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6L 5s

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6L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 6 large steps and 5 small steps, repeating every octave. 6L 5s is a child scale of 5L 1s, expanding it by 5 tones. Generators that produce this scale range from 981.8 ¢ to 1000 ¢, or from 200 ¢ to 218.2 ¢. The name amsochromic has been proposed for this scale by Lériendil, originally assigned to 5L 6s by Praveen Venkataramana and standing for "acute major second chromatic"; the name was moved to 6L 5s due to the existing use of "slentonic" for the other MOS.

↖ 5L 4s ↑ 6L 4s 7L 4s ↗
← 5L 5s 6L 5s 7L 5s →
↙ 5L 6s ↓ 6L 6s 7L 6s ↘
Scale structure
Step pattern LLsLsLsLsLs
sLsLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 9\11 to 5\6 (981.8 ¢ to 1000.0 ¢)
Dark 1\6 to 2\11 (200.0 ¢ to 218.2 ¢)
TAMNAMS information
Related to 5L 1s (machinoid)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 1s
Sister 5L 6s
Daughters 11L 6s, 6L 11s
Neutralized 1L 10s
2-Flought 17L 5s, 6L 16s
Equal tunings
Equalized (L:s = 1:1) 9\11 (981.8 ¢)
Supersoft (L:s = 4:3) 32\39 (984.6 ¢)
Soft (L:s = 3:2) 23\28 (985.7 ¢)
Semisoft (L:s = 5:3) 37\45 (986.7 ¢)
Basic (L:s = 2:1) 14\17 (988.2 ¢)
Semihard (L:s = 5:2) 33\40 (990.0 ¢)
Hard (L:s = 3:1) 19\23 (991.3 ¢)
Superhard (L:s = 4:1) 24\29 (993.1 ¢)
Collapsed (L:s = 1:0) 5\6 (1000.0 ¢)
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This MOS has a harmonic entropy minimum (Baldy) which is highly improper (L = 8, s = 1) in an optimal tuning, However, its saving grace is that it at least has index 2 in temperaments generated by wide fifths like superpyth (2.3.7) and pentacircle (2.3.11/7.13/11)[clarification needed].

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 6L 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 109.1 ¢
Major 1-mosstep M1ms L 109.1 ¢ to 200.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 200.0 ¢ to 218.2 ¢
Augmented 2-mosstep A2ms 2L 218.2 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 200.0 ¢ to 327.3 ¢
Major 3-mosstep M3ms 2L + s 327.3 ¢ to 400.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 400.0 ¢ to 436.4 ¢
Major 4-mosstep M4ms 3L + s 436.4 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 400.0 ¢ to 545.5 ¢
Major 5-mosstep M5ms 3L + 2s 545.5 ¢ to 600.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 600.0 ¢ to 654.5 ¢
Major 6-mosstep M6ms 4L + 2s 654.5 ¢ to 800.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 600.0 ¢ to 763.6 ¢
Major 7-mosstep M7ms 4L + 3s 763.6 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 800.0 ¢ to 872.7 ¢
Major 8-mosstep M8ms 5L + 3s 872.7 ¢ to 1000.0 ¢
9-mosstep Diminished 9-mosstep d9ms 4L + 5s 800.0 ¢ to 981.8 ¢
Perfect 9-mosstep P9ms 5L + 4s 981.8 ¢ to 1000.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 1000.0 ¢ to 1090.9 ¢
Major 10-mosstep M10ms 6L + 4s 1090.9 ¢ to 1200.0 ¢
11-mosstep Perfect 11-mosstep P11ms 6L + 5s 1200.0 ¢

Generator chain

Generator chain of 6L 5s
Bright gens Scale degree Abbrev.
16 Augmented 1-mosdegree A1md
15 Augmented 3-mosdegree A3md
14 Augmented 5-mosdegree A5md
13 Augmented 7-mosdegree A7md
12 Augmented 9-mosdegree A9md
11 Augmented 0-mosdegree A0md
10 Augmented 2-mosdegree A2md
9 Major 4-mosdegree M4md
8 Major 6-mosdegree M6md
7 Major 8-mosdegree M8md
6 Major 10-mosdegree M10md
5 Major 1-mosdegree M1md
4 Major 3-mosdegree M3md
3 Major 5-mosdegree M5md
2 Major 7-mosdegree M7md
1 Perfect 9-mosdegree P9md
0 Perfect 0-mosdegree
Perfect 11-mosdegree		 P0md
P11md
−1 Perfect 2-mosdegree P2md
−2 Minor 4-mosdegree m4md
−3 Minor 6-mosdegree m6md
−4 Minor 8-mosdegree m8md
−5 Minor 10-mosdegree m10md
−6 Minor 1-mosdegree m1md
−7 Minor 3-mosdegree m3md
−8 Minor 5-mosdegree m5md
−9 Minor 7-mosdegree m7md
−10 Diminished 9-mosdegree d9md
−11 Diminished 11-mosdegree d11md
−12 Diminished 2-mosdegree d2md
−13 Diminished 4-mosdegree d4md
−14 Diminished 6-mosdegree d6md
−15 Diminished 8-mosdegree d8md
−16 Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 6L 5s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11
10|0 1 LLsLsLsLsLs Perf. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
9|1 10 LsLLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
8|2 8 LsLsLLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
7|3 6 LsLsLsLLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Perf.
6|4 4 LsLsLsLsLLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Perf.
5|5 2 LsLsLsLsLsL Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
4|6 11 sLLsLsLsLsL Perf. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
3|7 9 sLsLLsLsLsL Perf. Min. Perf. Min. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
2|8 7 sLsLsLLsLsL Perf. Min. Perf. Min. Min. Min. Min. Maj. Min. Perf. Min. Perf.
1|9 5 sLsLsLsLLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|10 3 sLsLsLsLsLL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Dim. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 6L 5s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\11 981.818 218.182 1:1 1.000 Equalized 6L 5s
50\61 983.607 216.393 6:5 1.200
41\50 984.000 216.000 5:4 1.250
73\89 984.270 215.730 9:7 1.286
32\39 984.615 215.385 4:3 1.333 Supersoft 6L 5s
87\106 984.906 215.094 11:8 1.375
55\67 985.075 214.925 7:5 1.400
78\95 985.263 214.737 10:7 1.429
23\28 985.714 214.286 3:2 1.500 Soft 6L 5s
83\101 986.139 213.861 11:7 1.571
60\73 986.301 213.699 8:5 1.600
97\118 986.441 213.559 13:8 1.625
37\45 986.667 213.333 5:3 1.667 Semisoft 6L 5s
88\107 986.916 213.084 12:7 1.714
51\62 987.097 212.903 7:4 1.750
65\79 987.342 212.658 9:5 1.800
14\17 988.235 211.765 2:1 2.000 Basic 6L 5s
Scales with tunings softer than this are proper
61\74 989.189 210.811 9:4 2.250
47\57 989.474 210.526 7:3 2.333
80\97 989.691 210.309 12:5 2.400
33\40 990.000 210.000 5:2 2.500 Semihard 6L 5s
85\103 990.291 209.709 13:5 2.600
52\63 990.476 209.524 8:3 2.667
71\86 990.698 209.302 11:4 2.750
19\23 991.304 208.696 3:1 3.000 Hard 6L 5s
62\75 992.000 208.000 10:3 3.333
43\52 992.308 207.692 7:2 3.500
67\81 992.593 207.407 11:3 3.667
24\29 993.103 206.897 4:1 4.000 Superhard 6L 5s
53\64 993.750 206.250 9:2 4.500
29\35 994.286 205.714 5:1 5.000
34\41 995.122 204.878 6:1 6.000
5\6 1000.000 200.000 1:0 → ∞ Collapsed 6L 5s
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