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7L 2s (3/1-equivalent)

Revision as of 19:50, 6 March 2025 by ArrowHead294 (talk | contribs) (Throwing this out here)
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↖ 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 ¢)

7L 2s⟨3/1⟩, also called supertriatonic, 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 ¢.

Name

The name supertriatonic[idiosyncratic term] was coined by ArrowHead294, as a back-formation from "superdiatonic" with di- being interpreted as 2 (the octave) and tri- being interpreted as 3 (the tritave), though 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

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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