5L 2s (3/1-equivalent)

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↖ 4L 1s⟨3/1⟩ ↑ 5L 1s⟨3/1⟩ 6L 1s⟨3/1⟩ ↗
← 4L 2s⟨3/1⟩ 5L 2s (3/1-equivalent) 6L 2s⟨3/1⟩ →
↙ 4L 3s⟨3/1⟩ ↓ 5L 3s⟨3/1⟩ 6L 3s⟨3/1⟩ ↘
Scale structure
Step pattern LLLsLLs
sLLsLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 4\7 to 3\5 (1086.8 ¢ to 1141.2 ¢)
Dark 2\5 to 3\7 (760.8 ¢ to 815.1 ¢)
Related MOS scales
Parent 2L 3s⟨3/1⟩
Sister 2L 5s⟨3/1⟩
Daughters 7L 5s⟨3/1⟩, 5L 7s⟨3/1⟩
Neutralized 3L 4s⟨3/1⟩
2-Flought 12L 2s⟨3/1⟩, 5L 9s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 4\7 (1086.8 ¢)
Supersoft (L:s = 4:3) 15\26 (1097.3 ¢)
Soft (L:s = 3:2) 11\19 (1101.1 ¢)
Semisoft (L:s = 5:3) 18\31 (1104.4 ¢)
Basic (L:s = 2:1) 7\12 (1109.5 ¢)
Semihard (L:s = 5:2) 17\29 (1114.9 ¢)
Hard (L:s = 3:1) 10\17 (1118.8 ¢)
Superhard (L:s = 4:1) 13\22 (1123.9 ¢)
Collapsed (L:s = 1:0) 3\5 (1141.2 ¢)
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5L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1086.8 ¢ to 1141.2 ¢, or from 760.8 ¢ to 815.1 ¢.

Theory

As a macrodiatonic scale

It is the macrodiatonic scale with the period of a tritave. This means it is a diatonic scale, but has octaves stretched out to the size of a tritave. Other intervals are also stretched in a way that makes the unrecognizable–the diatonic fifth is now the size of a major seventh. Interestingly 19edt, an approximation of 12edo, has a tuning of this scale (being a stretched version of 19edo's diatonic scale), meaning it contains both the diatonic scale (identical to 12edo's) and the macrodiatonic scale.

Temperament interpretations

Although they have not been studied in detail, it is possible to construct no-twos rank-2 temperament interpretations of this scale, such as the as-of-yet unnamed b12 & b5 temperament in the 3.13.17 subgroup, in which the generator is ~17/9 and a stack of 4 generators tritave-reduced is ~13/9. See also the page for 12edt.

Modes

The modes have step patterns which are the same as the modes of the diatonic scale.

Modes of 5L 2s⟨3/1⟩
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

Scale degrees

Scale degrees of the modes of 5L 2s⟨3/1⟩
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.

Notation

Being a macrodiatonic scale, it can notated using the traditional diatonic notation, if all intervals are reinterpreted as their stretched versions (like octaves as tritaves). However, this approach involves 1-based indexing for a non-diatonic MOS which is generally discouraged. Alternatively, a generic MOS notation may be used like diamond MOS notation.

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 5L 2s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
4\7 1086.831 815.124 1:1 1.000 Equalized 5L 2s⟨3/1⟩
27\47 1092.612 809.343 7:6 1.167
23\40 1093.624 808.331 6:5 1.200
42\73 1094.275 807.680 11:9 1.222
19\33 1095.065 806.890 5:4 1.250
53\92 1095.691 806.264 14:11 1.273
34\59 1096.042 805.913 9:7 1.286
49\85 1096.421 805.534 13:10 1.300
15\26 1097.282 804.673 4:3 1.333 Supersoft 5L 2s⟨3/1⟩
56\97 1098.036 803.919 15:11 1.364
41\71 1098.312 803.643 11:8 1.375
67\116 1098.543 803.412 18:13 1.385
26\45 1098.907 803.048 7:5 1.400
63\109 1099.295 802.660 17:12 1.417
37\64 1099.568 802.387 10:7 1.429
48\83 1099.926 802.029 13:9 1.444
11\19 1101.132 800.823 3:2 1.500 Soft 5L 2s⟨3/1⟩
51\88 1102.269 799.686 14:9 1.556
40\69 1102.583 799.372 11:7 1.571
69\119 1102.814 799.141 19:12 1.583
29\50 1103.134 798.821 8:5 1.600
76\131 1103.424 798.531 21:13 1.615
47\81 1103.604 798.351 13:8 1.625
65\112 1103.813 798.142 18:11 1.636
18\31 1104.361 797.594 5:3 1.667 Semisoft 5L 2s⟨3/1⟩
61\105 1104.945 797.010 17:10 1.700
43\74 1105.190 796.765 12:7 1.714
68\117 1105.410 796.545 19:11 1.727
25\43 1105.788 796.167 7:4 1.750
57\98 1106.239 795.716 16:9 1.778
32\55 1106.592 795.363 9:5 1.800
39\67 1107.108 794.847 11:6 1.833
7\12 1109.474 792.481 2:1 2.000 Basic 5L 2s⟨3/1⟩
Scales with tunings softer than this are proper
CTE tuning for the b12 & b5 temperament (1109.689)
38\65 1111.912 790.043 11:5 2.200
31\53 1112.464 789.491 9:4 2.250
55\94 1112.846 789.109 16:7 2.286
24\41 1113.340 788.615 7:3 2.333
65\111 1113.757 788.198 19:8 2.375
41\70 1114.002 787.953 12:5 2.400
58\99 1114.277 787.678 17:7 2.429
17\29 1114.939 787.016 5:2 2.500 Semihard 5L 2s⟨3/1⟩
61\104 1115.570 786.385 18:7 2.571
44\75 1115.814 786.141 13:5 2.600
71\121 1116.023 785.932 21:8 2.625
27\46 1116.365 785.590 8:3 2.667
64\109 1116.744 785.211 19:7 2.714
37\63 1117.021 784.934 11:4 2.750
47\80 1117.399 784.556 14:5 2.800
10\17 1118.797 783.158 3:1 3.000 Hard 5L 2s⟨3/1⟩
43\73 1120.330 781.625 13:4 3.250
33\56 1120.795 781.160 10:3 3.333
56\95 1121.152 780.803 17:5 3.400
23\39 1121.666 780.289 7:2 3.500
59\100 1122.153 779.802 18:5 3.600
36\61 1122.465 779.490 11:3 3.667
49\83 1122.841 779.114 15:4 3.750
13\22 1123.883 778.073 4:1 4.000 Superhard 5L 2s⟨3/1⟩
42\71 1125.100 776.855 13:3 4.333
29\49 1125.647 776.308 9:2 4.500
45\76 1126.158 775.797 14:3 4.667
16\27 1127.084 774.871 5:1 5.000
35\59 1128.278 773.677 11:2 5.500
19\32 1129.286 772.669 6:1 6.000
22\37 1130.892 771.063 7:1 7.000
3\5 1141.173 760.782 1:0 → ∞ Collapsed 5L 2s⟨3/1⟩
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