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Created page with "'''42EDT''' is the equal division of the third harmonic into 42 parts of 45.2846 cents each, corresponding to 26.4990 edo. It is contorted in the no-twos..." Tags: Mobile edit Mobile web edit |
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'''42EDT''' is the [[Edt|equal division of the third harmonic]] into 42 parts of 45.2846 [[cent|cents]] each, corresponding to 26.4990 [[edo]]. It is contorted in the no-twos 17-limit, tempering out 77/75, 119/117, 147/143, 169/165, and 245/243. Using the patent val, it tempers out 363/361 in the 19-limit; 117/115, 119/115, 255/253, 299/297, and 391/375 in the 23-limit (no-twos subgroup). It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\53 of an octave. | {{Infobox ET}} | ||
'''42EDT''' is the [[Edt|equal division of the third harmonic]] into 42 parts of 45.2846 [[cent|cents]] each, corresponding to 26.4990 [[edo]]. It is [[contorted]] in the no-twos 17-limit, tempering out 77/75, 119/117, 147/143, 169/165, and 245/243. Using the patent val, it tempers out 363/361 in the 19-limit; 117/115, 119/115, 255/253, 299/297, and 391/375 in the 23-limit (no-twos subgroup). It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\53 of an octave. | |||
Lookalikes: [[53ed4|53ED4]] | Lookalikes: [[53ed4|53ED4]] | ||
== Intervals == | |||
{{Interval table}} | |||
== Harmonics == | |||
{{Harmonics in equal | |||
| steps = 42 | |||
| num = 3 | |||
| denom = 1 | |||
| intervals = integer | |||
}} | |||
{{Harmonics in equal | |||
| steps = 42 | |||
| num = 3 | |||
| denom = 1 | |||
| start = 12 | |||
| collapsed = 1 | |||
| intervals = integer | |||
}} | |||
{{stub}} | |||
Latest revision as of 19:23, 1 August 2025
| ← 41edt | 42edt | 43edt → |
42EDT is the equal division of the third harmonic into 42 parts of 45.2846 cents each, corresponding to 26.4990 edo. It is contorted in the no-twos 17-limit, tempering out 77/75, 119/117, 147/143, 169/165, and 245/243. Using the patent val, it tempers out 363/361 in the 19-limit; 117/115, 119/115, 255/253, 299/297, and 391/375 in the 23-limit (no-twos subgroup). It entirely misses 2/1, but nails the "double octave" 4/1, so it strongly resembles the scale with generator 2\53 of an octave.
Lookalikes: 53ED4
Intervals
| Steps | Cents | Hekts | Approximate ratios |
|---|---|---|---|
| 0 | 0 | 0 | 1/1 |
| 1 | 45.3 | 31 | |
| 2 | 90.6 | 61.9 | 21/20 |
| 3 | 135.9 | 92.9 | |
| 4 | 181.1 | 123.8 | 10/9 |
| 5 | 226.4 | 154.8 | |
| 6 | 271.7 | 185.7 | 7/6, 27/23 |
| 7 | 317 | 216.7 | |
| 8 | 362.3 | 247.6 | 21/17 |
| 9 | 407.6 | 278.6 | 19/15, 29/23 |
| 10 | 452.8 | 309.5 | 13/10, 22/17 |
| 11 | 498.1 | 340.5 | |
| 12 | 543.4 | 371.4 | 15/11 |
| 13 | 588.7 | 402.4 | |
| 14 | 634 | 433.3 | 13/9 |
| 15 | 679.3 | 464.3 | |
| 16 | 724.6 | 495.2 | |
| 17 | 769.8 | 526.2 | |
| 18 | 815.1 | 557.1 | |
| 19 | 860.4 | 588.1 | |
| 20 | 905.7 | 619 | 22/13 |
| 21 | 951 | 650 | 19/11 |
| 22 | 996.3 | 681 | |
| 23 | 1041.5 | 711.9 | |
| 24 | 1086.8 | 742.9 | |
| 25 | 1132.1 | 773.8 | |
| 26 | 1177.4 | 804.8 | |
| 27 | 1222.7 | 835.7 | |
| 28 | 1268 | 866.7 | 27/13 |
| 29 | 1313.3 | 897.6 | |
| 30 | 1358.5 | 928.6 | 11/5 |
| 31 | 1403.8 | 959.5 | |
| 32 | 1449.1 | 990.5 | 30/13 |
| 33 | 1494.4 | 1021.4 | |
| 34 | 1539.7 | 1052.4 | 17/7 |
| 35 | 1585 | 1083.3 | |
| 36 | 1630.2 | 1114.3 | 18/7, 23/9 |
| 37 | 1675.5 | 1145.2 | 29/11 |
| 38 | 1720.8 | 1176.2 | 27/10 |
| 39 | 1766.1 | 1207.1 | |
| 40 | 1811.4 | 1238.1 | 20/7 |
| 41 | 1856.7 | 1269 | |
| 42 | 1902 | 1300 | 3/1 |
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -22.6 | +0.0 | +0.1 | +21.3 | -22.6 | -17.8 | -22.5 | +0.0 | -1.3 | +14.9 | +0.1 |
| Relative (%) | -49.9 | +0.0 | +0.2 | +47.1 | -49.9 | -39.2 | -49.7 | +0.0 | -2.8 | +32.8 | +0.2 | |
| Steps (reduced) |
26 (26) |
42 (0) |
53 (11) |
62 (20) |
68 (26) |
74 (32) |
79 (37) |
84 (0) |
88 (4) |
92 (8) |
95 (11) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -2.6 | +4.9 | +21.3 | +0.2 | -14.2 | -22.6 | +19.7 | +21.4 | -17.8 | -7.7 | +5.9 |
| Relative (%) | -5.8 | +10.9 | +47.1 | +0.4 | -31.4 | -49.9 | +43.4 | +47.3 | -39.2 | -17.1 | +13.0 | |
| Steps (reduced) |
98 (14) |
101 (17) |
104 (20) |
106 (22) |
108 (24) |
110 (26) |
113 (29) |
115 (31) |
116 (32) |
118 (34) |
120 (36) | |
|
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