5L 6s

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↖4L 5s↑5L 5s 6L 5s↗
←4L 6s5L 6s6L 6s→
↙4L 7s↓5L 7s 6L 7s↘
Brightest mode LsLsLsLsLss
Period 2/1
Range for bright generator 2\11 (218.2¢) to 1\5 (240¢)
Range for dark generator 4\5 (960¢) to 9\11 (981.8¢)
Parent MOS 5L 1s
Sister MOS 6L 5s
Daughter MOSes 11L 5s, 5L 11s
Equal tunings
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¢)
Semihard (L:s = 5:2) 7\37 (227¢)
Hard (L:s = 3:1) 4\21 (228.6¢)
Superhard (L:s = 4:1) 5\26 (230.8¢)
Brightest-mode tunings on xenpaper
Supersoft Soft Semisoft Basic Semihard Hard Superhard

5L 6s is an 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.

Modes

Modes of 5L 6s
UDP Rotational order Step pattern
10|0 1 LsLsLsLsLss
9|1 3 LsLsLsLssLs
8|2 5 LsLsLssLsLs
7|3 7 LsLssLsLsLs
6|4 9 LssLsLsLsLs
5|5 11 sLsLsLsLsLs
4|6 2 sLsLsLsLssL
3|7 4 sLsLsLssLsL
2|8 6 sLsLssLsLsL
1|9 8 sLssLsLsLsL
0|10 10 ssLsLsLsLsL

Scale tree

Scale tree and tuning spectrum of 5L 6s
Generator (in steps of 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
Bright generators smaller 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