1260edo: Difference between revisions

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Created page with "{{Infobox ET}} {{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 fi..."
 
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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.
 
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]]


From a regular temperament perspective, 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.
=== As an interval size measure ===
One step of 1260edo bears the name ''triangular cent'', although for unclear reasons. See [[Interval_size_measure#Octave-based_fine_measures]]
=== Prime harmonics ===
=== Prime harmonics ===
{{harmonics in equal|1260}}
{{Harmonics in equal|1260}}

Revision as of 07:05, 13 March 2023

← 1259edo 1260edo 1261edo →
Prime factorization 22 × 32 × 5 × 7 (highly composite)
Step size 0.952381 ¢ 
Fifth 737\1260 (701.905 ¢)
Semitones (A1:m2) 119:95 (113.3 ¢ : 90.48 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO 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.

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

Approximation of prime harmonics in 1260edo
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)