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.

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 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 ¢

Generator chain

Generator chain of 5L 2s⟨4/1⟩
Bright gens Scale degree Abbrev.
11 Augmented 2-mosdegree A2md
10 Augmented 5-mosdegree A5md
9 Augmented 1-mosdegree A1md
8 Augmented 4-mosdegree A4md
7 Augmented 0-mosdegree A0md
6 Augmented 3-mosdegree A3md
5 Major 6-mosdegree M6md
4 Major 2-mosdegree M2md
3 Major 5-mosdegree M5md
2 Major 1-mosdegree M1md
1 Perfect 4-mosdegree P4md
0 Perfect 0-mosdegree
Perfect 7-mosdegree		 P0md
P7md
−1 Perfect 3-mosdegree P3md
−2 Minor 6-mosdegree m6md
−3 Minor 2-mosdegree m2md
−4 Minor 5-mosdegree m5md
−5 Minor 1-mosdegree m1md
−6 Diminished 4-mosdegree d4md
−7 Diminished 7-mosdegree d7md
−8 Diminished 3-mosdegree d3md
−9 Diminished 6-mosdegree d6md
−10 Diminished 2-mosdegree d2md
−11 Diminished 5-mosdegree d5md

Modes

Scale degrees of the modes of 5L 2s⟨4/1⟩
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7
6|0 1 LLLsLLs Perf. Maj. Maj. Aug. Perf. Maj. Maj. Perf.
5|1 5 LLsLLLs Perf. Maj. Maj. Perf. Perf. Maj. Maj. Perf.
4|2 2 LLsLLsL Perf. Maj. Maj. Perf. Perf. Maj. Min. Perf.
3|3 6 LsLLLsL Perf. Maj. Min. Perf. Perf. Maj. Min. Perf.
2|4 3 LsLLsLL Perf. Maj. Min. Perf. Perf. Min. Min. Perf.
1|5 7 sLLLsLL Perf. Min. Min. Perf. Perf. Min. Min. Perf.
0|6 4 sLLsLLL Perf. Min. Min. Perf. Dim. Min. Min. Perf.

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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