215edo: Difference between revisions

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{{EDO intro}}
{{EDO intro}}


The equal temperament [[tempering out|tempers out]] [[4000/3969]] and [[65625/65536]], and the [[patent val]] provides the [[optimal patent val]] for the 53 & 162 temperament ([[ditonic|ditonic extension]]) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out [[2401/2400]], [[5120/5103]], and [[support]]s [[hemififths]].
215edo [[tempers out]] [[4000/3969]] and [[65625/65536]], and the [[patent val]] provides the [[optimal patent val]] for the 53 & 162 temperament ([[ditonic|ditonic extension]]) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out [[2401/2400]], [[5120/5103]], and [[support]]s [[hemififths]].


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

Revision as of 15:59, 16 January 2025

← 214edo 215edo 216edo →
Prime factorization 5 × 43
Step size 5.5814 ¢ 
Fifth 126\215 (703.256 ¢)
Semitones (A1:m2) 22:15 (122.8 ¢ : 83.72 ¢)
Consistency limit 5
Distinct consistency limit 5

Template:EDO intro

215edo tempers out 4000/3969 and 65625/65536, and the patent val provides the optimal patent val for the 53 & 162 temperament (ditonic extension) tempering them both out, and the rank-3 temperament tempering 4000/3969 out. The 215c val tempers out 2401/2400, 5120/5103, and supports hemififths.

Odd harmonics

Approximation of odd harmonics in 215edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) +1.30 -1.20 +2.34 +2.60 +1.24 +2.26 +0.10 +1.09 -1.70 -1.94 +2.42
Relative (%) +23.3 -21.5 +41.9 +46.6 +22.2 +40.5 +1.9 +19.5 -30.4 -34.8 +43.4
Steps
(reduced)
341
(126)
499
(69)
604
(174)
682
(37)
744
(99)
796
(151)
840
(195)
879
(19)
913
(53)
944
(84)
973
(113)

Subsets and supersets

Since 215 factors into 5 × 43, 215edo contains 5edo and 43edo as its subsets.