5L 1s (3/2-equivalent)
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Step pattern
LLLLLs
sLLLLL
Equave
3/2 (702.0 ¢)
Period
3/2 (702.0 ¢)
Bright
1\6 to 1\5 (117.0 ¢ to 140.4 ¢)
Dark
4\5 to 5\6 (561.6 ¢ to 585.0 ¢)
Parent
1L 4s⟨3/2⟩
Sister
1L 5s⟨3/2⟩
Daughters
6L 5s⟨3/2⟩, 5L 6s⟨3/2⟩
Neutralized
4L 2s⟨3/2⟩
2-Flought
11L 1s⟨3/2⟩, 5L 7s⟨3/2⟩
Equalized (L:s = 1:1)
1\6 (117.0 ¢)
Supersoft (L:s = 4:3)
4\23 (122.1 ¢)
Soft (L:s = 3:2)
3\17 (123.9 ¢)
Semisoft (L:s = 5:3)
5\28 (125.3 ¢)
Basic (L:s = 2:1)
2\11 (127.6 ¢)
Semihard (L:s = 5:2)
5\27 (130.0 ¢)
Hard (L:s = 3:1)
3\16 (131.6 ¢)
Superhard (L:s = 4:1)
4\21 (133.7 ¢)
Collapsed (L:s = 1:0)
1\5 (140.4 ¢)
← 4L 1s⟨3/2⟩ | 5L 1s (3/2-equivalent) | 6L 1s⟨3/2⟩ → |
↙ 4L 2s⟨3/2⟩ | ↓ 5L 2s⟨3/2⟩ | 6L 2s⟨3/2⟩ ↘ |
┌╥╥╥╥╥┬┐ │║║║║║││ ││││││││ └┴┴┴┴┴┴┘
Scale structure
sLLLLL
Generator size(edf)
Related MOS scales
Equal tunings(edf)
5L 1s⟨3/2⟩ is a 3/2-equivalent (fifth-equivalent) moment of symmetry scale containing 5 large steps and 1 small step, repeating every interval of 3/2 (702.0 ¢). Generators that produce this scale range from 117 ¢ to 140.4 ¢, or from 561.6 ¢ to 585 ¢. Scales of this form are always proper because there is only one small step.
It is most notable as the hexatonic scale of halftone temperament, with the bright generator being a sharp 15/14 and the dark generator being a flat 7/5.
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 | Diminished 1-mosstep | d1ms | s | 0.0 ¢ to 117.0 ¢ |
Perfect 1-mosstep | P1ms | L | 117.0 ¢ to 140.4 ¢ | |
2-mosstep | Minor 2-mosstep | m2ms | L + s | 140.4 ¢ to 234.0 ¢ |
Major 2-mosstep | M2ms | 2L | 234.0 ¢ to 280.8 ¢ | |
3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 280.8 ¢ to 351.0 ¢ |
Major 3-mosstep | M3ms | 3L | 351.0 ¢ to 421.2 ¢ | |
4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 421.2 ¢ to 468.0 ¢ |
Major 4-mosstep | M4ms | 4L | 468.0 ¢ to 561.6 ¢ | |
5-mosstep | Perfect 5-mosstep | P5ms | 4L + s | 561.6 ¢ to 585.0 ¢ |
Augmented 5-mosstep | A5ms | 5L | 585.0 ¢ to 702.0 ¢ | |
6-mosstep | Perfect 6-mosstep | P6ms | 5L + s | 702.0 ¢ |
Generator chain
Bright gens | Scale degree | Abbrev. |
---|---|---|
10 | Augmented 4-mosdegree | A4md |
9 | Augmented 3-mosdegree | A3md |
8 | Augmented 2-mosdegree | A2md |
7 | Augmented 1-mosdegree | A1md |
6 | Augmented 0-mosdegree | A0md |
5 | Augmented 5-mosdegree | A5md |
4 | Major 4-mosdegree | M4md |
3 | Major 3-mosdegree | M3md |
2 | Major 2-mosdegree | M2md |
1 | Perfect 1-mosdegree | P1md |
0 | Perfect 0-mosdegree Perfect 6-mosdegree |
P0md P6md |
−1 | Perfect 5-mosdegree | P5md |
−2 | Minor 4-mosdegree | m4md |
−3 | Minor 3-mosdegree | m3md |
−4 | Minor 2-mosdegree | m2md |
−5 | Diminished 1-mosdegree | d1md |
−6 | Diminished 6-mosdegree | d6md |
−7 | Diminished 5-mosdegree | d5md |
−8 | Diminished 4-mosdegree | d4md |
−9 | Diminished 3-mosdegree | d3md |
−10 | Diminished 2-mosdegree | d2md |
Modes
UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | ||||||
---|---|---|---|---|---|---|---|---|---|
0 | 1 | 2 | 3 | 4 | 5 | 6 | |||
5|0 | 1 | LLLLLs | Perf. | Perf. | Maj. | Maj. | Maj. | Aug. | Perf. |
4|1 | 2 | LLLLsL | Perf. | Perf. | Maj. | Maj. | Maj. | Perf. | Perf. |
3|2 | 3 | LLLsLL | Perf. | Perf. | Maj. | Maj. | Min. | Perf. | Perf. |
2|3 | 4 | LLsLLL | Perf. | Perf. | Maj. | Min. | Min. | Perf. | Perf. |
1|4 | 5 | LsLLLL | Perf. | Perf. | Min. | Min. | Min. | Perf. | Perf. |
0|5 | 6 | sLLLLL | Perf. | Dim. | Min. | Min. | Min. | Perf. | Perf. |
Scale tree
Generator(edf) | Cents | Step ratio | Comments(always proper) | |||||||
---|---|---|---|---|---|---|---|---|---|---|
Bright | Dark | L:s | Hardness | |||||||
1\6 | 116.993 | 584.963 | 1:1 | 1.000 | Equalized 5L 1s⟨3/2⟩ | |||||
6\35 | 120.335 | 581.620 | 6:5 | 1.200 | ||||||
5\29 | 121.027 | 580.928 | 5:4 | 1.250 | ||||||
9\52 | 121.492 | 580.463 | 9:7 | 1.286 | ||||||
4\23 | 122.079 | 579.876 | 4:3 | 1.333 | Supersoft 5L 1s⟨3/2⟩ | |||||
11\63 | 122.564 | 579.391 | 11:8 | 1.375 | ||||||
7\40 | 122.842 | 579.113 | 7:5 | 1.400 | ||||||
10\57 | 123.150 | 578.805 | 10:7 | 1.429 | ||||||
3\17 | 123.874 | 578.081 | 3:2 | 1.500 | Soft 5L 1s⟨3/2⟩ | |||||
11\62 | 124.540 | 577.415 | 11:7 | 1.571 | ||||||
8\45 | 124.792 | 577.163 | 8:5 | 1.600 | ||||||
13\73 | 125.006 | 576.949 | 13:8 | 1.625 | ||||||
5\28 | 125.349 | 576.606 | 5:3 | 1.667 | Semisoft 5L 1s⟨3/2⟩ | |||||
12\67 | 125.723 | 576.232 | 12:7 | 1.714 | ||||||
7\39 | 125.992 | 575.963 | 7:4 | 1.750 | ||||||
9\50 | 126.352 | 575.603 | 9:5 | 1.800 | ||||||
2\11 | 127.628 | 574.327 | 2:1 | 2.000 | Basic 5L 1s⟨3/2⟩ | |||||
9\49 | 128.931 | 573.024 | 9:4 | 2.250 | ||||||
7\38 | 129.308 | 572.648 | 7:3 | 2.333 | ||||||
12\65 | 129.592 | 572.363 | 12:5 | 2.400 | ||||||
5\27 | 129.992 | 571.963 | 5:2 | 2.500 | Semihard 5L 1s⟨3/2⟩ Halftone is in this region | |||||
13\70 | 130.363 | 571.592 | 13:5 | 2.600 | ||||||
8\43 | 130.596 | 571.359 | 8:3 | 2.667 | ||||||
11\59 | 130.873 | 571.082 | 11:4 | 2.750 | ||||||
3\16 | 131.617 | 570.338 | 3:1 | 3.000 | Hard 5L 1s⟨3/2⟩ | |||||
10\53 | 132.444 | 569.511 | 10:3 | 3.333 | ||||||
7\37 | 132.802 | 569.153 | 7:2 | 3.500 | ||||||
11\58 | 133.129 | 568.826 | 11:3 | 3.667 | ||||||
4\21 | 133.706 | 568.249 | 4:1 | 4.000 | Superhard 5L 1s⟨3/2⟩ | |||||
9\47 | 134.417 | 567.538 | 9:2 | 4.500 | ||||||
5\26 | 134.991 | 566.964 | 5:1 | 5.000 | ||||||
6\31 | 135.862 | 566.093 | 6:1 | 6.000 | ||||||
1\5 | 140.391 | 561.564 | 1:0 | → ∞ | Collapsed 5L 1s⟨3/2⟩ |