5L 6s

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↖ 4L 5s ↑5L 5s 6L 5s ↗
← 4L 6s5L 6s 6L 6s →
↙ 4L 7s ↓5L 7s 6L 7s ↘
 
┌╥┬╥┬╥┬╥┬╥┬┬┐
│║│║│║│║│║│││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLss
ssLsLsLsLsL
Equave 2/1 (1200.0¢)
Period 1\11 (109.1¢)
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.


Intervals of 5L 6s
Intervals Steps subtended Range in cents Average of HE
(from HE Calc) 		Min of HE
Generic[1] Specific[2] Abbrev.[3]
0-mosstep Perfect 0-mosstep P0ms 0 0.0¢ ~2.4654 nats ~2.4654 nats
1-mosstep Minor 1-mosstep m1ms s 0.0¢ to 109.1¢ ~4.7415 nats ~4.6849 nats
Major 1-mosstep M1ms L 109.1¢ to 240.0¢ ~4.6211 nats ~4.5938 nats
2-mosstep Diminished 2-mosstep d2ms 2s 0.0¢ to 218.2¢ ~4.6299 nats ~4.5904 nats
Perfect 2-mosstep P2ms L + s 218.2¢ to 240.0¢ ~4.5842 nats ~4.5840 nats
3-mosstep Minor 3-mosstep m3ms L + 2s 240.0¢ to 327.3¢ ~4.5601 nats ~4.5379 nats
Major 3-mosstep M3ms 2L + s 327.3¢ to 480.0¢ ~4.5666 nats ~4.4854 nats
4-mosstep Minor 4-mosstep m4ms L + 3s 240.0¢ to 436.4¢ ~4.5568 nats ~4.4877 nats
Major 4-mosstep M4ms 2L + 2s 436.4¢ to 480.0¢ ~4.6112 nats ~4.6025 nats
5-mosstep Minor 5-mosstep m5ms 2L + 3s 480.0¢ to 545.5¢ ~4.5513 nats ~4.4076 nats
Major 5-mosstep M5ms 3L + 2s 545.5¢ to 720.0¢ ~4.5897 nats ~4.5598 nats
6-mosstep Minor 6-mosstep m6ms 2L + 4s 480.0¢ to 654.5¢ ~4.5919 nats ~4.5596 nats
Major 6-mosstep M6ms 3L + 3s 654.5¢ to 720.0¢ ~4.5105 nats ~4.2378 nats
7-mosstep Minor 7-mosstep m7ms 3L + 4s 720.0¢ to 763.6¢ ~4.6417 nats ~4.6332 nats
Major 7-mosstep M7ms 4L + 3s 763.6¢ to 960.0¢ ~4.5711 nats ~4.4505 nats
8-mosstep Minor 8-mosstep m8ms 3L + 5s 720.0¢ to 872.7¢ ~4.5958 nats ~4.5720 nats
Major 8-mosstep M8ms 4L + 4s 872.7¢ to 960.0¢ ~4.5091 nats ~4.4208 nats
9-mosstep Perfect 9-mosstep P9ms 4L + 5s 960.0¢ to 981.8¢ ~4.5350 nats ~4.5305 nats
Augmented 9-mosstep A9ms 5L + 4s 981.8¢ to 1200.0¢ ~4.6007 nats ~4.5800 nats
10-mosstep Minor 10-mosstep m10ms 4L + 6s 960.0¢ to 1090.9¢ ~4.5995 nats ~4.5784 nats
Major 10-mosstep M10ms 5L + 5s 1090.9¢ to 1200.0¢ ~4.6663 nats ~4.6227 nats
11-mosstep Perfect 11-mosstep P11ms 5L + 6s 1200.0¢ ~3.3273 nats ~3.3273 nats

  1. Generic intervals are denoted solely by the number of steps they subtend.
  2. Specific intervals denote whether an interval is major, minor, augmented, perfect, or diminished.
  3. Abbreviations can be further shortened to 'ms' if context allows.

Modes

Scale degree qualities of 5L 6s modes
UDP Rotational 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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