2-mosstep M2ms 2L 171.4 ¢ to 266.7 ¢
3-mosstep Diminished 3-mosstep d3ms L + 2s 133.3 ¢ to 257.1 ¢
Perfect 3-mosstep P3ms 2L + s 257.1 ¢ to 266.7 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 266.7 ¢ to 342.9 ¢
Major 4-mosstep M4ms 3L + s 342.9 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 400.0 ¢ to 428.6 ¢
Major 5-mosstep M5ms 4L + s 428.6 ¢ to 533.3 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 400.0 ¢ to 514.3 ¢
Major 6-mosstep M6ms 4L + 2s 514.3 ¢ to 533.3 ¢
7-mosstep Minor 7-mosstep m7ms 4L + 3s 533.3 ¢ to 600.0 ¢
Major 7-mosstep M7ms 5L + 2s 600.0 ¢ to 666.7 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 666.7 ¢ to 685.7 ¢
Major 8-mosstep M8ms 6L + 2s 685.7 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms 5L + 4s 666.7 ¢ to 771.4 ¢
Major 9-mosstep M9ms 6L + 3s 771.4 ¢ to 800.0 ¢
10-mosstep Minor 10-mosstep m10ms 6L + 4s 800.0 ¢ to 857.1 ¢
Major 10-mosstep M10ms 7L + 3s 857.1 ¢ to 933.3 ¢
11-mosstep Perfect 11-mosstep P11ms 7L + 4s 933.3 ¢ to 942.9 ¢
Augmented 11-mosstep A11ms 8L + 3s 942.9 ¢ to 1066.7 ¢
12-mosstep Minor 12-mosstep m12ms 7L + 5s 933.3 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 8L + 4s 1028.6 ¢ to 1066.7 ¢
13-mosstep Minor 13-mosstep m13ms 8L + 5s 1066.7 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 9L + 4s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 9L + 5s 1200.0 ¢

Generator chain

Generator chain of 9L 5s
Bright gens Scale degree Abbrev.
22 Augmented 10-mosdegree A10md
21 Augmented 7-mosdegree A7md
20 Augmented 4-mosdegree A4md
19 Augmented 1-mosdegree A1md
18 Augmented 12-mosdegree A12md
17 Augmented 9-mosdegree A9md
16 Augmented 6-mosdegree A6md
15 Augmented 3-mosdegree A3md
14 Augmented 0-mosdegree A0md
13 Augmented 11-mosdegree A11md
12 Major 8-mosdegree M8md
11 Major 5-mosdegree M5md
10 Major 2-mosdegree M2md
9 Major 13-mosdegree M13md
8 Major 10-mosdegree M10md
7 Major 7-mosdegree M7md
6 Major 4-mosdegree M4md
5 Major 1-mosdegree M1md
4 Major 12-mosdegree M12md
3 Major 9-mosdegree M9md
2 Major 6-mosdegree M6md
1 Perfect 3-mosdegree P3md
0 Perfect 0-mosdegree
Perfect 14-mosdegree		 P0md
P14md
−1 Perfect 11-mosdegree P11md
−2 Minor 8-mosdegree m8md
−3 Minor 5-mosdegree m5md
−4 Minor 2-mosdegree m2md
−5 Minor 13-mosdegree m13md
−6 Minor 10-mosdegree m10md
−7 Minor 7-mosdegree m7md
−8 Minor 4-mosdegree m4md
−9 Minor 1-mosdegree m1md
−10 Minor 12-mosdegree m12md
−11 Minor 9-mosdegree m9md
−12 Minor 6-mosdegree m6md
−13 Diminished 3-mosdegree d3md
−14 Diminished 14-mosdegree d14md
−15 Diminished 11-mosdegree d11md
−16 Diminished 8-mosdegree d8md
−17 Diminished 5-mosdegree d5md
−18 Diminished 2-mosdegree d2md
−19 Diminished 13-mosdegree d13md
−20 Diminished 10-mosdegree d10md
−21 Diminished 7-mosdegree d7md
−22 Diminished 4-mosdegree d4md

Modes

Scale degrees of the modes of 9L 5s
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
13|0 1 LLsLLsLLsLLsLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Perf.
12|1 4 LLsLLsLLsLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Perf.
11|2 7 LLsLLsLsLLsLLs Perf. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
10|3 10 LLsLsLLsLLsLLs Perf. Maj. Maj. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
9|4 13 LsLLsLLsLLsLLs Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Maj. Perf.
8|5 2 LsLLsLLsLLsLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Maj. Perf. Maj. Min. Perf.
7|6 5 LsLLsLLsLsLLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Maj. Min. Maj. Min. Perf. Maj. Min. Perf.
6|7 8 LsLLsLsLLsLLsL Perf. Maj. Min. Perf. Maj. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
5|8 11 LsLsLLsLLsLLsL Perf. Maj. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
4|9 14 sLLsLLsLLsLLsL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Maj. Min. Perf.
3|10 3 sLLsLLsLLsLsLL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Maj. Min. Perf. Min. Min. Perf.
2|11 6 sLLsLLsLsLLsLL Perf. Min. Min. Perf. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Perf.
1|12 9 sLLsLsLLsLLsLL Perf. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.
0|13 12 sLsLLsLLsLLsLL Perf. Min. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 9L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
3\14 257.143 942.857 1:1 1.000 Equalized 9L 5s
17\79 258.228 941.772 6:5 1.200
14\65 258.462 941.538 5:4 1.250
25\116 258.621 941.379 9:7 1.286
11\51 258.824 941.176 4:3 1.333 Supersoft 9L 5s
30\139 258.993 941.007 11:8 1.375
19\88 259.091 940.909 7:5 1.400
27\125 259.200 940.800 10:7 1.429
8\37 259.459 940.541 3:2 1.500 Soft 9L 5s
29\134 259.701 940.299 11:7 1.571
21\97 259.794 940.206 8:5 1.600
34\157 259.873 940.127 13:8 1.625
13\60 260.000 940.000 5:3 1.667 Semisoft 9L 5s
31\143 260.140 939.860 12:7 1.714
18\83 260.241 939.759 7:4 1.750
23\106 260.377 939.623 9:5 1.800
5\23 260.870 939.130 2:1 2.000 Basic 9L 5s
Scales with tunings softer than this are proper
22\101 261.386 938.614 9:4 2.250
17\78 261.538 938.462 7:3 2.333
29\133 261.654 938.346 12:5 2.400
12\55 261.818 938.182 5:2 2.500 Semihard 9L 5s
31\142 261.972 938.028 13:5 2.600
19\87 262.069 937.931 8:3 2.667
26\119 262.185 937.815 11:4 2.750
7\32 262.500 937.500 3:1 3.000 Hard 9L 5s
23\105 262.857 937.143 10:3 3.333
16\73 263.014 936.986 7:2 3.500
25\114 263.158 936.842 11:3 3.667
9\41 263.415 936.585 4:1 4.000 Superhard 9L 5s
20\91 263.736 936.264 9:2 4.500
11\50 264.000 936.000 5:1 5.000
13\59 264.407 935.593 6:1 6.000
2\9 266.667 933.333 1:0 → ∞ Collapsed 9L 5s
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