1260edo: Difference between revisions

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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]]

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=== Prime harmonics ===

=== 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 }}.

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 {{EDO intro|1260}}
-edo 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.
+edo 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]]
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 === Prime harmonics ===
 {{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 }}.