5L 2s
| ↖ 4L 1s | ↑ 5L 1s | 6L 1s ↗ |
| ← 4L 2s | 5L 2s | 6L 2s → |
| ↙ 4L 3s | ↓ 5L 3s | 6L 3s ↘ |
┌╥╥╥┬╥╥┬┐ │║║║│║║││ │││││││││ └┴┴┴┴┴┴┴┘
sLLsLLL
5L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 5 large steps and 2 small steps, repeating every octave. Generators that produce this scale range from 685.7¢ to 720¢, or from 480¢ to 514.3¢.
The familiar pattern of 5 whole steps and 2 half steps, commonly written as WWHWWWH for the major scale, takes on a generalized form of LLsLLLs, where the large and small steps—denoted as L's and s's—represent whole number step sizes, thus producing different edos. These step ratios affect the sizes of the diatonic scale's intervals and correspond to different tuning systems.
Among the most well-known forms of this scale are the Pythagorean diatonic scale, and scales produced by meantone systems (including 12edo).
Name
TAMNAMS suggests the temperament-agnostic name diatonic as the name of 5L 2s. The name commonly refers to a scale with 5 whole and 2 half steps, or 5 large and 2 small steps; see TAMNAMS/Appendix #On the term diatonic for more information.
Notation
- This article assumes TAMNAMS for naming step ratios.
Intervals
Intervals are identical to that of standard notation. As such, the usual interval qualities of major/minor and augmented/perfect/diminished apply here.
| 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 171.4¢ |
| Major 1-mosstep | M1ms | L | 171.4¢ to 240.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 240.0¢ to 342.9¢ |
| Major 2-mosstep | M2ms | 2L | 342.9¢ to 480.0¢ | |
| 3-mosstep | Perfect 3-mosstep | P3ms | 2L + s | 480.0¢ to 514.3¢ |
| Augmented 3-mosstep | A3ms | 3L | 514.3¢ to 720.0¢ | |
| 4-mosstep | Diminished 4-mosstep | d4ms | 2L + 2s | 480.0¢ to 685.7¢ |
| Perfect 4-mosstep | P4ms | 3L + s | 685.7¢ to 720.0¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 3L + 2s | 720.0¢ to 857.1¢ |
| Major 5-mosstep | M5ms | 4L + s | 857.1¢ to 960.0¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 4L + 2s | 960.0¢ to 1028.6¢ |
| Major 6-mosstep | M6ms | 5L + s | 1028.6¢ to 1200.0¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 5L + 2s | 1200.0¢ |
Note names
Note names are identical to that of standard notation. Thus, the basic gamut for 5L 2s is the following: J, J&/K@, K, L, L&/M@, M, M&/N@, N, N&/O@, O, P, P&/J@, J
Theory
Temperament interpretations
5L 2s has several rank-2 temperament interpretations, such as:
- Meantone, with generators around 696.2¢. This includes:
- Flattone, with generators around 693.7¢.
- Schismic, with generators around 702¢.
- Parapyth, with generators around 704.7¢.
- Archy, with generators around 709.3¢. This includes:
- Supra, with generators around 707.2¢
- Superpyth, with generators around 710.3¢
- Ultrapyth, with generators around 713.7¢.
Warped diatonic scales
Because of most listeners’ familiarity with the 5L 2s diatonic scale, listeners may sometimes experience an effect like pareidolia, hearing 5L 2s even when it isn’t there.
A larger scale can be constructed so that it contains chains of 5L 2s, but then breaks the pattern, exploiting that pareidolic effect to surprise and disorient the listener. Scales which have this effect are called warped diatonic scales.
Tuning ranges
|
Todo: Verify Populate/verify tables |
Simple tunings
17edo and 19edo are the smallest edos that offer a greater variety of pitches than 12edo. Note that any enharmonic equivalences that 12edo has no longer hold for either 17edo or 19edo, as shown in the table below.
| Scale degree | Abbrev. | Basic (2:1) 12edo |
Hard (3:1) 17edo |
Soft (3:2) 19edo | |||
|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\12 | 0.0 | 0\17 | 0.0 | 0\19 | 0.0 |
| Minor 1-mosdegree | m1md | 1\12 | 100.0 | 1\17 | 70.6 | 2\19 | 126.3 |
| Major 1-mosdegree | M1md | 2\12 | 200.0 | 3\17 | 211.8 | 3\19 | 189.5 |
| Minor 2-mosdegree | m2md | 3\12 | 300.0 | 4\17 | 282.4 | 5\19 | 315.8 |
| Major 2-mosdegree | M2md | 4\12 | 400.0 | 6\17 | 423.5 | 6\19 | 378.9 |
| Perfect 3-mosdegree | P3md | 5\12 | 500.0 | 7\17 | 494.1 | 8\19 | 505.3 |
| Augmented 3-mosdegree | A3md | 6\12 | 600.0 | 9\17 | 635.3 | 9\19 | 568.4 |
| Diminished 4-mosdegree | d4md | 6\12 | 600.0 | 8\17 | 564.7 | 10\19 | 631.6 |
| Perfect 4-mosdegree | P4md | 7\12 | 700.0 | 10\17 | 705.9 | 11\19 | 694.7 |
| Minor 5-mosdegree | m5md | 8\12 | 800.0 | 11\17 | 776.5 | 13\19 | 821.1 |
| Major 5-mosdegree | M5md | 9\12 | 900.0 | 13\17 | 917.6 | 14\19 | 884.2 |
| Minor 6-mosdegree | m6md | 10\12 | 1000.0 | 14\17 | 988.2 | 16\19 | 1010.5 |
| Major 6-mosdegree | M6md | 11\12 | 1100.0 | 16\17 | 1129.4 | 17\19 | 1073.7 |
| Perfect 7-mosdegree | P7md | 12\12 | 1200.0 | 17\17 | 1200.0 | 19\19 | 1200.0 |
Ultrasoft tunings
| Scale degree | Abbrev. | 6:5 40edo |
5:4 33edo |
Supersoft (4:3) 26edo | |||
|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\40 | 0.0 | 0\33 | 0.0 | 0\26 | 0.0 |
| Minor 1-mosdegree | m1md | 5\40 | 150.0 | 4\33 | 145.5 | 3\26 | 138.5 |
| Major 1-mosdegree | M1md | 6\40 | 180.0 | 5\33 | 181.8 | 4\26 | 184.6 |
| Minor 2-mosdegree | m2md | 11\40 | 330.0 | 9\33 | 327.3 | 7\26 | 323.1 |
| Major 2-mosdegree | M2md | 12\40 | 360.0 | 10\33 | 363.6 | 8\26 | 369.2 |
| Perfect 3-mosdegree | P3md | 17\40 | 510.0 | 14\33 | 509.1 | 11\26 | 507.7 |
| Augmented 3-mosdegree | A3md | 18\40 | 540.0 | 15\33 | 545.5 | 12\26 | 553.8 |
| Diminished 4-mosdegree | d4md | 22\40 | 660.0 | 18\33 | 654.5 | 14\26 | 646.2 |
| Perfect 4-mosdegree | P4md | 23\40 | 690.0 | 19\33 | 690.9 | 15\26 | 692.3 |
| Minor 5-mosdegree | m5md | 28\40 | 840.0 | 23\33 | 836.4 | 18\26 | 830.8 |
| Major 5-mosdegree | M5md | 29\40 | 870.0 | 24\33 | 872.7 | 19\26 | 876.9 |
| Minor 6-mosdegree | m6md | 34\40 | 1020.0 | 28\33 | 1018.2 | 22\26 | 1015.4 |
| Major 6-mosdegree | M6md | 35\40 | 1050.0 | 29\33 | 1054.5 | 23\26 | 1061.5 |
| Perfect 7-mosdegree | P7md | 40\40 | 1200.0 | 33\33 | 1200.0 | 26\26 | 1200.0 |
Parasoft tunings
Parasoft diatonic tunings (4:3 to 3:2) correspond to flattone temperaments, characterized by flattened perfect 5ths (3/2, flat of 702¢) to produce major 3rds that are flatter than 5/4 (386¢).
Edos include 19edo, 26edo, 45edo, and 64edo.
| Scale degree | Abbrev. | Supersoft (4:3) 26edo |
7:5 45edo |
10:7 64edo |
Soft (3:2) 19edo | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\26 | 0.0 | 0\45 | 0.0 | 0\64 | 0.0 | 0\19 | 0.0 |
| Minor 1-mosdegree | m1md | 3\26 | 138.5 | 5\45 | 133.3 | 7\64 | 131.2 | 2\19 | 126.3 |
| Major 1-mosdegree | M1md | 4\26 | 184.6 | 7\45 | 186.7 | 10\64 | 187.5 | 3\19 | 189.5 |
| Minor 2-mosdegree | m2md | 7\26 | 323.1 | 12\45 | 320.0 | 17\64 | 318.8 | 5\19 | 315.8 |
| Major 2-mosdegree | M2md | 8\26 | 369.2 | 14\45 | 373.3 | 20\64 | 375.0 | 6\19 | 378.9 |
| Perfect 3-mosdegree | P3md | 11\26 | 507.7 | 19\45 | 506.7 | 27\64 | 506.2 | 8\19 | 505.3 |
| Augmented 3-mosdegree | A3md | 12\26 | 553.8 | 21\45 | 560.0 | 30\64 | 562.5 | 9\19 | 568.4 |
| Diminished 4-mosdegree | d4md | 14\26 | 646.2 | 24\45 | 640.0 | 34\64 | 637.5 | 10\19 | 631.6 |
| Perfect 4-mosdegree | P4md | 15\26 | 692.3 | 26\45 | 693.3 | 37\64 | 693.8 | 11\19 | 694.7 |
| Minor 5-mosdegree | m5md | 18\26 | 830.8 | 31\45 | 826.7 | 44\64 | 825.0 | 13\19 | 821.1 |
| Major 5-mosdegree | M5md | 19\26 | 876.9 | 33\45 | 880.0 | 47\64 | 881.2 | 14\19 | 884.2 |
| Minor 6-mosdegree | m6md | 22\26 | 1015.4 | 38\45 | 1013.3 | 54\64 | 1012.5 | 16\19 | 1010.5 |
| Major 6-mosdegree | M6md | 23\26 | 1061.5 | 40\45 | 1066.7 | 57\64 | 1068.8 | 17\19 | 1073.7 |
| Perfect 7-mosdegree | P7md | 26\26 | 1200.0 | 45\45 | 1200.0 | 64\64 | 1200.0 | 19\19 | 1200.0 |
Hyposoft tunings
Hyposoft diatonic tunings (3:2 to 2:1) correspond to meantone temperaments, characterized by flattened perfect 5ths (flat of 702¢) to produce diatonic major 3rds that approximate 5/4 (386¢).
Edos include 19edo, 31edo, 43edo, and 50edo.
| Scale degree | Abbrev. | Soft (3:2) 19edo |
8:5 50edo |
Semisoft (5:3) 31edo |
7:4 43edo |
Basic (2:1) 12edo | |||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\19 | 0.0 | 0\50 | 0.0 | 0\31 | 0.0 | 0\43 | 0.0 | 0\12 | 0.0 |
| Minor 1-mosdegree | m1md | 2\19 | 126.3 | 5\50 | 120.0 | 3\31 | 116.1 | 4\43 | 111.6 | 1\12 | 100.0 |
| Major 1-mosdegree | M1md | 3\19 | 189.5 | 8\50 | 192.0 | 5\31 | 193.5 | 7\43 | 195.3 | 2\12 | 200.0 |
| Minor 2-mosdegree | m2md | 5\19 | 315.8 | 13\50 | 312.0 | 8\31 | 309.7 | 11\43 | 307.0 | 3\12 | 300.0 |
| Major 2-mosdegree | M2md | 6\19 | 378.9 | 16\50 | 384.0 | 10\31 | 387.1 | 14\43 | 390.7 | 4\12 | 400.0 |
| Perfect 3-mosdegree | P3md | 8\19 | 505.3 | 21\50 | 504.0 | 13\31 | 503.2 | 18\43 | 502.3 | 5\12 | 500.0 |
| Augmented 3-mosdegree | A3md | 9\19 | 568.4 | 24\50 | 576.0 | 15\31 | 580.6 | 21\43 | 586.0 | 6\12 | 600.0 |
| Diminished 4-mosdegree | d4md | 10\19 | 631.6 | 26\50 | 624.0 | 16\31 | 619.4 | 22\43 | 614.0 | 6\12 | 600.0 |
| Perfect 4-mosdegree | P4md | 11\19 | 694.7 | 29\50 | 696.0 | 18\31 | 696.8 | 25\43 | 697.7 | 7\12 | 700.0 |
| Minor 5-mosdegree | m5md | 13\19 | 821.1 | 34\50 | 816.0 | 21\31 | 812.9 | 29\43 | 809.3 | 8\12 | 800.0 |
| Major 5-mosdegree | M5md | 14\19 | 884.2 | 37\50 | 888.0 | 23\31 | 890.3 | 32\43 | 893.0 | 9\12 | 900.0 |
| Minor 6-mosdegree | m6md | 16\19 | 1010.5 | 42\50 | 1008.0 | 26\31 | 1006.5 | 36\43 | 1004.7 | 10\12 | 1000.0 |
| Major 6-mosdegree | M6md | 17\19 | 1073.7 | 45\50 | 1080.0 | 28\31 | 1083.9 | 39\43 | 1088.4 | 11\12 | 1100.0 |
| Perfect 7-mosdegree | P7md | 19\19 | 1200.0 | 50\50 | 1200.0 | 31\31 | 1200.0 | 43\43 | 1200.0 | 12\12 | 1200.0 |
Hypohard tunings
- See also: Pythagorean tuning and schismatic temperament
The range of hypohard tunings can be divided into a minihard range (2:1 to 5:2) and quasihard range (5:2 to 3:1).
| Scale degree | Abbrev. | Basic (2:1) 12edo |
Semihard (5:2) 29edo |
Hard (3:1) 17edo | |||
|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\12 | 0.0 | 0\29 | 0.0 | 0\17 | 0.0 |
| Minor 1-mosdegree | m1md | 1\12 | 100.0 | 2\29 | 82.8 | 1\17 | 70.6 |
| Major 1-mosdegree | M1md | 2\12 | 200.0 | 5\29 | 206.9 | 3\17 | 211.8 |
| Minor 2-mosdegree | m2md | 3\12 | 300.0 | 7\29 | 289.7 | 4\17 | 282.4 |
| Major 2-mosdegree | M2md | 4\12 | 400.0 | 10\29 | 413.8 | 6\17 | 423.5 |
| Perfect 3-mosdegree | P3md | 5\12 | 500.0 | 12\29 | 496.6 | 7\17 | 494.1 |
| Augmented 3-mosdegree | A3md | 6\12 | 600.0 | 15\29 | 620.7 | 9\17 | 635.3 |
| Diminished 4-mosdegree | d4md | 6\12 | 600.0 | 14\29 | 579.3 | 8\17 | 564.7 |
| Perfect 4-mosdegree | P4md | 7\12 | 700.0 | 17\29 | 703.4 | 10\17 | 705.9 |
| Minor 5-mosdegree | m5md | 8\12 | 800.0 | 19\29 | 786.2 | 11\17 | 776.5 |
| Major 5-mosdegree | M5md | 9\12 | 900.0 | 22\29 | 910.3 | 13\17 | 917.6 |
| Minor 6-mosdegree | m6md | 10\12 | 1000.0 | 24\29 | 993.1 | 14\17 | 988.2 |
| Major 6-mosdegree | M6md | 11\12 | 1100.0 | 27\29 | 1117.2 | 16\17 | 1129.4 |
| Perfect 7-mosdegree | P7md | 12\12 | 1200.0 | 29\29 | 1200.0 | 17\17 | 1200.0 |
Minihard tunings
Minihard diatonic tunings correspond to Pythagorean tuning and schismatic temperament, characterized by having a perfect 5th that is as close to just (701.96¢) as possible, resulting in a major 3rd of 81/64 (407¢).
| Scale degree | Abbrev. | Basic (2:1) 12edo |
9:4 53edo |
7:3 41edo |
Semihard (5:2) 29edo | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\12 | 0.0 | 0\53 | 0.0 | 0\41 | 0.0 | 0\29 | 0.0 |
| Minor 1-mosdegree | m1md | 1\12 | 100.0 | 4\53 | 90.6 | 3\41 | 87.8 | 2\29 | 82.8 |
| Major 1-mosdegree | M1md | 2\12 | 200.0 | 9\53 | 203.8 | 7\41 | 204.9 | 5\29 | 206.9 |
| Minor 2-mosdegree | m2md | 3\12 | 300.0 | 13\53 | 294.3 | 10\41 | 292.7 | 7\29 | 289.7 |
| Major 2-mosdegree | M2md | 4\12 | 400.0 | 18\53 | 407.5 | 14\41 | 409.8 | 10\29 | 413.8 |
| Perfect 3-mosdegree | P3md | 5\12 | 500.0 | 22\53 | 498.1 | 17\41 | 497.6 | 12\29 | 496.6 |
| Augmented 3-mosdegree | A3md | 6\12 | 600.0 | 27\53 | 611.3 | 21\41 | 614.6 | 15\29 | 620.7 |
| Diminished 4-mosdegree | d4md | 6\12 | 600.0 | 26\53 | 588.7 | 20\41 | 585.4 | 14\29 | 579.3 |
| Perfect 4-mosdegree | P4md | 7\12 | 700.0 | 31\53 | 701.9 | 24\41 | 702.4 | 17\29 | 703.4 |
| Minor 5-mosdegree | m5md | 8\12 | 800.0 | 35\53 | 792.5 | 27\41 | 790.2 | 19\29 | 786.2 |
| Major 5-mosdegree | M5md | 9\12 | 900.0 | 40\53 | 905.7 | 31\41 | 907.3 | 22\29 | 910.3 |
| Minor 6-mosdegree | m6md | 10\12 | 1000.0 | 44\53 | 996.2 | 34\41 | 995.1 | 24\29 | 993.1 |
| Major 6-mosdegree | M6md | 11\12 | 1100.0 | 49\53 | 1109.4 | 38\41 | 1112.2 | 27\29 | 1117.2 |
| Perfect 7-mosdegree | P7md | 12\12 | 1200.0 | 53\53 | 1200.0 | 41\41 | 1200.0 | 29\29 | 1200.0 |
Quasihard tunings
Quasihard diatonic tunings correspond to "neogothic" or "parapyth" systems whose perfect 5th is slightly sharper than just, resulting in major 3rds that are sharper than 81/64 and minor 3rds that are slightly flat of 32/27 (294¢).
Edos include 17edo, 29edo, and 46edo. 17edo is considered to be on the sharper end of the neogothic spectrum, with a major 3rd that is more discordant than flatter neogothic tunings.
| Scale degree | Abbrev. | Semihard (5:2) 29edo |
8:3 46edo |
Hard (3:1) 17edo | |||
|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\29 | 0.0 | 0\46 | 0.0 | 0\17 | 0.0 |
| Minor 1-mosdegree | m1md | 2\29 | 82.8 | 3\46 | 78.3 | 1\17 | 70.6 |
| Major 1-mosdegree | M1md | 5\29 | 206.9 | 8\46 | 208.7 | 3\17 | 211.8 |
| Minor 2-mosdegree | m2md | 7\29 | 289.7 | 11\46 | 287.0 | 4\17 | 282.4 |
| Major 2-mosdegree | M2md | 10\29 | 413.8 | 16\46 | 417.4 | 6\17 | 423.5 |
| Perfect 3-mosdegree | P3md | 12\29 | 496.6 | 19\46 | 495.7 | 7\17 | 494.1 |
| Augmented 3-mosdegree | A3md | 15\29 | 620.7 | 24\46 | 626.1 | 9\17 | 635.3 |
| Diminished 4-mosdegree | d4md | 14\29 | 579.3 | 22\46 | 573.9 | 8\17 | 564.7 |
| Perfect 4-mosdegree | P4md | 17\29 | 703.4 | 27\46 | 704.3 | 10\17 | 705.9 |
| Minor 5-mosdegree | m5md | 19\29 | 786.2 | 30\46 | 782.6 | 11\17 | 776.5 |
| Major 5-mosdegree | M5md | 22\29 | 910.3 | 35\46 | 913.0 | 13\17 | 917.6 |
| Minor 6-mosdegree | m6md | 24\29 | 993.1 | 38\46 | 991.3 | 14\17 | 988.2 |
| Major 6-mosdegree | M6md | 27\29 | 1117.2 | 43\46 | 1121.7 | 16\17 | 1129.4 |
| Perfect 7-mosdegree | P7md | 29\29 | 1200.0 | 46\46 | 1200.0 | 17\17 | 1200.0 |
Parahard and ultrahard tunings
Parahard (3:1 to 4:1) and ultrahard (4:1 to 1:0) diatonic tunings correspond to archy systems, with perfect 5ths that are significantly sharper than than 702¢.
Edos include 17edo, 22edo, 27edo, and 32edo, among others.
| Scale degree | Abbrev. | Hard (3:1) 17edo |
Superhard (4:1) 22edo |
5:1 27edo |
6:1 32edo | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\17 | 0.0 | 0\22 | 0.0 | 0\27 | 0.0 | 0\32 | 0.0 |
| Minor 1-mosdegree | m1md | 1\17 | 70.6 | 1\22 | 54.5 | 1\27 | 44.4 | 1\32 | 37.5 |
| Major 1-mosdegree | M1md | 3\17 | 211.8 | 4\22 | 218.2 | 5\27 | 222.2 | 6\32 | 225.0 |
| Minor 2-mosdegree | m2md | 4\17 | 282.4 | 5\22 | 272.7 | 6\27 | 266.7 | 7\32 | 262.5 |
| Major 2-mosdegree | M2md | 6\17 | 423.5 | 8\22 | 436.4 | 10\27 | 444.4 | 12\32 | 450.0 |
| Perfect 3-mosdegree | P3md | 7\17 | 494.1 | 9\22 | 490.9 | 11\27 | 488.9 | 13\32 | 487.5 |
| Augmented 3-mosdegree | A3md | 9\17 | 635.3 | 12\22 | 654.5 | 15\27 | 666.7 | 18\32 | 675.0 |
| Diminished 4-mosdegree | d4md | 8\17 | 564.7 | 10\22 | 545.5 | 12\27 | 533.3 | 14\32 | 525.0 |
| Perfect 4-mosdegree | P4md | 10\17 | 705.9 | 13\22 | 709.1 | 16\27 | 711.1 | 19\32 | 712.5 |
| Minor 5-mosdegree | m5md | 11\17 | 776.5 | 14\22 | 763.6 | 17\27 | 755.6 | 20\32 | 750.0 |
| Major 5-mosdegree | M5md | 13\17 | 917.6 | 17\22 | 927.3 | 21\27 | 933.3 | 25\32 | 937.5 |
| Minor 6-mosdegree | m6md | 14\17 | 988.2 | 18\22 | 981.8 | 22\27 | 977.8 | 26\32 | 975.0 |
| Major 6-mosdegree | M6md | 16\17 | 1129.4 | 21\22 | 1145.5 | 26\27 | 1155.6 | 31\32 | 1162.5 |
| Perfect 7-mosdegree | P7md | 17\17 | 1200.0 | 22\22 | 1200.0 | 27\27 | 1200.0 | 32\32 | 1200.0 |
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |||
| 6|0 | 1 | LLLsLLs | Perf. | Maj. | Maj. | Aug. | Perf. | Maj. | Maj. | Perf. |
| 5|1 | 5 | LLsLLLs | Perf. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Perf. |
| 4|2 | 2 | LLsLLsL | Perf. | Maj. | Maj. | Perf. | Perf. | Maj. | Min. | Perf. |
| 3|3 | 6 | LsLLLsL | Perf. | Maj. | Min. | Perf. | Perf. | Maj. | Min. | Perf. |
| 2|4 | 3 | LsLLsLL | Perf. | Maj. | Min. | Perf. | Perf. | Min. | Min. | Perf. |
| 1|5 | 7 | sLLLsLL | Perf. | Min. | Min. | Perf. | Perf. | Min. | Min. | Perf. |
| 0|6 | 4 | sLLsLLL | Perf. | Min. | Min. | Perf. | Dim. | Min. | Min. | Perf. |
Diatonic modes have standard names from classical music theory.
| UDP | Cyclic order |
Step pattern |
Mode names |
|---|---|---|---|
| 6|0 | 1 | LLLsLLs | Lydian |
| 5|1 | 5 | LLsLLLs | Ionian (major) |
| 4|2 | 2 | LLsLLsL | Mixolydian |
| 3|3 | 6 | LsLLLsL | Dorian |
| 2|4 | 3 | LsLLsLL | Aeolian (minor) |
| 1|5 | 7 | sLLLsLL | Phrygian |
| 0|6 | 4 | sLLsLLL | Locrian |
Scales
Subset and superset scales
5L 2s has a parent scale of 2L 3s, a pentatonic scale, meaning 2L 3s is a subset. 5L 2s also has two child scales, which are supersets of 5L 2s:
- 7L 5s, a chromatic scale produced using soft-of-basic step ratios.
- 5L 7s, a chromatic scale produced using hard-of-basic step ratios.
12edo, the equalized form of both 7L 5s and 5L 7s, is also a superset of 5L 2s.
MODMOS scales and muddles
Scala files
- Meantone7 – 19edo and 31edo tunings
- Nestoria7 – 171edo tuning
- Pythagorean7 – Pythagorean tuning
- Garibaldi7 – 94edo tuning
- Cotoneum7 – 217edo tuning
- Edson7 – 29edo tuning
- Pepperoni7 – 271edo tuning
- Supra7 – 56edo tuning
- Archy7 – 472edo tuning
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | ||||||||
| 4\7 | 685.714 | 514.286 | 1:1 | 1.000 | Equalized 5L 2s | ||||||
| 27\47 | 689.362 | 510.638 | 7:6 | 1.167 | |||||||
| 23\40 | 690.000 | 510.000 | 6:5 | 1.200 | |||||||
| 42\73 | 690.411 | 509.589 | 11:9 | 1.222 | |||||||
| 19\33 | 690.909 | 509.091 | 5:4 | 1.250 | |||||||
| 53\92 | 691.304 | 508.696 | 14:11 | 1.273 | |||||||
| 34\59 | 691.525 | 508.475 | 9:7 | 1.286 | |||||||
| 49\85 | 691.765 | 508.235 | 13:10 | 1.300 | |||||||
| 15\26 | 692.308 | 507.692 | 4:3 | 1.333 | Supersoft 5L 2s | ||||||
| 56\97 | 692.784 | 507.216 | 15:11 | 1.364 | |||||||
| 41\71 | 692.958 | 507.042 | 11:8 | 1.375 | |||||||
| 67\116 | 693.103 | 506.897 | 18:13 | 1.385 | |||||||
| 26\45 | 693.333 | 506.667 | 7:5 | 1.400 | Flattone is in this region | ||||||
| 63\109 | 693.578 | 506.422 | 17:12 | 1.417 | |||||||
| 37\64 | 693.750 | 506.250 | 10:7 | 1.429 | |||||||
| 48\83 | 693.976 | 506.024 | 13:9 | 1.444 | |||||||
| 11\19 | 694.737 | 505.263 | 3:2 | 1.500 | Soft 5L 2s | ||||||
| 51\88 | 695.455 | 504.545 | 14:9 | 1.556 | |||||||
| 40\69 | 695.652 | 504.348 | 11:7 | 1.571 | |||||||
| 69\119 | 695.798 | 504.202 | 19:12 | 1.583 | |||||||
| 29\50 | 696.000 | 504.000 | 8:5 | 1.600 | |||||||
| 76\131 | 696.183 | 503.817 | 21:13 | 1.615 | Golden meantone (696.214¢) | ||||||
| 47\81 | 696.296 | 503.704 | 13:8 | 1.625 | |||||||
| 65\112 | 696.429 | 503.571 | 18:11 | 1.636 | |||||||
| 18\31 | 696.774 | 503.226 | 5:3 | 1.667 | Semisoft 5L 2s Meantone is in this region | ||||||
| 61\105 | 697.143 | 502.857 | 17:10 | 1.700 | |||||||
| 43\74 | 697.297 | 502.703 | 12:7 | 1.714 | |||||||
| 68\117 | 697.436 | 502.564 | 19:11 | 1.727 | |||||||
| 25\43 | 697.674 | 502.326 | 7:4 | 1.750 | |||||||
| 57\98 | 697.959 | 502.041 | 16:9 | 1.778 | |||||||
| 32\55 | 698.182 | 501.818 | 9:5 | 1.800 | |||||||
| 39\67 | 698.507 | 501.493 | 11:6 | 1.833 | |||||||
| 7\12 | 700.000 | 500.000 | 2:1 | 2.000 | Basic 5L 2s Scales with tunings softer than this are proper | ||||||
| 38\65 | 701.538 | 498.462 | 11:5 | 2.200 | |||||||
| 31\53 | 701.887 | 498.113 | 9:4 | 2.250 | Pythagorean tuning (701.955¢) | ||||||
| 55\94 | 702.128 | 497.872 | 16:7 | 2.286 | Garibaldi / cassandra | ||||||
| 24\41 | 702.439 | 497.561 | 7:3 | 2.333 | |||||||
| 65\111 | 702.703 | 497.297 | 19:8 | 2.375 | |||||||
| 41\70 | 702.857 | 497.143 | 12:5 | 2.400 | |||||||
| 58\99 | 703.030 | 496.970 | 17:7 | 2.429 | |||||||
| 17\29 | 703.448 | 496.552 | 5:2 | 2.500 | Semihard 5L 2s Dominant is in this region | ||||||
| 61\104 | 703.846 | 496.154 | 18:7 | 2.571 | |||||||
| 44\75 | 704.000 | 496.000 | 13:5 | 2.600 | |||||||
| 71\121 | 704.132 | 495.868 | 21:8 | 2.625 | Golden neogothic (704.096¢) | ||||||
| 27\46 | 704.348 | 495.652 | 8:3 | 2.667 | Neogothic is in this region | ||||||
| 64\109 | 704.587 | 495.413 | 19:7 | 2.714 | |||||||
| 37\63 | 704.762 | 495.238 | 11:4 | 2.750 | |||||||
| 47\80 | 705.000 | 495.000 | 14:5 | 2.800 | |||||||
| 10\17 | 705.882 | 494.118 | 3:1 | 3.000 | Hard 5L 2s | ||||||
| 43\73 | 706.849 | 493.151 | 13:4 | 3.250 | |||||||
| 33\56 | 707.143 | 492.857 | 10:3 | 3.333 | |||||||
| 56\95 | 707.368 | 492.632 | 17:5 | 3.400 | |||||||
| 23\39 | 707.692 | 492.308 | 7:2 | 3.500 | |||||||
| 59\100 | 708.000 | 492.000 | 18:5 | 3.600 | |||||||
| 36\61 | 708.197 | 491.803 | 11:3 | 3.667 | |||||||
| 49\83 | 708.434 | 491.566 | 15:4 | 3.750 | |||||||
| 13\22 | 709.091 | 490.909 | 4:1 | 4.000 | Superhard 5L 2s Archy is in this region | ||||||
| 42\71 | 709.859 | 490.141 | 13:3 | 4.333 | |||||||
| 29\49 | 710.204 | 489.796 | 9:2 | 4.500 | |||||||
| 45\76 | 710.526 | 489.474 | 14:3 | 4.667 | |||||||
| 16\27 | 711.111 | 488.889 | 5:1 | 5.000 | |||||||
| 35\59 | 711.864 | 488.136 | 11:2 | 5.500 | |||||||
| 19\32 | 712.500 | 487.500 | 6:1 | 6.000 | |||||||
| 22\37 | 713.514 | 486.486 | 7:1 | 7.000 | |||||||
| 3\5 | 720.000 | 480.000 | 1:0 | → ∞ | Collapsed 5L 2s | ||||||
Step ratio diagram
See also
- Diatonic functional harmony
- Diatonic (disambiguation page)