10L 5s

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Scale structure
Step pattern LLsLLsLLsLLsLLs
sLLsLLsLLsLLsLL
Equave 2/1 (1200.0 ¢)
Period 1\5 (240.0 ¢)
Generator size
Bright 1\15 to 1\10 (80.0 ¢ to 120.0 ¢)
Dark 1\10 to 2\15 (120.0 ¢ to 160.0 ¢)
TAMNAMS information
Related to 5L 5s (pentawood)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 5L 5s
Sister 5L 10s
Daughters 15L 10s, 10L 15s
Neutralized 5L 10s
2-Flought 25L 5s, 10L 20s
Equal tunings
Equalized (L:s = 1:1) 1\15 (80.0 ¢)
Supersoft (L:s = 4:3) 4\55 (87.3 ¢)
Soft (L:s = 3:2) 3\40 (90.0 ¢)
Semisoft (L:s = 5:3) 5\65 (92.3 ¢)
Basic (L:s = 2:1) 2\25 (96.0 ¢)
Semihard (L:s = 5:2) 5\60 (100.0 ¢)
Hard (L:s = 3:1) 3\35 (102.9 ¢)
Superhard (L:s = 4:1) 4\45 (106.7 ¢)
Collapsed (L:s = 1:0) 1\10 (120.0 ¢)

10L 5s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 5 small steps, with a period of 2 large steps and 1 small step that repeats every 240.0 ¢, or 5 times every octave. 10L 5s is a child scale of 5L 5s, expanding it by 5 tones. Generators that produce this scale range from 80 ¢ to 120 ¢, or from 120 ¢ to 160 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Theory

Intervals

Intervals of 10L 5s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 80.0 ¢
Perfect 1-mosstep P1ms L 80.0 ¢ to 120.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 120.0 ¢ to 160.0 ¢
Augmented 2-mosstep A2ms 2L 160.0 ¢ to 240.0 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 240.0 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 240.0 ¢ to 320.0 ¢
Perfect 4-mosstep P4ms 3L + s 320.0 ¢ to 360.0 ¢
5-mosstep Perfect 5-mosstep P5ms 3L + 2s 360.0 ¢ to 400.0 ¢
Augmented 5-mosstep A5ms 4L + s 400.0 ¢ to 480.0 ¢
6-mosstep Perfect 6-mosstep P6ms 4L + 2s 480.0 ¢
7-mosstep Diminished 7-mosstep d7ms 4L + 3s 480.0 ¢ to 560.0 ¢
Perfect 7-mosstep P7ms 5L + 2s 560.0 ¢ to 600.0 ¢
8-mosstep Perfect 8-mosstep P8ms 5L + 3s 600.0 ¢ to 640.0 ¢
Augmented 8-mosstep A8ms 6L + 2s 640.0 ¢ to 720.0 ¢
9-mosstep Perfect 9-mosstep P9ms 6L + 3s 720.0 ¢
10-mosstep Diminished 10-mosstep d10ms 6L + 4s 720.0 ¢ to 800.0 ¢
Perfect 10-mosstep P10ms 7L + 3s 800.0 ¢ to 840.0 ¢
11-mosstep Perfect 11-mosstep P11ms 7L + 4s 840.0 ¢ to 880.0 ¢
Augmented 11-mosstep A11ms 8L + 3s 880.0 ¢ to 960.0 ¢
12-mosstep Perfect 12-mosstep P12ms 8L + 4s 960.0 ¢
13-mosstep Diminished 13-mosstep d13ms 8L + 5s 960.0 ¢ to 1040.0 ¢
Perfect 13-mosstep P13ms 9L + 4s 1040.0 ¢ to 1080.0 ¢
14-mosstep Perfect 14-mosstep P14ms 9L + 5s 1080.0 ¢ to 1120.0 ¢
Augmented 14-mosstep A14ms 10L + 4s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 10L + 5s 1200.0 ¢

Generator chain

Generator chain of 10L 5s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
4 Augmented 1-mosdegree A1md Augmented 4-mosdegree A4md Augmented 7-mosdegree A7md Augmented 10-mosdegree A10md Augmented 13-mosdegree A13md
3 Augmented 0-mosdegree A0md Augmented 3-mosdegree A3md Augmented 6-mosdegree A6md Augmented 9-mosdegree A9md Augmented 12-mosdegree A12md
2 Augmented 2-mosdegree A2md Augmented 5-mosdegree A5md Augmented 8-mosdegree A8md Augmented 11-mosdegree A11md Augmented 14-mosdegree A14md
1 Perfect 1-mosdegree P1md Perfect 4-mosdegree P4md Perfect 7-mosdegree P7md Perfect 10-mosdegree P10md Perfect 13-mosdegree P13md
0 Perfect 0-mosdegree
Perfect 3-mosdegree		 P0md
P3md		 Perfect 3-mosdegree
Perfect 6-mosdegree		 P3md
P6md		 Perfect 6-mosdegree
Perfect 9-mosdegree		 P6md
P9md		 Perfect 9-mosdegree
Perfect 12-mosdegree		 P9md
P12md		 Perfect 12-mosdegree
Perfect 15-mosdegree		 P12md
P15md
−1 Perfect 2-mosdegree P2md Perfect 5-mosdegree P5md Perfect 8-mosdegree P8md Perfect 11-mosdegree P11md Perfect 14-mosdegree P14md
−2 Diminished 1-mosdegree d1md Diminished 4-mosdegree d4md Diminished 7-mosdegree d7md Diminished 10-mosdegree d10md Diminished 13-mosdegree d13md
−3 Diminished 3-mosdegree d3md Diminished 6-mosdegree d6md Diminished 9-mosdegree d9md Diminished 12-mosdegree d12md Diminished 15-mosdegree d15md
−4 Diminished 2-mosdegree d2md Diminished 5-mosdegree d5md Diminished 8-mosdegree d8md Diminished 11-mosdegree d11md Diminished 14-mosdegree d14md

Modes

Modes of 10L 5s
UDP Cyclic
order		 Step
pattern
10|0(5) 1 LLsLLsLLsLLsLLs
5|5(5) 2 LsLLsLLsLLsLLsL
0|10(5) 3 sLLsLLsLLsLLsLL

Scale tree

Scale tree and tuning spectrum of 10L 5s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 80.000 160.000 1:1 1.000 Equalized 10L 5s
6\85 84.706 155.294 6:5 1.200
5\70 85.714 154.286 5:4 1.250
9\125 86.400 153.600 9:7 1.286
4\55 87.273 152.727 4:3 1.333 Supersoft 10L 5s
11\150 88.000 152.000 11:8 1.375
7\95 88.421 151.579 7:5 1.400
10\135 88.889 151.111 10:7 1.429
3\40 90.000 150.000 3:2 1.500 Soft 10L 5s
11\145 91.034 148.966 11:7 1.571
8\105 91.429 148.571 8:5 1.600
13\170 91.765 148.235 13:8 1.625
5\65 92.308 147.692 5:3 1.667 Semisoft 10L 5s
12\155 92.903 147.097 12:7 1.714
7\90 93.333 146.667 7:4 1.750
9\115 93.913 146.087 9:5 1.800
2\25 96.000 144.000 2:1 2.000 Basic 10L 5s
9\110 98.182 141.818 9:4 2.250
7\85 98.824 141.176 7:3 2.333
12\145 99.310 140.690 12:5 2.400
5\60 100.000 140.000 5:2 2.500 Semihard 10L 5s
13\155 100.645 139.355 13:5 2.600
8\95 101.053 138.947 8:3 2.667
11\130 101.538 138.462 11:4 2.750
3\35 102.857 137.143 3:1 3.000 Hard 10L 5s
10\115 104.348 135.652 10:3 3.333
7\80 105.000 135.000 7:2 3.500
11\125 105.600 134.400 11:3 3.667
4\45 106.667 133.333 4:1 4.000 Superhard 10L 5s
9\100 108.000 132.000 9:2 4.500
5\55 109.091 130.909 5:1 5.000
6\65 110.769 129.231 6:1 6.000
1\10 120.000 120.000 1:0 → ∞ Collapsed 10L 5s
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