1260edo: Difference between revisions
mNo edit summary |
m changed EDO intro to ED intro |
||
| (One intermediate revision by one other user not shown) | |||
| Line 1: | Line 1: | ||
{{Infobox ET}} | {{Infobox ET}} | ||
{{ | {{ED intro}} | ||
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]] | ||
| Line 10: | Line 10: | ||
=== 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 }}. | |||
Latest revision as of 17:13, 20 February 2025
| ← 1259edo | 1260edo | 1261edo → |
1260 equal divisions of the octave (abbreviated 1260edo or 1260ed2), also called 1260-tone equal temperament (1260tet) or 1260 equal temperament (1260et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1260 equal parts of about 0.952 ¢ each. Each step represents a frequency ratio of 21/1260, or the 1260th root of 2.
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.