1260edo: Difference between revisions
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{{EDO intro|1260}} | {{EDO intro|1260}} | ||
1260edo is the 16th [[highly composite edo]], and the first one after [[12edo]] which has a good (only 5% error) and also coprime perfect fifth, so that a circle of fifths goes through every step. | 1260edo is the 16th [[highly composite edo]], and the first one after [[12edo]] which has a good (only 5% error) and also coprime perfect fifth, so that a circle of fifths goes through every step. Unfortunately, it is only [[consistent]] to the [[5-odd-limit]] since the errors of both [[harmonic]]s [[5/1|5]] and [[7/1|7]] are quite large and on the opposite side. | ||
It tunes well the 2.3.7.11.17.29 [[subgroup]]. It tempers out the [[parakleisma]] in the 5-limit on the patent val, and in the 13-limit in the 1260cf val it provides an alternative extension to the [[oquatonic]] temperament. | It tunes well the 2.3.7.11.17.29 [[subgroup]]. It tempers out the [[parakleisma]] in the 5-limit on the [[patent val]], and in the 13-limit in the 1260cf [[val]] it provides an alternative extension to the [[oquatonic]] temperament. | ||
One step of 1260edo bears the name ''triangular cent'', although for unclear reasons. See [[Interval size measure #Octave-based fine measures]] | One step of 1260edo bears the name ''triangular cent'', although for unclear reasons. See [[Interval size measure #Octave-based fine measures]] | ||
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|1260}} | {{Harmonics in equal|1260}} | ||
=== Subsets and supersets === | |||
Since 1260 factors into {{factorization|1260}}, 1260edo has subset edos {{EDOs| 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, and 630 }}. | |||
Revision as of 09:52, 31 October 2023
| ← 1259edo | 1260edo | 1261edo → |
1260edo is the 16th highly composite edo, and the first one after 12edo which has a good (only 5% error) and also coprime perfect fifth, so that a circle of fifths goes through every step. Unfortunately, it is only consistent to the 5-odd-limit since the errors of both harmonics 5 and 7 are quite large and on the opposite side.
It tunes well the 2.3.7.11.17.29 subgroup. It tempers out the parakleisma in the 5-limit on the patent val, and in the 13-limit in the 1260cf val it provides an alternative extension to the oquatonic temperament.
One step of 1260edo bears the name triangular cent, although for unclear reasons. See Interval size measure #Octave-based fine measures
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.000 | -0.050 | +0.353 | -0.254 | +0.111 | +0.425 | -0.194 | -0.370 | +0.297 | -0.053 | -0.274 |
| Relative (%) | +0.0 | -5.3 | +37.1 | -26.7 | +11.6 | +44.6 | -20.3 | -38.9 | +31.2 | -5.6 | -28.7 | |
| Steps (reduced) |
1260 (0) |
1997 (737) |
2926 (406) |
3537 (1017) |
4359 (579) |
4663 (883) |
5150 (110) |
5352 (312) |
5700 (660) |
6121 (1081) |
6242 (1202) | |
Subsets and supersets
Since 1260 factors into 22 × 32 × 5 × 7, 1260edo has subset edos 2, 3, 4, 5, 6, 7, 9, 10, 12, 14, 15, 18, 20, 21, 28, 30, 35, 36, 42, 45, 60, 63, 70, 84, 90, 105, 126, 140, 180, 210, 252, 315, 420, and 630.