13L 2s (3/1-equivalent)
13L 2s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 13 large steps and 2 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 1014.4 ¢ to 1024.1 ¢, or from 877.8 ¢ to 887.6 ¢.
| ↖ 12L 1s⟨3/1⟩ | ↑ 13L 1s⟨3/1⟩ | 14L 1s⟨3/1⟩ ↗ |
| ← 12L 2s⟨3/1⟩ | 13L 2s (3/1-equivalent) | 14L 2s⟨3/1⟩ → |
| ↙ 12L 3s⟨3/1⟩ | ↓ 13L 3s⟨3/1⟩ | 14L 3s⟨3/1⟩ ↘ |
Scale structure
sLLLLLLsLLLLLLL
Generator size(edt)
Related MOS scales
Equal tunings(edt)
This MOS scale pattern is most notable for corresponding to the 15-note 3.5 subgroup scale generated by a just 5/3, which has an L:s ratio of approximately 1.57. In this case, the large step represents 27/25 and the small step represents 1220703125/1162261467. It is the smallest MOS generated by the 3.5 subgroup which does not have 2 large steps, and the smallest in which the entire range of generators can reasonably be taken as an approximation of 5/3.
Tritave-equivalent temperaments generated by a near-just or slightly flat 5/3 will also produce this MOS scale. The 3.5.11 subgroup microtemperament delta centauri (which is generated by a near-just ~5/3 such that 9 generators stacked represent ~11/9) has this as its 15-note MOS scale. Interestingly, the chroma (L-s) represents 125/121 in this case. If you want the high accuracy offered by this temperament then a ~5/3 generator between 15\28edt and 23\43edt is best (corresponding to L:s between 3:2 and 2:1).
The most optimized tunings of Arcturus temperament have the ~5/3 slightly sharper than in 13edt and thus generate this MOS, but Arcturus has a quite wide range of reasonable generators so it is not a given that it will generate this MOS.
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 | 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 126.8 ¢ |
| Major 1-mosstep | M1ms | L | 126.8 ¢ to 146.3 ¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | L + s | 146.3 ¢ to 253.6 ¢ |
| Major 2-mosstep | M2ms | 2L | 253.6 ¢ to 292.6 ¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 2L + s | 292.6 ¢ to 380.4 ¢ |
| Major 3-mosstep | M3ms | 3L | 380.4 ¢ to 438.9 ¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 3L + s | 438.9 ¢ to 507.2 ¢ |
| Major 4-mosstep | M4ms | 4L | 507.2 ¢ to 585.2 ¢ | |
| 5-mosstep | Minor 5-mosstep | m5ms | 4L + s | 585.2 ¢ to 634.0 ¢ |
| Major 5-mosstep | M5ms | 5L | 634.0 ¢ to 731.5 ¢ | |
| 6-mosstep | Minor 6-mosstep | m6ms | 5L + s | 731.5 ¢ to 760.8 ¢ |
| Major 6-mosstep | M6ms | 6L | 760.8 ¢ to 877.8 ¢ | |
| 7-mosstep | Perfect 7-mosstep | P7ms | 6L + s | 877.8 ¢ to 887.6 ¢ |
| Augmented 7-mosstep | A7ms | 7L | 887.6 ¢ to 1024.1 ¢ | |
| 8-mosstep | Diminished 8-mosstep | d8ms | 6L + 2s | 877.8 ¢ to 1014.4 ¢ |
| Perfect 8-mosstep | P8ms | 7L + s | 1014.4 ¢ to 1024.1 ¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | 7L + 2s | 1024.1 ¢ to 1141.2 ¢ |
| Major 9-mosstep | M9ms | 8L + s | 1141.2 ¢ to 1170.4 ¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | 8L + 2s | 1170.4 ¢ to 1268.0 ¢ |
| Major 10-mosstep | M10ms | 9L + s | 1268.0 ¢ to 1316.7 ¢ | |
| 11-mosstep | Minor 11-mosstep | m11ms | 9L + 2s | 1316.7 ¢ to 1394.8 ¢ |
| Major 11-mosstep | M11ms | 10L + s | 1394.8 ¢ to 1463.0 ¢ | |
| 12-mosstep | Minor 12-mosstep | m12ms | 10L + 2s | 1463.0 ¢ to 1521.6 ¢ |
| Major 12-mosstep | M12ms | 11L + s | 1521.6 ¢ to 1609.3 ¢ | |
| 13-mosstep | Minor 13-mosstep | m13ms | 11L + 2s | 1609.3 ¢ to 1648.4 ¢ |
| Major 13-mosstep | M13ms | 12L + s | 1648.4 ¢ to 1755.7 ¢ | |
| 14-mosstep | Minor 14-mosstep | m14ms | 12L + 2s | 1755.7 ¢ to 1775.2 ¢ |
| Major 14-mosstep | M14ms | 13L + s | 1775.2 ¢ to 1902.0 ¢ | |
| 15-mosstep | Perfect 15-mosstep | P15ms | 13L + 2s | 1902.0 ¢ |
Generator chain
| Bright gens | Scale degree | Abbrev. |
|---|---|---|
| 27 | Augmented 6-mosdegree | A6md |
| 26 | Augmented 13-mosdegree | A13md |
| 25 | Augmented 5-mosdegree | A5md |
| 24 | Augmented 12-mosdegree | A12md |
| 23 | Augmented 4-mosdegree | A4md |
| 22 | Augmented 11-mosdegree | A11md |
| 21 | Augmented 3-mosdegree | A3md |
| 20 | Augmented 10-mosdegree | A10md |
| 19 | Augmented 2-mosdegree | A2md |
| 18 | Augmented 9-mosdegree | A9md |
| 17 | Augmented 1-mosdegree | A1md |
| 16 | Augmented 8-mosdegree | A8md |
| 15 | Augmented 0-mosdegree | A0md |
| 14 | Augmented 7-mosdegree | A7md |
| 13 | Major 14-mosdegree | M14md |
| 12 | Major 6-mosdegree | M6md |
| 11 | Major 13-mosdegree | M13md |
| 10 | Major 5-mosdegree | M5md |
| 9 | Major 12-mosdegree | M12md |
| 8 | Major 4-mosdegree | M4md |
| 7 | Major 11-mosdegree | M11md |
| 6 | Major 3-mosdegree | M3md |
| 5 | Major 10-mosdegree | M10md |
| 4 | Major 2-mosdegree | M2md |
| 3 | Major 9-mosdegree | M9md |
| 2 | Major 1-mosdegree | M1md |
| 1 | Perfect 8-mosdegree | P8md |
| 0 | Perfect 0-mosdegree Perfect 15-mosdegree |
P0md P15md |
| −1 | Perfect 7-mosdegree | P7md |
| −2 | Minor 14-mosdegree | m14md |
| −3 | Minor 6-mosdegree | m6md |
| −4 | Minor 13-mosdegree | m13md |
| −5 | Minor 5-mosdegree | m5md |
| −6 | Minor 12-mosdegree | m12md |
| −7 | Minor 4-mosdegree | m4md |
| −8 | Minor 11-mosdegree | m11md |
| −9 | Minor 3-mosdegree | m3md |
| −10 | Minor 10-mosdegree | m10md |
| −11 | Minor 2-mosdegree | m2md |
| −12 | Minor 9-mosdegree | m9md |
| −13 | Minor 1-mosdegree | m1md |
| −14 | Diminished 8-mosdegree | d8md |
| −15 | Diminished 15-mosdegree | d15md |
| −16 | Diminished 7-mosdegree | d7md |
| −17 | Diminished 14-mosdegree | d14md |
| −18 | Diminished 6-mosdegree | d6md |
| −19 | Diminished 13-mosdegree | d13md |
| −20 | Diminished 5-mosdegree | d5md |
| −21 | Diminished 12-mosdegree | d12md |
| −22 | Diminished 4-mosdegree | d4md |
| −23 | Diminished 11-mosdegree | d11md |
| −24 | Diminished 3-mosdegree | d3md |
| −25 | Diminished 10-mosdegree | d10md |
| −26 | Diminished 2-mosdegree | d2md |
| −27 | Diminished 9-mosdegree | d9md |
Modes
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 14|0 | 1 | LLLLLLLsLLLLLLs |
| 13|1 | 9 | LLLLLLsLLLLLLLs |
| 12|2 | 2 | LLLLLLsLLLLLLsL |
| 11|3 | 10 | LLLLLsLLLLLLLsL |
| 10|4 | 3 | LLLLLsLLLLLLsLL |
| 9|5 | 11 | LLLLsLLLLLLLsLL |
| 8|6 | 4 | LLLLsLLLLLLsLLL |
| 7|7 | 12 | LLLsLLLLLLLsLLL |
| 6|8 | 5 | LLLsLLLLLLsLLLL |
| 5|9 | 13 | LLsLLLLLLLsLLLL |
| 4|10 | 6 | LLsLLLLLLsLLLLL |
| 3|11 | 14 | LsLLLLLLLsLLLLL |
| 2|12 | 7 | LsLLLLLLsLLLLLL |
| 1|13 | 15 | sLLLLLLLsLLLLLL |
| 0|14 | 8 | sLLLLLLsLLLLLLL |
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | |||
| 14|0 | 1 | LLLLLLLsLLLLLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Aug. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 13|1 | 9 | LLLLLLsLLLLLLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 12|2 | 2 | LLLLLLsLLLLLLsL | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Perf. |
| 11|3 | 10 | LLLLLsLLLLLLLsL | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Perf. |
| 10|4 | 3 | LLLLLsLLLLLLsLL | Perf. | Maj. | Maj. | Maj. | Maj. | Maj. | Min. | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Perf. |
| 9|5 | 11 | LLLLsLLLLLLLsLL | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Perf. |
| 8|6 | 4 | LLLLsLLLLLLsLLL | Perf. | Maj. | Maj. | Maj. | Maj. | Min. | Min. | Perf. | Perf. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Perf. |
| 7|7 | 12 | LLLsLLLLLLLsLLL | Perf. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Perf. | Perf. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Perf. |
| 6|8 | 5 | LLLsLLLLLLsLLLL | Perf. | Maj. | Maj. | Maj. | Min. | Min. | Min. | Perf. | Perf. | Maj. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 5|9 | 13 | LLsLLLLLLLsLLLL | Perf. | Maj. | Maj. | Min. | Min. | Min. | Min. | Perf. | Perf. | Maj. | Maj. | Min. | Min. | Min. | Min. | Perf. |
| 4|10 | 6 | LLsLLLLLLsLLLLL | Perf. | Maj. | Maj. | Min. | Min. | Min. | Min. | Perf. | Perf. | Maj. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 3|11 | 14 | LsLLLLLLLsLLLLL | Perf. | Maj. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. | Maj. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 2|12 | 7 | LsLLLLLLsLLLLLL | Perf. | Maj. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 1|13 | 15 | sLLLLLLLsLLLLLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
| 0|14 | 8 | sLLLLLLsLLLLLLL | Perf. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. | Dim. | Min. | Min. | Min. | Min. | Min. | Min. | Perf. |
Tuning ranges
Simple tunings
| Scale degree | Abbrev. | Basic (2:1) 28edt |
Hard (3:1) 41edt |
Soft (3:2) 43edt | |||
|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\28 | 0.0 | 0\41 | 0.0 | 0\43 | 0.0 |
| Minor 1-mosdegree | m1md | 1\28 | 67.9 | 1\41 | 46.4 | 2\43 | 88.5 |
| Major 1-mosdegree | M1md | 2\28 | 135.9 | 3\41 | 139.2 | 3\43 | 132.7 |
| Minor 2-mosdegree | m2md | 3\28 | 203.8 | 4\41 | 185.6 | 5\43 | 221.2 |
| Major 2-mosdegree | M2md | 4\28 | 271.7 | 6\41 | 278.3 | 6\43 | 265.4 |
| Minor 3-mosdegree | m3md | 5\28 | 339.6 | 7\41 | 324.7 | 8\43 | 353.9 |
| Major 3-mosdegree | M3md | 6\28 | 407.6 | 9\41 | 417.5 | 9\43 | 398.1 |
| Minor 4-mosdegree | m4md | 7\28 | 475.5 | 10\41 | 463.9 | 11\43 | 486.5 |
| Major 4-mosdegree | M4md | 8\28 | 543.4 | 12\41 | 556.7 | 12\43 | 530.8 |
| Minor 5-mosdegree | m5md | 9\28 | 611.3 | 13\41 | 603.1 | 14\43 | 619.2 |
| Major 5-mosdegree | M5md | 10\28 | 679.3 | 15\41 | 695.8 | 15\43 | 663.5 |
| Minor 6-mosdegree | m6md | 11\28 | 747.2 | 16\41 | 742.2 | 17\43 | 751.9 |
| Major 6-mosdegree | M6md | 12\28 | 815.1 | 18\41 | 835.0 | 18\43 | 796.2 |
| Perfect 7-mosdegree | P7md | 13\28 | 883.1 | 19\41 | 881.4 | 20\43 | 884.6 |
| Augmented 7-mosdegree | A7md | 14\28 | 951.0 | 21\41 | 974.2 | 21\43 | 928.9 |
| Diminished 8-mosdegree | d8md | 14\28 | 951.0 | 20\41 | 927.8 | 22\43 | 973.1 |
| Perfect 8-mosdegree | P8md | 15\28 | 1018.9 | 22\41 | 1020.6 | 23\43 | 1017.3 |
| Minor 9-mosdegree | m9md | 16\28 | 1086.8 | 23\41 | 1067.0 | 25\43 | 1105.8 |
| Major 9-mosdegree | M9md | 17\28 | 1154.8 | 25\41 | 1159.7 | 26\43 | 1150.0 |
| Minor 10-mosdegree | m10md | 18\28 | 1222.7 | 26\41 | 1206.1 | 28\43 | 1238.5 |
| Major 10-mosdegree | M10md | 19\28 | 1290.6 | 28\41 | 1298.9 | 29\43 | 1282.7 |
| Minor 11-mosdegree | m11md | 20\28 | 1358.5 | 29\41 | 1345.3 | 31\43 | 1371.2 |
| Major 11-mosdegree | M11md | 21\28 | 1426.5 | 31\41 | 1438.1 | 32\43 | 1415.4 |
| Minor 12-mosdegree | m12md | 22\28 | 1494.4 | 32\41 | 1484.5 | 34\43 | 1503.9 |
| Major 12-mosdegree | M12md | 23\28 | 1562.3 | 34\41 | 1577.2 | 35\43 | 1548.1 |
| Minor 13-mosdegree | m13md | 24\28 | 1630.2 | 35\41 | 1623.6 | 37\43 | 1636.6 |
| Major 13-mosdegree | M13md | 25\28 | 1698.2 | 37\41 | 1716.4 | 38\43 | 1680.8 |
| Minor 14-mosdegree | m14md | 26\28 | 1766.1 | 38\41 | 1762.8 | 40\43 | 1769.3 |
| Major 14-mosdegree | M14md | 27\28 | 1834.0 | 40\41 | 1855.6 | 41\43 | 1813.5 |
| Perfect 15-mosdegree | P15md | 28\28 | 1902.0 | 41\41 | 1902.0 | 43\43 | 1902.0 |
Soft-of-basic tunings
| Scale degree | Abbrev. | 5:4 73edt |
Supersoft (4:3) 58edt |
Soft (3:2) 43edt |
Semisoft (5:3) 71edt | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\73 | 0.0 | 0\58 | 0.0 | 0\43 | 0.0 | 0\71 | 0.0 |
| Minor 1-mosdegree | m1md | 4\73 | 104.2 | 3\58 | 98.4 | 2\43 | 88.5 | 3\71 | 80.4 |
| Major 1-mosdegree | M1md | 5\73 | 130.3 | 4\58 | 131.2 | 3\43 | 132.7 | 5\71 | 133.9 |
| Minor 2-mosdegree | m2md | 9\73 | 234.5 | 7\58 | 229.5 | 5\43 | 221.2 | 8\71 | 214.3 |
| Major 2-mosdegree | M2md | 10\73 | 260.5 | 8\58 | 262.3 | 6\43 | 265.4 | 10\71 | 267.9 |
| Minor 3-mosdegree | m3md | 14\73 | 364.8 | 11\58 | 360.7 | 8\43 | 353.9 | 13\71 | 348.2 |
| Major 3-mosdegree | M3md | 15\73 | 390.8 | 12\58 | 393.5 | 9\43 | 398.1 | 15\71 | 401.8 |
| Minor 4-mosdegree | m4md | 19\73 | 495.0 | 15\58 | 491.9 | 11\43 | 486.5 | 18\71 | 482.2 |
| Major 4-mosdegree | M4md | 20\73 | 521.1 | 16\58 | 524.7 | 12\43 | 530.8 | 20\71 | 535.8 |
| Minor 5-mosdegree | m5md | 24\73 | 625.3 | 19\58 | 623.1 | 14\43 | 619.2 | 23\71 | 616.1 |
| Major 5-mosdegree | M5md | 25\73 | 651.4 | 20\58 | 655.8 | 15\43 | 663.5 | 25\71 | 669.7 |
| Minor 6-mosdegree | m6md | 29\73 | 755.6 | 23\58 | 754.2 | 17\43 | 751.9 | 28\71 | 750.1 |
| Major 6-mosdegree | M6md | 30\73 | 781.6 | 24\58 | 787.0 | 18\43 | 796.2 | 30\71 | 803.6 |
| Perfect 7-mosdegree | P7md | 34\73 | 885.8 | 27\58 | 885.4 | 20\43 | 884.6 | 33\71 | 884.0 |
| Augmented 7-mosdegree | A7md | 35\73 | 911.9 | 28\58 | 918.2 | 21\43 | 928.9 | 35\71 | 937.6 |
| Diminished 8-mosdegree | d8md | 38\73 | 990.1 | 30\58 | 983.8 | 22\43 | 973.1 | 36\71 | 964.4 |
| Perfect 8-mosdegree | P8md | 39\73 | 1016.1 | 31\58 | 1016.6 | 23\43 | 1017.3 | 38\71 | 1017.9 |
| Minor 9-mosdegree | m9md | 43\73 | 1120.3 | 34\58 | 1114.9 | 25\43 | 1105.8 | 41\71 | 1098.3 |
| Major 9-mosdegree | M9md | 44\73 | 1146.4 | 35\58 | 1147.7 | 26\43 | 1150.0 | 43\71 | 1151.9 |
| Minor 10-mosdegree | m10md | 48\73 | 1250.6 | 38\58 | 1246.1 | 28\43 | 1238.5 | 46\71 | 1232.3 |
| Major 10-mosdegree | M10md | 49\73 | 1276.7 | 39\58 | 1278.9 | 29\43 | 1282.7 | 48\71 | 1285.8 |
| Minor 11-mosdegree | m11md | 53\73 | 1380.9 | 42\58 | 1377.3 | 31\43 | 1371.2 | 51\71 | 1366.2 |
| Major 11-mosdegree | M11md | 54\73 | 1406.9 | 43\58 | 1410.1 | 32\43 | 1415.4 | 53\71 | 1419.8 |
| Minor 12-mosdegree | m12md | 58\73 | 1511.1 | 46\58 | 1508.4 | 34\43 | 1503.9 | 56\71 | 1500.1 |
| Major 12-mosdegree | M12md | 59\73 | 1537.2 | 47\58 | 1541.2 | 35\43 | 1548.1 | 58\71 | 1553.7 |
| Minor 13-mosdegree | m13md | 63\73 | 1641.4 | 50\58 | 1639.6 | 37\43 | 1636.6 | 61\71 | 1634.1 |
| Major 13-mosdegree | M13md | 64\73 | 1667.5 | 51\58 | 1672.4 | 38\43 | 1680.8 | 63\71 | 1687.7 |
| Minor 14-mosdegree | m14md | 68\73 | 1771.7 | 54\58 | 1770.8 | 40\43 | 1769.3 | 66\71 | 1768.0 |
| Major 14-mosdegree | M14md | 69\73 | 1797.7 | 55\58 | 1803.6 | 41\43 | 1813.5 | 68\71 | 1821.6 |
| Perfect 15-mosdegree | P15md | 73\73 | 1902.0 | 58\58 | 1902.0 | 43\43 | 1902.0 | 71\71 | 1902.0 |
Hard-of-basic tunings
| Scale degree | Abbrev. | Semihard (5:2) 69edt |
Hard (3:1) 41edt |
Superhard (4:1) 54edt |
5:1 67edt | ||||
|---|---|---|---|---|---|---|---|---|---|
| Steps | ¢ | Steps | ¢ | Steps | ¢ | Steps | ¢ | ||
| Perfect 0-mosdegree | P0md | 0\69 | 0.0 | 0\41 | 0.0 | 0\54 | 0.0 | 0\67 | 0.0 |
| Minor 1-mosdegree | m1md | 2\69 | 55.1 | 1\41 | 46.4 | 1\54 | 35.2 | 1\67 | 28.4 |
| Major 1-mosdegree | M1md | 5\69 | 137.8 | 3\41 | 139.2 | 4\54 | 140.9 | 5\67 | 141.9 |
| Minor 2-mosdegree | m2md | 7\69 | 193.0 | 4\41 | 185.6 | 5\54 | 176.1 | 6\67 | 170.3 |
| Major 2-mosdegree | M2md | 10\69 | 275.6 | 6\41 | 278.3 | 8\54 | 281.8 | 10\67 | 283.9 |
| Minor 3-mosdegree | m3md | 12\69 | 330.8 | 7\41 | 324.7 | 9\54 | 317.0 | 11\67 | 312.3 |
| Major 3-mosdegree | M3md | 15\69 | 413.5 | 9\41 | 417.5 | 12\54 | 422.7 | 15\67 | 425.8 |
| Minor 4-mosdegree | m4md | 17\69 | 468.6 | 10\41 | 463.9 | 13\54 | 457.9 | 16\67 | 454.2 |
| Major 4-mosdegree | M4md | 20\69 | 551.3 | 12\41 | 556.7 | 16\54 | 563.5 | 20\67 | 567.7 |
| Minor 5-mosdegree | m5md | 22\69 | 606.4 | 13\41 | 603.1 | 17\54 | 598.8 | 21\67 | 596.1 |
| Major 5-mosdegree | M5md | 25\69 | 689.1 | 15\41 | 695.8 | 20\54 | 704.4 | 25\67 | 709.7 |
| Minor 6-mosdegree | m6md | 27\69 | 744.2 | 16\41 | 742.2 | 21\54 | 739.6 | 26\67 | 738.1 |
| Major 6-mosdegree | M6md | 30\69 | 826.9 | 18\41 | 835.0 | 24\54 | 845.3 | 30\67 | 851.6 |
| Perfect 7-mosdegree | P7md | 32\69 | 882.1 | 19\41 | 881.4 | 25\54 | 880.5 | 31\67 | 880.0 |
| Augmented 7-mosdegree | A7md | 35\69 | 964.8 | 21\41 | 974.2 | 28\54 | 986.2 | 35\67 | 993.6 |
| Diminished 8-mosdegree | d8md | 34\69 | 937.2 | 20\41 | 927.8 | 26\54 | 915.8 | 32\67 | 908.4 |
| Perfect 8-mosdegree | P8md | 37\69 | 1019.9 | 22\41 | 1020.6 | 29\54 | 1021.4 | 36\67 | 1021.9 |
| Minor 9-mosdegree | m9md | 39\69 | 1075.0 | 23\41 | 1067.0 | 30\54 | 1056.6 | 37\67 | 1050.3 |
| Major 9-mosdegree | M9md | 42\69 | 1157.7 | 25\41 | 1159.7 | 33\54 | 1162.3 | 41\67 | 1163.9 |
| Minor 10-mosdegree | m10md | 44\69 | 1212.8 | 26\41 | 1206.1 | 34\54 | 1197.5 | 42\67 | 1192.3 |
| Major 10-mosdegree | M10md | 47\69 | 1295.5 | 28\41 | 1298.9 | 37\54 | 1303.2 | 46\67 | 1305.8 |
| Minor 11-mosdegree | m11md | 49\69 | 1350.7 | 29\41 | 1345.3 | 38\54 | 1338.4 | 47\67 | 1334.2 |
| Major 11-mosdegree | M11md | 52\69 | 1433.4 | 31\41 | 1438.1 | 41\54 | 1444.1 | 51\67 | 1447.8 |
| Minor 12-mosdegree | m12md | 54\69 | 1488.5 | 32\41 | 1484.5 | 42\54 | 1479.3 | 52\67 | 1476.1 |
| Major 12-mosdegree | M12md | 57\69 | 1571.2 | 34\41 | 1577.2 | 45\54 | 1585.0 | 56\67 | 1589.7 |
| Minor 13-mosdegree | m13md | 59\69 | 1626.3 | 35\41 | 1623.6 | 46\54 | 1620.2 | 57\67 | 1618.1 |
| Major 13-mosdegree | M13md | 62\69 | 1709.0 | 37\41 | 1716.4 | 49\54 | 1725.8 | 61\67 | 1731.6 |
| Minor 14-mosdegree | m14md | 64\69 | 1764.1 | 38\41 | 1762.8 | 50\54 | 1761.1 | 62\67 | 1760.0 |
| Major 14-mosdegree | M14md | 67\69 | 1846.8 | 40\41 | 1855.6 | 53\54 | 1866.7 | 66\67 | 1873.6 |
| Perfect 15-mosdegree | P15md | 69\69 | 1902.0 | 41\41 | 1902.0 | 54\54 | 1902.0 | 67\67 | 1902.0 |
Scale tree
| Generator(edt) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 8\15 | 1014.376 | 887.579 | 1:1 | 1.000 | Equalized 13L 2s⟨3/1⟩ | |||||
| 47\88 | 1015.817 | 886.138 | 6:5 | 1.200 | ||||||
| 39\73 | 1016.113 | 885.842 | 5:4 | 1.250 | ||||||
| 70\131 | 1016.312 | 885.643 | 9:7 | 1.286 | ||||||
| 31\58 | 1016.562 | 885.393 | 4:3 | 1.333 | Supersoft 13L 2s⟨3/1⟩ | |||||
| 85\159 | 1016.768 | 885.187 | 11:8 | 1.375 | ||||||
| 54\101 | 1016.887 | 885.068 | 7:5 | 1.400 | ||||||
| 77\144 | 1017.018 | 884.937 | 10:7 | 1.429 | ||||||
| 23\43 | 1017.325 | 884.630 | 3:2 | 1.500 | Soft 13L 2s⟨3/1⟩ | |||||
| 84\157 | 1017.606 | 884.349 | 11:7 | 1.571 | Just-5/3 a.k.a. Trithagorean tuning (884.359 ¢) | |||||
| 61\114 | 1017.713 | 884.242 | 8:5 | 1.600 | ||||||
| 99\185 | 1017.803 | 884.152 | 13:8 | 1.625 | ||||||
| 38\71 | 1017.948 | 884.007 | 5:3 | 1.667 | Semisoft 13L 2s⟨3/1⟩ | |||||
| 91\170 | 1018.105 | 883.850 | 12:7 | 1.714 | CWE-optimized Delta centauri (883.901 ¢) | |||||
| 53\99 | 1018.218 | 883.737 | 7:4 | 1.750 | ||||||
| 68\127 | 1018.370 | 883.585 | 9:5 | 1.800 | ||||||
| 15\28 | 1018.904 | 883.051 | 2:1 | 2.000 | Basic 13L 2s⟨3/1⟩ Scales with tunings softer than this are proper | |||||
| 67\125 | 1019.448 | 882.507 | 9:4 | 2.250 | ||||||
| 52\97 | 1019.605 | 882.350 | 7:3 | 2.333 | ||||||
| 89\166 | 1019.723 | 882.232 | 12:5 | 2.400 | ||||||
| 37\69 | 1019.889 | 882.066 | 5:2 | 2.500 | Semihard 13L 2s⟨3/1⟩ | |||||
| 96\179 | 1020.043 | 881.912 | 13:5 | 2.600 | ||||||
| 59\110 | 1020.140 | 881.816 | 8:3 | 2.667 | ||||||
| 81\151 | 1020.254 | 881.701 | 11:4 | 2.750 | ||||||
| 22\41 | 1020.561 | 881.394 | 3:1 | 3.000 | Hard 13L 2s⟨3/1⟩ | |||||
| 73\136 | 1020.902 | 881.053 | 10:3 | 3.333 | ||||||
| 51\95 | 1021.050 | 880.905 | 7:2 | 3.500 | ||||||
| 80\149 | 1021.184 | 880.771 | 11:3 | 3.667 | ||||||
| 29\54 | 1021.420 | 880.535 | 4:1 | 4.000 | Superhard 13L 2s⟨3/1⟩ | |||||
| 65\121 | 1021.711 | 880.244 | 9:2 | 4.500 | ||||||
| 36\67 | 1021.946 | 880.009 | 5:1 | 5.000 | ||||||
| 43\80 | 1022.301 | 879.654 | 6:1 | 6.000 | ||||||
| 7\13 | 1024.130 | 877.825 | 1:0 | → ∞ | Collapsed 13L 2s⟨3/1⟩ CWE-optimized Arcturus (878.291 ¢) | |||||
|
This page is a stub. You can help the Xenharmonic Wiki by expanding it. |