7L 2s (3/1-equivalent)
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Step pattern
LLLLsLLLs
sLLLsLLLL
Equave
3/1 (1902.0 ¢)
Period
3/1 (1902.0 ¢)
Bright
5\9 to 4\7 (1056.6 ¢ to 1086.8 ¢)
Dark
3\7 to 4\9 (815.1 ¢ to 845.3 ¢)
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⟩
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 ¢)
| ↖ 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
sLLLsLLLL
Generator size(edt)
Related MOS scales
Equal tunings(edt)
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 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 diatonic interval categories.
Intervals
| 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
| 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
| 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
| 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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