2L 5s (3/1-equivalent)
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Scale structure
Step pattern
LssLsss
sssLssL
Equave
3/1 (1902.0¢)
Period
3/1 (1902.0¢)
Generator size(edt)
Bright
3\7 to 1\2 (815.1¢ to 951.0¢)
Dark
1\2 to 4\7 (951.0¢ to 1086.8¢)
Related MOS scales
Parent
2L 3s⟨3/1⟩
Sister
5L 2s⟨3/1⟩
Daughters
7L 2s⟨3/1⟩, 2L 7s⟨3/1⟩
Neutralized
4L 3s⟨3/1⟩
2-Flought
9L 5s⟨3/1⟩, 2L 12s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1)
3\7 (815.1¢)
Supersoft (L:s = 4:3)
10\23 (826.9¢)
Soft (L:s = 3:2)
7\16 (832.1¢)
Semisoft (L:s = 5:3)
11\25 (836.9¢)
Basic (L:s = 2:1)
4\9 (845.3¢)
Semihard (L:s = 5:2)
9\20 (855.9¢)
Hard (L:s = 3:1)
5\11 (864.5¢)
Superhard (L:s = 4:1)
6\13 (877.8¢)
Collapsed (L:s = 1:0)
1\2 (951.0¢)
| ↖ 1L 4s⟨3/1⟩ | ↑ 2L 4s⟨3/1⟩ | 3L 4s⟨3/1⟩ ↗ |
| ← 1L 5s⟨3/1⟩ | 2L 5s (3/1-equivalent) | 3L 5s⟨3/1⟩ → |
| ↙ 1L 6s⟨3/1⟩ | ↓ 2L 6s⟨3/1⟩ | 3L 6s⟨3/1⟩ ↘ |
┌╥┬┬╥┬┬┬┐ │║││║││││ │││││││││ └┴┴┴┴┴┴┴┘
sssLssL
2L 5s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 2 large steps and 5 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 815.1 ¢ to 951 ¢, or from 951 ¢ to 1086.8 ¢.
Theory
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 6|0 | 1 | LssLsss |
| 5|1 | 4 | LsssLss |
| 4|2 | 7 | sLssLss |
| 3|3 | 3 | sLsssLs |
| 2|4 | 6 | ssLssLs |
| 1|5 | 2 | ssLsssL |
| 0|6 | 5 | sssLssL |
Temperament interpretations
|
Todo: expand |
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 271.7 ¢ |
| Major 1-mosstep | M1ms | L | 271.7 ¢ to 951.0 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0 ¢ to 543.4 ¢ |
| Major 2-mosstep | M2ms | L + s | 543.4 ¢ to 951.0 ¢ | |
| 3-mosstep | Diminished 3-mosstep | d3ms | 3s | 0.0 ¢ to 815.1 ¢ |
| Perfect 3-mosstep | P3ms | L + 2s | 815.1 ¢ to 951.0 ¢ | |
| 4-mosstep | Perfect 4-mosstep | P4ms | L + 3s | 951.0 ¢ to 1086.8 ¢ |
| Augmented 4-mosstep | A4ms | 2L + 2s | 1086.8 ¢ to 1902.0 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | L + 4s | 951.0 ¢ to 1358.5 ¢ |
| Major 5-mosstep | M5ms | 2L + 3s | 1358.5 ¢ to 1902.0 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | L + 5s | 951.0 ¢ to 1630.2 ¢ |
| Major 6-mosstep | M6ms | 2L + 4s | 1630.2 ¢ to 1902.0 ¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 2L + 5s | 1902.0¢ |
Scale degrees
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||
| 6|0 | 1 | LssLsss | Perf. | Maj. | Maj. | Perf. | Aug. | Maj. | Maj. | Perf. |
| 5|1 | 4 | LsssLss | Perf. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Perf. |
| 4|2 | 7 | sLssLss | Perf. | Min. | Maj. | Perf. | Perf. | Maj. | Maj. | Perf. |
| 3|3 | 3 | sLsssLs | Perf. | Min. | Maj. | Perf. | Perf. | Min. | Maj. | Perf. |
| 2|4 | 6 | ssLssLs | Perf. | Min. | Min. | Perf. | Perf. | Min. | Maj. | Perf. |
| 1|5 | 2 | ssLsssL | Perf. | Min. | Min. | Perf. | Perf. | Min. | Min. | Perf. |
| 0|6 | 5 | sssLssL | Perf. | Min. | Min. | Dim. | Perf. | Min. | Min. | Perf. |
Scale tree
| Generator(edt) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 3\7 | 815.124 | 1086.831 | 1:1 | 1.000 | Equalized 2L 5s⟨3/1⟩ | |||||
| 16\37 | 822.467 | 1079.488 | 6:5 | 1.200 | ||||||
| 13\30 | 824.181 | 1077.775 | 5:4 | 1.250 | ||||||
| 23\53 | 825.377 | 1076.578 | 9:7 | 1.286 | ||||||
| 10\23 | 826.937 | 1075.018 | 4:3 | 1.333 | Supersoft 2L 5s⟨3/1⟩ | |||||
| 27\62 | 828.271 | 1073.684 | 11:8 | 1.375 | ||||||
| 17\39 | 829.057 | 1072.898 | 7:5 | 1.400 | ||||||
| 24\55 | 829.944 | 1072.011 | 10:7 | 1.429 | ||||||
| 7\16 | 832.105 | 1069.850 | 3:2 | 1.500 | Soft 2L 5s⟨3/1⟩ | |||||
| 25\57 | 834.191 | 1067.764 | 11:7 | 1.571 | ||||||
| 18\41 | 835.005 | 1066.950 | 8:5 | 1.600 | ||||||
| 29\66 | 835.708 | 1066.248 | 13:8 | 1.625 | ||||||
| 11\25 | 836.860 | 1065.095 | 5:3 | 1.667 | Semisoft 2L 5s⟨3/1⟩ | |||||
| 26\59 | 838.150 | 1063.805 | 12:7 | 1.714 | ||||||
| 15\34 | 839.098 | 1062.857 | 7:4 | 1.750 | ||||||
| 19\43 | 840.399 | 1061.556 | 9:5 | 1.800 | ||||||
| 4\9 | 845.313 | 1056.642 | 2:1 | 2.000 | Basic 2L 5s⟨3/1⟩ Scales with tunings softer than this are proper | |||||
| 17\38 | 850.875 | 1051.080 | 9:4 | 2.250 | ||||||
| 13\29 | 852.601 | 1049.354 | 7:3 | 2.333 | ||||||
| 22\49 | 853.939 | 1048.016 | 12:5 | 2.400 | ||||||
| 9\20 | 855.880 | 1046.075 | 5:2 | 2.500 | Semihard 2L 5s⟨3/1⟩ | |||||
| 23\51 | 857.744 | 1044.211 | 13:5 | 2.600 | ||||||
| 14\31 | 858.947 | 1043.008 | 8:3 | 2.667 | ||||||
| 19\42 | 860.408 | 1041.547 | 11:4 | 2.750 | ||||||
| 5\11 | 864.525 | 1037.430 | 3:1 | 3.000 | Hard 2L 5s⟨3/1⟩ | |||||
| 16\35 | 869.465 | 1032.490 | 10:3 | 3.333 | ||||||
| 11\24 | 871.729 | 1030.226 | 7:2 | 3.500 | ||||||
| 17\37 | 873.871 | 1028.084 | 11:3 | 3.667 | ||||||
| 6\13 | 877.825 | 1024.130 | 4:1 | 4.000 | Superhard 2L 5s⟨3/1⟩ | |||||
| 13\28 | 883.051 | 1018.904 | 9:2 | 4.500 | ||||||
| 7\15 | 887.579 | 1014.376 | 5:1 | 5.000 | ||||||
| 8\17 | 895.038 | 1006.917 | 6:1 | 6.000 | ||||||
| 1\2 | 950.978 | 950.978 | 1:0 | → ∞ | Collapsed 2L 5s⟨3/1⟩ | |||||
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