42edt: Difference between revisions
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{{Infobox ET}} | {{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. | '''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. | ||
{{Harmonics in equal|42|3|1|intervals=prime|columns=15}} | |||
Lookalikes: [[53ed4|53ED4]] | Lookalikes: [[53ed4|53ED4]] | ||
Revision as of 19:00, 30 September 2024
| ← 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.
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | 41 | 43 | 47 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -22.6 | +0.0 | +21.3 | -17.8 | +14.9 | -2.6 | -14.2 | +19.7 | +5.9 | +12.1 | -12.7 | -2.1 | +1.4 | +9.5 | -8.7 |
| Relative (%) | -49.9 | +0.0 | +47.1 | -39.2 | +32.8 | -5.8 | -31.4 | +43.4 | +13.0 | +26.8 | -28.1 | -4.6 | +3.0 | +20.9 | -19.1 | |
| Steps (reduced) |
26 (26) |
42 (0) |
62 (20) |
74 (32) |
92 (8) |
98 (14) |
108 (24) |
113 (29) |
120 (36) |
129 (3) |
131 (5) |
138 (12) |
142 (16) |
144 (18) |
147 (21) | |
Lookalikes: 53ED4