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7L 2s (3/1-equivalent)

7L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 7 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1056.6 ¢ to 1086.8 ¢, or from 815.1 ¢ to 845.3 ¢.

↖ 6L 1s⟨3/1⟩ ↑ 7L 1s⟨3/1⟩ 8L 1s⟨3/1⟩ ↗
← 6L 2s⟨3/1⟩ 7L 2s (3/1-equivalent) 8L 2s⟨3/1⟩ →
↙ 6L 3s⟨3/1⟩ ↓ 7L 3s⟨3/1⟩ 8L 3s⟨3/1⟩ ↘
Scale structure
Step pattern LLLLsLLLs
sLLLsLLLL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 5\9 to 4\7 (1056.6 ¢ to 1086.8 ¢)
Dark 3\7 to 4\9 (815.1 ¢ to 845.3 ¢)
Related MOS scales
Parent 2L 5s⟨3/1⟩
Sister 2L 7s⟨3/1⟩
Daughters 9L 7s⟨3/1⟩, 7L 9s⟨3/1⟩
Neutralized 5L 4s⟨3/1⟩
2-Flought 16L 2s⟨3/1⟩, 7L 11s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 5\9 (1056.6 ¢)
Supersoft (L:s = 4:3) 19\34 (1062.9 ¢)
Soft (L:s = 3:2) 14\25 (1065.1 ¢)
Semisoft (L:s = 5:3) 23\41 (1067.0 ¢)
Basic (L:s = 2:1) 9\16 (1069.8 ¢)
Semihard (L:s = 5:2) 22\39 (1072.9 ¢)
Hard (L:s = 3:1) 13\23 (1075.0 ¢)
Superhard (L:s = 4:1) 17\30 (1077.8 ¢)
Collapsed (L:s = 1:0) 4\7 (1086.8 ¢)
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Name

The name supertriatonic[idiosyncratic term] was coined by ArrowHead294, as a back-formation from the name "superdiatonic" for the octave-equivalent 7L 2s scale with di- being interpreted as 2 (the octave) and tri- being interpreted as 3 (the tritave). It is not an official name in TAMNAMS.

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 7L 2s⟨3/1⟩
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 211.3 ¢
Major 1-mosstep M1ms L 211.3 ¢ to 271.7 ¢
2-mosstep Minor 2-mosstep m2ms L + s 271.7 ¢ to 422.7 ¢
Major 2-mosstep M2ms 2L 422.7 ¢ to 543.4 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 543.4 ¢ to 634.0 ¢
Major 3-mosstep M3ms 3L 634.0 ¢ to 815.1 ¢
4-mosstep Perfect 4-mosstep P4ms 3L + s 815.1 ¢ to 845.3 ¢
Augmented 4-mosstep A4ms 4L 845.3 ¢ to 1086.8 ¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 815.1 ¢ to 1056.6 ¢
Perfect 5-mosstep P5ms 4L + s 1056.6 ¢ to 1086.8 ¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 1086.8 ¢ to 1268.0 ¢
Major 6-mosstep M6ms 5L + s 1268.0 ¢ to 1358.5 ¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 1358.5 ¢ to 1479.3 ¢
Major 7-mosstep M7ms 6L + s 1479.3 ¢ to 1630.2 ¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 1630.2 ¢ to 1690.6 ¢
Major 8-mosstep M8ms 7L + s 1690.6 ¢ to 1902.0 ¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 1902.0 ¢

Generator chain

Generator chain of 7L 2s⟨3/1⟩
Bright gens Scale degree Abbrev.
15 Augmented 3-mosdegree A3md
14 Augmented 7-mosdegree A7md
13 Augmented 2-mosdegree A2md
12 Augmented 6-mosdegree A6md
11 Augmented 1-mosdegree A1md
10 Augmented 5-mosdegree A5md
9 Augmented 0-mosdegree A0md
8 Augmented 4-mosdegree A4md
7 Major 8-mosdegree M8md
6 Major 3-mosdegree M3md
5 Major 7-mosdegree M7md
4 Major 2-mosdegree M2md
3 Major 6-mosdegree M6md
2 Major 1-mosdegree M1md
1 Perfect 5-mosdegree P5md
0 Perfect 0-mosdegree
Perfect 9-mosdegree		 P0md
P9md
−1 Perfect 4-mosdegree P4md
−2 Minor 8-mosdegree m8md
−3 Minor 3-mosdegree m3md
−4 Minor 7-mosdegree m7md
−5 Minor 2-mosdegree m2md
−6 Minor 6-mosdegree m6md
−7 Minor 1-mosdegree m1md
−8 Diminished 5-mosdegree d5md
−9 Diminished 9-mosdegree d9md
−10 Diminished 4-mosdegree d4md
−11 Diminished 8-mosdegree d8md
−12 Diminished 3-mosdegree d3md
−13 Diminished 7-mosdegree d7md
−14 Diminished 2-mosdegree d2md
−15 Diminished 6-mosdegree d6md

Modes

Scale degrees of the modes of 7L 2s⟨3/1⟩
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9
8|0 1 LLLLsLLLs Perf. Maj. Maj. Maj. Aug. Perf. Maj. Maj. Maj. Perf.
7|1 6 LLLsLLLLs Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Perf.
6|2 2 LLLsLLLsL Perf. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Min. Perf.
5|3 7 LLsLLLLsL Perf. Maj. Maj. Min. Perf. Perf. Maj. Maj. Min. Perf.
4|4 3 LLsLLLsLL Perf. Maj. Maj. Min. Perf. Perf. Maj. Min. Min. Perf.
3|5 8 LsLLLLsLL Perf. Maj. Min. Min. Perf. Perf. Maj. Min. Min. Perf.
2|6 4 LsLLLsLLL Perf. Maj. Min. Min. Perf. Perf. Min. Min. Min. Perf.
1|7 9 sLLLLsLLL Perf. Min. Min. Min. Perf. Perf. Min. Min. Min. Perf.
0|8 5 sLLLsLLLL Perf. Min. Min. Min. Perf. Dim. Min. Min. Min. Perf.

Temperament interpretations

  Todo: expand

The primary temperament interpretation of the hyposoft range of this scale is pure-tritave lemba.

Tuning ranges

Simple tunings

Simple Tunings of 7L 2s⟨3/1⟩
Scale degree Abbrev. Basic (2:1)
16edt 		Hard (3:1)
23edt 		Soft (3:2)
25edt
Steps ¢ Steps ¢ Steps ¢
Perfect 0-mosdegree P0md 0\16 0.0 0\23 0.0 0\25 0.0
Minor 1-mosdegree m1md 1\16 118.9 1\23 82.7 2\25 152.2
Major 1-mosdegree M1md 2\16 237.7 3\23 248.1 3\25 228.2
Minor 2-mosdegree m2md 3\16 356.6 4\23 330.8 5\25 380.4
Major 2-mosdegree M2md 4\16 475.5 6\23 496.2 6\25 456.5
Minor 3-mosdegree m3md 5\16 594.4 7\23 578.9 8\25 608.6
Major 3-mosdegree M3md 6\16 713.2 9\23 744.2 9\25 684.7
Perfect 4-mosdegree P4md 7\16 832.1 10\23 826.9 11\25 836.9
Augmented 4-mosdegree A4md 8\16 951.0 12\23 992.3 12\25 912.9
Diminished 5-mosdegree d5md 8\16 951.0 11\23 909.6 13\25 989.0
Perfect 5-mosdegree P5md 9\16 1069.8 13\23 1075.0 14\25 1065.1
Minor 6-mosdegree m6md 10\16 1188.7 14\23 1157.7 16\25 1217.3
Major 6-mosdegree M6md 11\16 1307.6 16\23 1323.1 17\25 1293.3
Minor 7-mosdegree m7md 12\16 1426.5 17\23 1405.8 19\25 1445.5
Major 7-mosdegree M7md 13\16 1545.3 19\23 1571.2 20\25 1521.6
Minor 8-mosdegree m8md 14\16 1664.2 20\23 1653.9 22\25 1673.7
Major 8-mosdegree M8md 15\16 1783.1 22\23 1819.3 23\25 1749.8
Perfect 9-mosdegree P9md 16\16 1902.0 23\23 1902.0 25\25 1902.0

Scale tree

Scale tree and tuning spectrum of 7L 2s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
5\9 1056.642 845.313 1:1 1.000 Equalized 7L 2s⟨3/1⟩
29\52 1060.706 841.249 6:5 1.200
24\43 1061.556 840.399 5:4 1.250
43\77 1062.131 839.824 9:7 1.286
19\34 1062.857 839.098 4:3 1.333 Supersoft 7L 2s⟨3/1⟩
52\93 1063.459 838.496 11:8 1.375
33\59 1063.805 838.150 7:5 1.400
47\84 1064.189 837.766 10:7 1.429
14\25 1065.095 836.860 3:2 1.500 Soft 7L 2s⟨3/1⟩
51\91 1065.931 836.024 11:7 1.571
37\66 1066.248 835.708 8:5 1.600
60\107 1066.517 835.438 13:8 1.625
23\41 1066.950 835.005 5:3 1.667 Semisoft 7L 2s⟨3/1⟩
55\98 1067.424 834.531 12:7 1.714
32\57 1067.764 834.191 7:4 1.750
41\73 1068.221 833.734 9:5 1.800
9\16 1069.850 832.105 2:1 2.000 Basic 7L 2s⟨3/1⟩
Scales with tunings softer than this are proper
40\71 1071.524 830.431 9:4 2.250
31\55 1072.011 829.944 7:3 2.333
53\94 1072.379 829.576 12:5 2.400
22\39 1072.898 829.057 5:2 2.500 Semihard 7L 2s⟨3/1⟩
57\101 1073.381 828.574 13:5 2.600
35\62 1073.684 828.271 8:3 2.667
48\85 1074.045 827.910 11:4 2.750
13\23 1075.018 826.937 3:1 3.000 Hard 7L 2s⟨3/1⟩
43\76 1076.106 825.849 10:3 3.333
30\53 1076.578 825.377 7:2 3.500
47\83 1077.011 824.944 11:3 3.667
17\30 1077.775 824.181 4:1 4.000 Superhard 7L 2s⟨3/1⟩
38\67 1078.721 823.234 9:2 4.500
21\37 1079.488 822.467 5:1 5.000
25\44 1080.656 821.299 6:1 6.000
4\7 1086.831 815.124 1:0 → ∞ Collapsed 7L 2s⟨3/1⟩
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