6L 5s

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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
Descends from 5L 1s (machinoid)
Ancestor's step ratio range 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 ¢)

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 ¢.

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 syntonic temperaments with 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 diatonic interval categories.

Intervals

The intervals of 6L 5s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 11-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

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

A chain of bright generators, each a perfect 9-mosstep, produces the following scale degrees. A chain of 11 bright generators contains the scale degrees of one of the modes of 6L 5s. Expanding the chain to 17 scale degrees produces the modes of either 11L 6s (for soft-of-basic tunings) or 6L 11s (for hard-of-basic tunings).

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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