10L 4s

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↖ 9L 3s ↑ 10L 3s 11L 3s ↗
← 9L 4s 10L 4s 11L 4s →
↙ 9L 5s ↓ 10L 5s 11L 5s ↘ 
┌╥╥╥┬╥╥┬╥╥╥┬╥╥┬┐
│║║║│║║│║║║│║║││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLsLLLsLLs
sLLsLLLsLLsLLL
Equave 2/1 (1200.0 ¢)
Period 1\2 (600.0 ¢)
Generator size
Bright 4\14 to 3\10 (342.9 ¢ to 360.0 ¢)
Dark 2\10 to 3\14 (240.0 ¢ to 257.1 ¢)
TAMNAMS information
Related to 4L 6s (lime)
With tunings 1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent 4L 6s
Sister 4L 10s
Daughters 14L 10s, 10L 14s
Neutralized 6L 8s
2-Flought 24L 4s, 10L 18s
Equal tunings
Equalized (L:s = 1:1) 4\14 (342.9 ¢)
Supersoft (L:s = 4:3) 15\52 (346.2 ¢)
Soft (L:s = 3:2) 11\38 (347.4 ¢)
Semisoft (L:s = 5:3) 18\62 (348.4 ¢)
Basic (L:s = 2:1) 7\24 (350.0 ¢)
Semihard (L:s = 5:2) 17\58 (351.7 ¢)
Hard (L:s = 3:1) 10\34 (352.9 ¢)
Superhard (L:s = 4:1) 13\44 (354.5 ¢)
Collapsed (L:s = 1:0) 3\10 (360.0 ¢)

10L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 4 small steps, with a period of 5 large steps and 2 small steps that repeats every 600.0 ¢, or twice every octave. 10L 4s is a child scale of 4L 6s, expanding it by 4 tones. Generators that produce this scale range from 342.9 ¢ to 360 ¢, or from 240 ¢ to 257.1 ¢.

10L 4s is significant as the "diatonic scale" of hemipythagorean tuning, and contains the intervals of diatonic alongside neutral intervals.

Name

Vector Graphics proposes hemidiatonic for this scale, by analogy with the hemipythagorean system which generates it.

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 interval regions.

Intervals

Intervals of 10L 4s
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 85.7 ¢
Major 1-mosstep M1ms L 85.7 ¢ to 120.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 120.0 ¢ to 171.4 ¢
Major 2-mosstep M2ms 2L 171.4 ¢ to 240.0 ¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 240.0 ¢ to 257.1 ¢
Augmented 3-mosstep A3ms 3L 257.1 ¢ to 360.0 ¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 240.0 ¢ to 342.9 ¢
Perfect 4-mosstep P4ms 3L + s 342.9 ¢ to 360.0 ¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 360.0 ¢ to 428.6 ¢
Major 5-mosstep M5ms 4L + s 428.6 ¢ to 480.0 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 480.0 ¢ to 514.3 ¢
Major 6-mosstep M6ms 5L + s 514.3 ¢ to 600.0 ¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 600.0 ¢
8-mosstep Minor 8-mosstep m8ms 5L + 3s 600.0 ¢ to 685.7 ¢
Major 8-mosstep M8ms 6L + 2s 685.7 ¢ to 720.0 ¢
9-mosstep Minor 9-mosstep m9ms 6L + 3s 720.0 ¢ to 771.4 ¢
Major 9-mosstep M9ms 7L + 2s 771.4 ¢ to 840.0 ¢
10-mosstep Perfect 10-mosstep P10ms 7L + 3s 840.0 ¢ to 857.1 ¢
Augmented 10-mosstep A10ms 8L + 2s 857.1 ¢ to 960.0 ¢
11-mosstep Diminished 11-mosstep d11ms 7L + 4s 840.0 ¢ to 942.9 ¢
Perfect 11-mosstep P11ms 8L + 3s 942.9 ¢ to 960.0 ¢
12-mosstep Minor 12-mosstep m12ms 8L + 4s 960.0 ¢ to 1028.6 ¢
Major 12-mosstep M12ms 9L + 3s 1028.6 ¢ to 1080.0 ¢
13-mosstep Minor 13-mosstep m13ms 9L + 4s 1080.0 ¢ to 1114.3 ¢
Major 13-mosstep M13ms 10L + 3s 1114.3 ¢ to 1200.0 ¢
14-mosstep Perfect 14-mosstep P14ms 10L + 4s 1200.0 ¢

Generator chain

Generator chain of 10L 4s
Bright gens Scale degree Abbrev. Scale degree Abbrev.
11 Augmented 2-mosdegree A2md Augmented 9-mosdegree A9md
10 Augmented 5-mosdegree A5md Augmented 12-mosdegree A12md
9 Augmented 1-mosdegree A1md Augmented 8-mosdegree A8md
8 Augmented 4-mosdegree A4md Augmented 11-mosdegree A11md
7 Augmented 0-mosdegree A0md Augmented 7-mosdegree A7md
6 Augmented 3-mosdegree A3md Augmented 10-mosdegree A10md
5 Major 6-mosdegree M6md Major 13-mosdegree M13md
4 Major 2-mosdegree M2md Major 9-mosdegree M9md
3 Major 5-mosdegree M5md Major 12-mosdegree M12md
2 Major 1-mosdegree M1md Major 8-mosdegree M8md
1 Perfect 4-mosdegree P4md Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 7-mosdegree		 P0md
P7md		 Perfect 7-mosdegree
Perfect 14-mosdegree		 P7md
P14md
−1 Perfect 3-mosdegree P3md Perfect 10-mosdegree P10md
−2 Minor 6-mosdegree m6md Minor 13-mosdegree m13md
−3 Minor 2-mosdegree m2md Minor 9-mosdegree m9md
−4 Minor 5-mosdegree m5md Minor 12-mosdegree m12md
−5 Minor 1-mosdegree m1md Minor 8-mosdegree m8md
−6 Diminished 4-mosdegree d4md Diminished 11-mosdegree d11md
−7 Diminished 7-mosdegree d7md Diminished 14-mosdegree d14md
−8 Diminished 3-mosdegree d3md Diminished 10-mosdegree d10md
−9 Diminished 6-mosdegree d6md Diminished 13-mosdegree d13md
−10 Diminished 2-mosdegree d2md Diminished 9-mosdegree d9md
−11 Diminished 5-mosdegree d5md Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 10L 4s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14
12|0(2) 1 LLLsLLsLLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
10|2(2) 5 LLsLLLsLLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
8|4(2) 2 LLsLLsLLLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
6|6(2) 6 LsLLLsLLsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
4|8(2) 3 LsLLsLLLsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
2|10(2) 7 sLLLsLLsLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|12(2) 4 sLLsLLLsLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf. Min. Min. Perf. Dim. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 10L 4s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\14 342.857 257.143 1:1 1.000 Equalized 10L 4s
23\80 345.000 255.000 6:5 1.200
19\66 345.455 254.545 5:4 1.250
34\118 345.763 254.237 9:7 1.286
15\52 346.154 253.846 4:3 1.333 Supersoft 10L 4s
41\142 346.479 253.521 11:8 1.375
26\90 346.667 253.333 7:5 1.400
37\128 346.875 253.125 10:7 1.429
11\38 347.368 252.632 3:2 1.500 Soft 10L 4s
40\138 347.826 252.174 11:7 1.571
29\100 348.000 252.000 8:5 1.600
47\162 348.148 251.852 13:8 1.625
18\62 348.387 251.613 5:3 1.667 Semisoft 10L 4s
43\148 348.649 251.351 12:7 1.714
25\86 348.837 251.163 7:4 1.750
32\110 349.091 250.909 9:5 1.800
7\24 350.000 250.000 2:1 2.000 Basic 10L 4s
Scales with tunings softer than this are proper
31\106 350.943 249.057 9:4 2.250
24\82 351.220 248.780 7:3 2.333
41\140 351.429 248.571 12:5 2.400 Semihemi
17\58 351.724 248.276 5:2 2.500 Semihard 10L 4s
Sruti, anguirus
44\150 352.000 248.000 13:5 2.600
27\92 352.174 247.826 8:3 2.667
37\126 352.381 247.619 11:4 2.750
10\34 352.941 247.059 3:1 3.000 Hard 10L 4s
Hemifourths
33\112 353.571 246.429 10:3 3.333
23\78 353.846 246.154 7:2 3.500
36\122 354.098 245.902 11:3 3.667
13\44 354.545 245.455 4:1 4.000 Superhard 10L 4s
29\98 355.102 244.898 9:2 4.500
16\54 355.556 244.444 5:1 5.000
19\64 356.250 243.750 6:1 6.000 ↓ Semiseptiquarter
3\10 360.000 240.000 1:0 → ∞ Collapsed 10L 4s
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