5L 2s (4/1-equivalent)

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↖ 4L 1s⟨4/1⟩ ↑ 5L 1s⟨4/1⟩ 6L 1s⟨4/1⟩ ↗
← 4L 2s⟨4/1⟩ 5L 2s (4/1-equivalent) 6L 2s⟨4/1⟩ →
↙ 4L 3s⟨4/1⟩ ↓ 5L 3s⟨4/1⟩ 6L 3s⟨4/1⟩ ↘ 
┌╥╥╥┬╥╥┬┐
│║║║│║║││
│││││││││
└┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLs
sLLsLLL
Equave 4/1 (2400.0¢)
Period 4/1 (2400.0¢)
Generator size(ed4/1)
Bright 4\7 to 3\5 (1371.4¢ to 1440.0¢)
Dark 2\5 to 3\7 (960.0¢ to 1028.6¢)
Related MOS scales
Parent 2L 3s⟨4/1⟩
Sister 2L 5s⟨4/1⟩
Daughters 7L 5s⟨4/1⟩, 5L 7s⟨4/1⟩
Neutralized 3L 4s⟨4/1⟩
2-Flought 12L 2s⟨4/1⟩, 5L 9s⟨4/1⟩
Equal tunings(ed4/1)
Equalized (L:s = 1:1) 4\7 (1371.4¢)
Supersoft (L:s = 4:3) 15\26 (1384.6¢)
Soft (L:s = 3:2) 11\19 (1389.5¢)
Semisoft (L:s = 5:3) 18\31 (1393.5¢)
Basic (L:s = 2:1) 7\12 (1400.0¢)
Semihard (L:s = 5:2) 17\29 (1406.9¢)
Hard (L:s = 3:1) 10\17 (1411.8¢)
Superhard (L:s = 4:1) 13\22 (1418.2¢)
Collapsed (L:s = 1:0) 3\5 (1440.0¢)

5L 2s⟨4/1⟩ is a 4/1-equivalent (non-octave) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every interval of 4/1 (2400.0¢). Generators that produce this scale range from 1371.4¢ to 1440¢, or from 960¢ to 1028.6¢.

Theory

It is the macrodiatonic scale with the period of a tetratave. This means it is a diatonic scale, but has octaves stretched by a factor of exactly 2 (squared). The generator is also stretched out from ~3/2 to ~9/4. Although the structure of the scale is the same, the melodic and harmonic properties are completely different from the diatonic scale.

Modes

Modes of 5L 2s⟨4/1⟩
UDP Cyclic
order		 Step
pattern
6|0 1 LLLsLLs
5|1 5 LLsLLLs
4|2 2 LLsLLsL
3|3 6 LsLLLsL
2|4 3 LsLLsLL
1|5 7 sLLLsLL
0|6 4 sLLsLLL

Intervals

Intervals of 5L 2s⟨4/1⟩
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 342.9¢
Major 1-mosstep M1ms L 342.9¢ to 480.0¢
2-mosstep Minor 2-mosstep m2ms L + s 480.0¢ to 685.7¢
Major 2-mosstep M2ms 2L 685.7¢ to 960.0¢
3-mosstep Perfect 3-mosstep P3ms 2L + s 960.0¢ to 1028.6¢
Augmented 3-mosstep A3ms 3L 1028.6¢ to 1440.0¢
4-mosstep Diminished 4-mosstep d4ms 2L + 2s 960.0¢ to 1371.4¢
Perfect 4-mosstep P4ms 3L + s 1371.4¢ to 1440.0¢
5-mosstep Minor 5-mosstep m5ms 3L + 2s 1440.0¢ to 1714.3¢
Major 5-mosstep M5ms 4L + s 1714.3¢ to 1920.0¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 1920.0¢ to 2057.1¢
Major 6-mosstep M6ms 5L + s 2057.1¢ to 2400.0¢
7-mosstep Perfect 7-mosstep P7ms 5L + 2s 2400.0¢

Scale tree

Scale Tree and Tuning Spectrum of 5L 2s⟨4/1⟩
Generator(ed4/1) Cents Step ratio Comments
Bright Dark L:s Hardness
4\7 1371.429 1028.571 1:1 1.000 Equalized 5L 2s⟨4/1⟩
23\40 1380.000 1020.000 6:5 1.200
19\33 1381.818 1018.182 5:4 1.250
34\59 1383.051 1016.949 9:7 1.286
15\26 1384.615 1015.385 4:3 1.333 Supersoft 5L 2s⟨4/1⟩
41\71 1385.915 1014.085 11:8 1.375
26\45 1386.667 1013.333 7:5 1.400
37\64 1387.500 1012.500 10:7 1.429
11\19 1389.474 1010.526 3:2 1.500 Soft 5L 2s⟨4/1⟩
40\69 1391.304 1008.696 11:7 1.571
29\50 1392.000 1008.000 8:5 1.600
47\81 1392.593 1007.407 13:8 1.625
18\31 1393.548 1006.452 5:3 1.667 Semisoft 5L 2s⟨4/1⟩
43\74 1394.595 1005.405 12:7 1.714 Meansquared
25\43 1395.349 1004.651 7:4 1.750
32\55 1396.364 1003.636 9:5 1.800
7\12 1400.000 1000.000 2:1 2.000 Basic 5L 2s⟨4/1⟩
Scales with tunings softer than this are proper
31\53 1403.774 996.226 9:4 2.250
24\41 1404.878 995.122 7:3 2.333
41\70 1405.714 994.286 12:5 2.400
17\29 1406.897 993.103 5:2 2.500 Semihard 5L 2s⟨4/1⟩
44\75 1408.000 992.000 13:5 2.600
27\46 1408.696 991.304 8:3 2.667
37\63 1409.524 990.476 11:4 2.750
10\17 1411.765 988.235 3:1 3.000 Hard 5L 2s⟨4/1⟩
33\56 1414.286 985.714 10:3 3.333
23\39 1415.385 984.615 7:2 3.500
36\61 1416.393 983.607 11:3 3.667
13\22 1418.182 981.818 4:1 4.000 Superhard 5L 2s⟨4/1⟩
29\49 1420.408 979.592 9:2 4.500
16\27 1422.222 977.778 5:1 5.000
19\32 1425.000 975.000 6:1 6.000
3\5 1440.000 960.000 1:0 → ∞ Collapsed 5L 2s⟨4/1⟩
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