5L 6s

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↖ 4L 5s↑ 5L 5s 6L 5s ↗
← 4L 6s5L 6s6L 6s →
↙ 4L 7s↓ 5L 7s 6L 7s ↘
 
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Scale structure
Step pattern LsLsLsLsLss
ssLsLsLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 2\11 to 1\5 (218.2¢ to 240.0¢)
Dark 4\5 to 9\11 (960.0¢ to 981.8¢)
TAMNAMS information
Descends from 5L 1s (machinoid)
Ancestor's step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 5L 1s
Sister 6L 5s
Daughters 11L 5s, 5L 11s
Neutralized 10L 1s
2-Flought 16L 6s, 5L 17s
Equal tunings
Equalized (L:s = 1:1) 2\11 (218.2¢)
Supersoft (L:s = 4:3) 7\38 (221.1¢)
Soft (L:s = 3:2) 5\27 (222.2¢)
Semisoft (L:s = 5:3) 8\43 (223.3¢)
Basic (L:s = 2:1) 3\16 (225.0¢)
Semihard (L:s = 5:2) 7\37 (227.0¢)
Hard (L:s = 3:1) 4\21 (228.6¢)
Superhard (L:s = 4:1) 5\26 (230.8¢)
Collapsed (L:s = 1:0) 1\5 (240.0¢)

5L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 6 small steps, repeating every octave. 5L 6s is a child scale of 5L 1s, expanding it by 5 tones. Generators that produce this scale range from 218.2¢ to 240¢, or from 960¢ to 981.8¢.

This pattern has multiple significant harmonic entropy minima, but they are all improper. The only saving grace for it is that is has harmonic entropy minima where the ratio between the large and small steps is optimal for melody, and that the generator for these scales is less than 6 cents flat of 8/7. The saving grace of the more lopsided scales is that a syntonic fifth is three generators up from the root. The name for this MOS pattern is p-chro machinoid, although the alternative name mothroid was given by CompactStar as part of their temperament-centric MOS naming system (TCMNAMS).

Scale properties

Intervals

The intervals of 5L 6s 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 5L 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 109.1¢
Major 1-mosstep M1ms L 109.1¢ to 240.0¢
2-mosstep Diminished 2-mosstep d2ms 2s 0.0¢ to 218.2¢
Perfect 2-mosstep P2ms L + s 218.2¢ to 240.0¢
3-mosstep Minor 3-mosstep m3ms L + 2s 240.0¢ to 327.3¢
Major 3-mosstep M3ms 2L + s 327.3¢ to 480.0¢
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0¢ to 436.4¢
Major 4-mosstep M4ms 2L + 2s 436.4¢ to 480.0¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 480.0¢ to 545.5¢
Major 5-mosstep M5ms 3L + 2s 545.5¢ to 720.0¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 480.0¢ to 654.5¢
Major 6-mosstep M6ms 3L + 3s 654.5¢ to 720.0¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 720.0¢ to 763.6¢
Major 7-mosstep M7ms 4L + 3s 763.6¢ to 960.0¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 720.0¢ to 872.7¢
Major 8-mosstep M8ms 4L + 4s 872.7¢ to 960.0¢
9-mosstep Perfect 9-mosstep P9ms 4L + 5s 960.0¢ to 981.8¢
Augmented 9-mosstep A9ms 5L + 4s 981.8¢ to 1200.0¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 960.0¢ to 1090.9¢
Major 10-mosstep M10ms 5L + 5s 1090.9¢ to 1200.0¢
11-mosstep Perfect 11-mosstep P11ms 5L + 6s 1200.0¢

Generator chain

A chain of bright generators, each a perfect 2-mosstep, produces the following scale degrees. A chain of 11 bright generators contains the scale degrees of one of the modes of 5L 6s. Expanding the chain to 16 scale degrees produces the modes of either 11L 5s (for soft-of-basic tunings) or 5L 11s (for hard-of-basic tunings).

Generator chain of 5L 6s
Bright gens Scale Degree Abbrev.
15 Augmented 8-mosdegree A8md
14 Augmented 6-mosdegree A6md
13 Augmented 4-mosdegree A4md
12 Augmented 2-mosdegree A2md
11 Augmented 0-mosdegree A0md
10 Augmented 9-mosdegree A9md
9 Major 7-mosdegree M7md
8 Major 5-mosdegree M5md
7 Major 3-mosdegree M3md
6 Major 1-mosdegree M1md
5 Major 10-mosdegree M10md
4 Major 8-mosdegree M8md
3 Major 6-mosdegree M6md
2 Major 4-mosdegree M4md
1 Perfect 2-mosdegree P2md
0 Perfect 0-mosdegree
Perfect 11-mosdegree		 P0md
P11md
-1 Perfect 9-mosdegree P9md
-2 Minor 7-mosdegree m7md
-3 Minor 5-mosdegree m5md
-4 Minor 3-mosdegree m3md
-5 Minor 1-mosdegree m1md
-6 Minor 10-mosdegree m10md
-7 Minor 8-mosdegree m8md
-8 Minor 6-mosdegree m6md
-9 Minor 4-mosdegree m4md
-10 Diminished 2-mosdegree d2md
-11 Diminished 11-mosdegree d11md
-12 Diminished 9-mosdegree d9md
-13 Diminished 7-mosdegree d7md
-14 Diminished 5-mosdegree d5md
-15 Diminished 3-mosdegree d3md

Modes

Scale degrees of the modes of 5L 6s 
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11
10|0 1 LsLsLsLsLss Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf.
9|1 3 LsLsLsLssLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
8|2 5 LsLsLssLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf.
7|3 7 LsLssLsLsLs Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
6|4 9 LssLsLsLsLs Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
5|5 11 sLsLsLsLsLs Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf.
4|6 2 sLsLsLsLssL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf.
3|7 4 sLsLsLssLsL Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf.
2|8 6 sLsLssLsLsL Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf.
1|9 8 sLssLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|10 10 ssLsLsLsLsL Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.

Scale tree

Scale Tree and Tuning Spectrum of 5L 6s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
2\11 218.182 981.818 1:1 1.000 Equalized 5L 6s
11\60 220.000 980.000 6:5 1.200
9\49 220.408 979.592 5:4 1.250
16\87 220.690 979.310 9:7 1.286
7\38 221.053 978.947 4:3 1.333 Supersoft 5L 6s
19\103 221.359 978.641 11:8 1.375
12\65 221.538 978.462 7:5 1.400
17\92 221.739 978.261 10:7 1.429
5\27 222.222 977.778 3:2 1.500 Soft 5L 6s
18\97 222.680 977.320 11:7 1.571
13\70 222.857 977.143 8:5 1.600
21\113 223.009 976.991 13:8 1.625
8\43 223.256 976.744 5:3 1.667 Semisoft 5L 6s
19\102 223.529 976.471 12:7 1.714
11\59 223.729 976.271 7:4 1.750
14\75 224.000 976.000 9:5 1.800
3\16 225.000 975.000 2:1 2.000 Basic 5L 6s
Scales with tunings softer than this are proper
13\69 226.087 973.913 9:4 2.250
10\53 226.415 973.585 7:3 2.333
17\90 226.667 973.333 12:5 2.400
7\37 227.027 972.973 5:2 2.500 Semihard 5L 6s
18\95 227.368 972.632 13:5 2.600
11\58 227.586 972.414 8:3 2.667
15\79 227.848 972.152 11:4 2.750
4\21 228.571 971.429 3:1 3.000 Hard 5L 6s
13\68 229.412 970.588 10:3 3.333
9\47 229.787 970.213 7:2 3.500
14\73 230.137 969.863 11:3 3.667
5\26 230.769 969.231 4:1 4.000 Superhard 5L 6s
11\57 231.579 968.421 9:2 4.500 Cynder
6\31 232.258 967.742 5:1 5.000 Mothra
7\36 233.333 966.667 6:1 6.000 Slendric, ↓ Rodan
1\5 240.000 960.000 1:0 → ∞ Collapsed 5L 6s
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