1272edo: Difference between revisions

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{{EDO intro|1272}}
{{EDO intro|1272}}


1272edo is [[consistent]] in the [[5-odd-limit]], as well as being a strong 2.3.7.13.21.23 subgroup tuning.
1272edo is [[consistent]] in the [[5-odd-limit]], though the error on the harmonic 5 is quite large. It is better read as a strong 2.3.7.13.21.23 subgroup tuning.


=== Odd harmonics ===  
=== Odd harmonics ===  

Revision as of 19:46, 19 December 2024

← 1271edo 1272edo 1273edo →
Prime factorization 23 × 3 × 53
Step size 0.943396 ¢ 
Fifth 744\1272 (701.887 ¢) (→ 31\53)
Semitones (A1:m2) 120:96 (113.2 ¢ : 90.57 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

1272edo is consistent in the 5-odd-limit, though the error on the harmonic 5 is quite large. It is better read as a strong 2.3.7.13.21.23 subgroup tuning.

Odd harmonics

Approximation of odd harmonics in 1272edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -0.068 -0.465 +0.042 -0.136 -0.375 +0.038 +0.411 -0.238 -0.343 -0.026 +0.028
Relative (%) -7.2 -49.3 +4.5 -14.5 -39.7 +4.1 +43.5 -25.3 -36.4 -2.8 +2.9
Steps
(reduced)
2016
(744)
2953
(409)
3571
(1027)
4032
(216)
4400
(584)
4707
(891)
4970
(1154)
5199
(111)
5403
(315)
5587
(499)
5754
(666)

Subsets and supersets

Since 1272 factors as 23 × 3 × 53, 1272edo has subset edos 1, 2, 3, 4, 6, 8, 12, 24, 53, 106, 159, 212, 318, 424, 636. This list has many notable systems such as 12edo, 24edo, 53edo, 159edo, and 212edo.

2544edo, twice as large, provides consistent corrections for the 15-odd-limit.