269edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''269edo''' is the [[EDO|equal division of the octave]] into 269 parts of 4.4610 [[cent]]s each. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it [[support]]s and provides an excellent tuning for [[Kleismic_family#Catakleismic|catakleismic]] and [[Marvel_family|marvel]] temperaments.
{{EDO intro}}


269edo is the 57th [[prime EDO]].
269edo is in[[consistent]] in the [[5-odd-limit]] and the errors of both [[harmonic]]s [[3/1|3]] and [[5/1|5]] are quite large. The [[patent val]] [[tempering out|tempers out]] [[6144/6125]] in the 7-limit, [[540/539]] and [[5632/5625]] in the 11-limit and [[364/363]] and [[676/675]] in the 13-limit. The 269c val tempers out [[225/224]] and [[4375/4374]] in the 7-limit, and 269ce [[385/384]] in the 11-limit, so that it [[support]]s and provides an excellent tuning for [[catakleismic]] and [[marvel]] temperaments.


=== Odd harmonics ===
{{Harmonics in equal|269}}
{{Harmonics in equal|269}}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 
[[Category:Prime EDO]]
=== Subsets and supersets ===
269edo is the 57th [[prime edo]].

Revision as of 04:37, 11 March 2024

← 268edo 269edo 270edo →
Prime factorization 269 (prime)
Step size 4.46097 ¢ 
Fifth 157\269 (700.372 ¢)
Semitones (A1:m2) 23:22 (102.6 ¢ : 98.14 ¢)
Dual sharp fifth 158\269 (704.833 ¢)
Dual flat fifth 157\269 (700.372 ¢)
Dual major 2nd 46\269 (205.204 ¢)
Consistency limit 3
Distinct consistency limit 3

Template:EDO intro

269edo is inconsistent in the 5-odd-limit and the errors of both harmonics 3 and 5 are quite large. The patent val tempers out 6144/6125 in the 7-limit, 540/539 and 5632/5625 in the 11-limit and 364/363 and 676/675 in the 13-limit. The 269c val tempers out 225/224 and 4375/4374 in the 7-limit, and 269ce 385/384 in the 11-limit, so that it supports and provides an excellent tuning for catakleismic and marvel temperaments.

Odd harmonics

Approximation of odd harmonics in 269edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error Absolute (¢) -1.58 +1.79 -0.80 +1.29 +1.84 -1.87 +0.21 +2.11 +1.37 +2.08 +0.72
Relative (%) -35.5 +40.1 -17.8 +29.0 +41.3 -41.8 +4.6 +47.2 +30.7 +46.7 +16.2
Steps
(reduced)
426
(157)
625
(87)
755
(217)
853
(46)
931
(124)
995
(188)
1051
(244)
1100
(24)
1143
(67)
1182
(106)
1217
(141)

Subsets and supersets

269edo is the 57th prime edo.