10L 3s (19/9-equivalent)

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↖ 9L 2s⟨19/9⟩ ↑ 10L 2s⟨19/9⟩ 11L 2s⟨19/9⟩ ↗
← 9L 3s⟨19/9⟩ 10L 3s (19/9-equivalent) 11L 3s⟨19/9⟩ →
↙ 9L 4s⟨19/9⟩ ↓ 10L 4s⟨19/9⟩ 11L 4s⟨19/9⟩ ↘ 
┌╥╥╥╥┬╥╥╥┬╥╥╥┬┐
│║║║║│║║║│║║║││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLsLLLs
sLLLsLLLsLLLL
Equave 19/9 (1293.6 ¢)
Period 19/9 (1293.6 ¢)
Generator size(ed19/9)
Bright 9\13 to 7\10 (895.6 ¢ to 905.5 ¢)
Dark 3\10 to 4\13 (388.1 ¢ to 398.0 ¢)
Related MOS scales
Parent 3L 7s⟨19/9⟩
Sister 3L 10s⟨19/9⟩
Daughters 13L 10s⟨19/9⟩, 10L 13s⟨19/9⟩
Neutralized 7L 6s⟨19/9⟩
2-Flought 23L 3s⟨19/9⟩, 10L 16s⟨19/9⟩
Equal tunings(ed19/9)
Equalized (L:s = 1:1) 9\13 (895.6 ¢)
Supersoft (L:s = 4:3) 34\49 (897.6 ¢)
Soft (L:s = 3:2) 25\36 (898.3 ¢)
Semisoft (L:s = 5:3) 41\59 (898.9 ¢)
Basic (L:s = 2:1) 16\23 (899.9 ¢)
Semihard (L:s = 5:2) 39\56 (900.9 ¢)
Hard (L:s = 3:1) 23\33 (901.6 ¢)
Superhard (L:s = 4:1) 30\43 (902.5 ¢)
Collapsed (L:s = 1:0) 7\10 (905.5 ¢)

10L 3s⟨19/9⟩ is a 19/9-equivalent (non-octave) moment of symmetry scale containing 10 large steps and 3 small steps, repeating every interval of 19/9 (1293.6 ¢). Generators that produce this scale range from 895.6 ¢ to 905.5 ¢, or from 388.1 ¢ to 398 ¢.

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 3s⟨19/9⟩
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 99.5 ¢
Major 1-mosstep M1ms L 99.5 ¢ to 129.4 ¢
2-mosstep Minor 2-mosstep m2ms L + s 129.4 ¢ to 199.0 ¢
Major 2-mosstep M2ms 2L 199.0 ¢ to 258.7 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 258.7 ¢ to 298.5 ¢
Major 3-mosstep M3ms 3L 298.5 ¢ to 388.1 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 388.1 ¢ to 398.0 ¢
Augmented 4-mosstep A4ms 4L 398.0 ¢ to 517.4 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 388.1 ¢ to 497.5 ¢
Major 5-mosstep M5ms 4L + s 497.5 ¢ to 517.4 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 517.4 ¢ to 597.0 ¢
Major 6-mosstep M6ms 5L + s 597.0 ¢ to 646.8 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 646.8 ¢ to 696.6 ¢
Major 7-mosstep M7ms 6L + s 696.6 ¢ to 776.2 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 776.2 ¢ to 796.1 ¢
Major 8-mosstep M8ms 7L + s 796.1 ¢ to 905.5 ¢
9-mosstep Diminished 9-mosstep d9ms 6L + 3s 776.2 ¢ to 895.6 ¢
Perfect 9-mosstep P9ms 7L + 2s 895.6 ¢ to 905.5 ¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 905.5 ¢ to 995.1 ¢
Major 10-mosstep M10ms 8L + 2s 995.1 ¢ to 1034.9 ¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 1034.9 ¢ to 1094.6 ¢
Major 11-mosstep M11ms 9L + 2s 1094.6 ¢ to 1164.2 ¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 1164.2 ¢ to 1194.1 ¢
Major 12-mosstep M12ms 10L + 2s 1194.1 ¢ to 1293.6 ¢
13-mosstep Perfect 13-mosstep P13ms 10L + 3s 1293.6 ¢

Generator chain

Generator chain of 10L 3s⟨19/9⟩
Bright gens Scale degree Abbrev.
22 Augmented 3-mosdegree A3md
21 Augmented 7-mosdegree A7md
20 Augmented 11-mosdegree A11md
19 Augmented 2-mosdegree A2md
18 Augmented 6-mosdegree A6md
17 Augmented 10-mosdegree A10md
16 Augmented 1-mosdegree A1md
15 Augmented 5-mosdegree A5md
14 Augmented 9-mosdegree A9md
13 Augmented 0-mosdegree A0md
12 Augmented 4-mosdegree A4md
11 Major 8-mosdegree M8md
10 Major 12-mosdegree M12md
9 Major 3-mosdegree M3md
8 Major 7-mosdegree M7md
7 Major 11-mosdegree M11md
6 Major 2-mosdegree M2md
5 Major 6-mosdegree M6md
4 Major 10-mosdegree M10md
3 Major 1-mosdegree M1md
2 Major 5-mosdegree M5md
1 Perfect 9-mosdegree P9md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 4-mosdegree P4md
−2 Minor 8-mosdegree m8md
−3 Minor 12-mosdegree m12md
−4 Minor 3-mosdegree m3md
−5 Minor 7-mosdegree m7md
−6 Minor 11-mosdegree m11md
−7 Minor 2-mosdegree m2md
−8 Minor 6-mosdegree m6md
−9 Minor 10-mosdegree m10md
−10 Minor 1-mosdegree m1md
−11 Minor 5-mosdegree m5md
−12 Diminished 9-mosdegree d9md
−13 Diminished 13-mosdegree d13md
−14 Diminished 4-mosdegree d4md
−15 Diminished 8-mosdegree d8md
−16 Diminished 12-mosdegree d12md
−17 Diminished 3-mosdegree d3md
−18 Diminished 7-mosdegree d7md
−19 Diminished 11-mosdegree d11md
−20 Diminished 2-mosdegree d2md
−21 Diminished 6-mosdegree d6md
−22 Diminished 10-mosdegree d10md

Modes

Scale degrees of the modes of 10L 3s⟨19/9⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
12|0 1 LLLLsLLLsLLLs Perf. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
11|1 10 LLLsLLLLsLLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Perf.
10|2 6 LLLsLLLsLLLLs Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Perf. Maj. Maj. Maj. Perf.
9|3 2 LLLsLLLsLLLsL Perf. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf.
8|4 11 LLsLLLLsLLLsL Perf. Maj. Maj. Min. Perf. Maj. Maj. Maj. Min. Perf. Maj. Maj. Min. Perf.
7|5 7 LLsLLLsLLLLsL Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Perf. Maj. Maj. Min. Perf.
6|6 3 LLsLLLsLLLsLL Perf. Maj. Maj. Min. Perf. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf.
5|7 12 LsLLLLsLLLsLL Perf. Maj. Min. Min. Perf. Maj. Maj. Min. Min. Perf. Maj. Min. Min. Perf.
4|8 8 LsLLLsLLLLsLL Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Perf. Maj. Min. Min. Perf.
3|9 4 LsLLLsLLLsLLL Perf. Maj. Min. Min. Perf. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
2|10 13 sLLLLsLLLsLLL Perf. Min. Min. Min. Perf. Maj. Min. Min. Min. Perf. Min. Min. Min. Perf.
1|11 9 sLLLsLLLLsLLL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Perf.
0|12 5 sLLLsLLLsLLLL Perf. Min. Min. Min. Perf. Min. Min. Min. Min. Dim. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 10L 3s⟨19/9⟩
Generator(ed19/9) Cents Step ratio Comments
Bright Dark L:s Hardness
9\13 895.571 398.032 1:1 1.000 Equalized 10L 3s⟨19/9⟩
52\75 896.898 396.705 6:5 1.200
43\62 897.176 396.427 5:4 1.250
77\111 897.364 396.239 9:7 1.286
34\49 897.602 396.001 4:3 1.333 Supersoft 10L 3s⟨19/9⟩
93\134 897.799 395.804 11:8 1.375
59\85 897.913 395.690 7:5 1.400
84\121 898.038 395.565 10:7 1.429
25\36 898.335 395.268 3:2 1.500 Soft 10L 3s⟨19/9⟩
91\131 898.610 394.993 11:7 1.571
66\95 898.714 394.889 8:5 1.600
107\154 898.802 394.801 13:8 1.625
41\59 898.944 394.659 5:3 1.667 Semisoft 10L 3s⟨19/9⟩
98\141 899.100 394.503 12:7 1.714
57\82 899.212 394.391 7:4 1.750
73\105 899.362 394.241 9:5 1.800
16\23 899.898 393.705 2:1 2.000 Basic 10L 3s⟨19/9⟩
Scales with tunings softer than this are proper
71\102 900.449 393.154 9:4 2.250
55\79 900.610 392.993 7:3 2.333
94\135 900.731 392.872 12:5 2.400
39\56 900.902 392.701 5:2 2.500 Semihard 10L 3s⟨19/9⟩
101\145 901.061 392.542 13:5 2.600
62\89 901.162 392.441 8:3 2.667
85\122 901.281 392.322 11:4 2.750
23\33 901.602 392.001 3:1 3.000 Hard 10L 3s⟨19/9⟩
76\109 901.962 391.641 10:3 3.333
53\76 902.118 391.485 7:2 3.500
83\119 902.261 391.342 11:3 3.667
30\43 902.514 391.089 4:1 4.000 Superhard 10L 3s⟨19/9⟩
67\96 902.827 390.776 9:2 4.500
37\53 903.081 390.522 5:1 5.000
44\63 903.469 390.134 6:1 6.000
7\10 905.522 388.081 1:0 → ∞ Collapsed 10L 3s⟨19/9⟩
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