10L 5s (21/10-equivalent)

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↖ 9L 4s⟨21/10⟩ ↑ 10L 4s⟨21/10⟩ 11L 4s⟨21/10⟩ ↗
← 9L 5s⟨21/10⟩ 10L 5s (21/10-equivalent) 11L 5s⟨21/10⟩ →
↙ 9L 6s⟨21/10⟩ ↓ 10L 6s⟨21/10⟩ 11L 6s⟨21/10⟩ ↘ 
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Scale structure
Step pattern LLsLLsLLsLLsLLs
sLLsLLsLLsLLsLL
Equave 21/10 (1284.5 ¢)
Period 1\5 (256.9 ¢)
Generator size(ed21/10)
Bright 1\15 to 1\10 (85.6 ¢ to 128.4 ¢)
Dark 1\10 to 2\15 (128.4 ¢ to 171.3 ¢)
Related MOS scales
Parent 5L 5s⟨21/10⟩
Sister 5L 10s⟨21/10⟩
Daughters 15L 10s⟨21/10⟩, 10L 15s⟨21/10⟩
Neutralized 5L 10s⟨21/10⟩
2-Flought 25L 5s⟨21/10⟩, 10L 20s⟨21/10⟩
Equal tunings(ed21/10)
Equalized (L:s = 1:1) 1\15 (85.6 ¢)
Supersoft (L:s = 4:3) 4\55 (93.4 ¢)
Soft (L:s = 3:2) 3\40 (96.3 ¢)
Semisoft (L:s = 5:3) 5\65 (98.8 ¢)
Basic (L:s = 2:1) 2\25 (102.8 ¢)
Semihard (L:s = 5:2) 5\60 (107.0 ¢)
Hard (L:s = 3:1) 3\35 (110.1 ¢)
Superhard (L:s = 4:1) 4\45 (114.2 ¢)
Collapsed (L:s = 1:0) 1\10 (128.4 ¢)

10L 5s⟨21/10⟩ is a 21/10-equivalent (non-octave) 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 256.9 ¢, or 5 times every interval of 21/10 (1284.5 ¢). Generators that produce this scale range from 85.6 ¢ to 128.4 ¢, or from 128.4 ¢ to 171.3 ¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

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

Intervals of 10L 5s⟨21/10⟩
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 85.6 ¢
Perfect 1-mosstep P1ms L 85.6 ¢ to 128.4 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 128.4 ¢ to 171.3 ¢
Augmented 2-mosstep A2ms 2L 171.3 ¢ to 256.9 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 256.9 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 256.9 ¢ to 342.5 ¢
Perfect 4-mosstep P4ms 3L + s 342.5 ¢ to 385.3 ¢
5-mosstep Perfect 5-mosstep P5ms 3L + 2s 385.3 ¢ to 428.2 ¢
Augmented 5-mosstep A5ms 4L + s 428.2 ¢ to 513.8 ¢
6-mosstep Perfect 6-mosstep P6ms 4L + 2s 513.8 ¢
7-mosstep Diminished 7-mosstep d7ms 4L + 3s 513.8 ¢ to 599.4 ¢
Perfect 7-mosstep P7ms 5L + 2s 599.4 ¢ to 642.2 ¢
8-mosstep Perfect 8-mosstep P8ms 5L + 3s 642.2 ¢ to 685.0 ¢
Augmented 8-mosstep A8ms 6L + 2s 685.0 ¢ to 770.7 ¢
9-mosstep Perfect 9-mosstep P9ms 6L + 3s 770.7 ¢
10-mosstep Diminished 10-mosstep d10ms 6L + 4s 770.7 ¢ to 856.3 ¢
Perfect 10-mosstep P10ms 7L + 3s 856.3 ¢ to 899.1 ¢
11-mosstep Perfect 11-mosstep P11ms 7L + 4s 899.1 ¢ to 941.9 ¢
Augmented 11-mosstep A11ms 8L + 3s 941.9 ¢ to 1027.6 ¢
12-mosstep Perfect 12-mosstep P12ms 8L + 4s 1027.6 ¢
13-mosstep Diminished 13-mosstep d13ms 8L + 5s 1027.6 ¢ to 1113.2 ¢
Perfect 13-mosstep P13ms 9L + 4s 1113.2 ¢ to 1156.0 ¢
14-mosstep Perfect 14-mosstep P14ms 9L + 5s 1156.0 ¢ to 1198.8 ¢
Augmented 14-mosstep A14ms 10L + 4s 1198.8 ¢ to 1284.5 ¢
15-mosstep Perfect 15-mosstep P15ms 10L + 5s 1284.5 ¢

Generator chain

Generator chain of 10L 5s⟨21/10⟩
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

Scale degrees of the modes of 10L 5s⟨21/10⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
10|0(5) 1 LLsLLsLLsLLsLLs Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf. Perf. Aug. Perf.
5|5(5) 2 LsLLsLLsLLsLLsL Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf. Perf.
0|10(5) 3 sLLsLLsLLsLLsLL Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf. Dim. Perf. Perf.

Scale tree

Scale tree and tuning spectrum of 10L 5s⟨21/10⟩
Generator(ed21/10) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\15 85.631 171.262 1:1 1.000 Equalized 10L 5s⟨21/10⟩
6\85 90.668 166.225 6:5 1.200
5\70 91.748 165.146 5:4 1.250
9\125 92.482 164.412 9:7 1.286
4\55 93.416 163.478 4:3 1.333 Supersoft 10L 5s⟨21/10⟩
11\150 94.194 162.699 11:8 1.375
7\95 94.645 162.248 7:5 1.400
10\135 95.146 161.748 10:7 1.429
3\40 96.335 160.558 3:2 1.500 Soft 10L 5s⟨21/10⟩
11\145 97.442 159.451 11:7 1.571
8\105 97.864 159.029 8:5 1.600
13\170 98.224 158.669 13:8 1.625
5\65 98.805 158.088 5:3 1.667 Semisoft 10L 5s⟨21/10⟩
12\155 99.443 157.451 12:7 1.714
7\90 99.903 156.990 7:4 1.750
9\115 100.524 156.370 9:5 1.800
2\25 102.757 154.136 2:1 2.000 Basic 10L 5s⟨21/10⟩
9\110 105.093 151.801 9:4 2.250
7\85 105.780 151.114 7:3 2.333
12\145 106.301 150.593 12:5 2.400
5\60 107.039 149.855 5:2 2.500 Semihard 10L 5s⟨21/10⟩
13\155 107.730 149.164 13:5 2.600
8\95 108.166 148.728 8:3 2.667
11\130 108.686 148.208 11:4 2.750
3\35 110.097 146.796 3:1 3.000 Hard 10L 5s⟨21/10⟩
10\115 111.693 145.201 10:3 3.333
7\80 112.391 144.503 7:2 3.500
11\125 113.033 143.860 11:3 3.667
4\45 114.175 142.719 4:1 4.000 Superhard 10L 5s⟨21/10⟩
9\100 115.602 141.291 9:2 4.500
5\55 116.770 140.124 5:1 5.000
6\65 118.566 138.327 6:1 6.000
1\10 128.447 128.447 1:0 → ∞ Collapsed 10L 5s⟨21/10⟩
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