267edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
'''267edo''' is the [[EDO|equal division of the octave]] into 267 parts of 4.494382 [[cent]]s each.  In the 5-limit, it tempers out both [[Graviton|129140163/128000000]] and 274877906944/274658203125, enabling it to support both [[Gravity_family|gravity]] and [[Luna_family|luna]] temperaments.  In the 7-limit, it tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, enabling it to support [[Gamelismic_clan|gamelismic]], [[Hemimean_family|hemimean]] and [[Trimyna_family|trimyna]] temperaments among others.  In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and [[Quartisma|117440512/117406179]].  In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, [[4096/4095]], 4225/4224 and 59535/59488.
'''267edo''' is the [[EDO|equal division of the octave]] into 267 parts of 4.494382 [[cent]]s each.   


In the 5-limit, it tempers out both [[Graviton|129140163/128000000]] and 274877906944/274658203125, enabling it to support both [[Gravity_family|gravity]] and [[Luna_family|luna]] temperaments.  In the 7-limit, it tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, enabling it to support [[Gamelismic_clan|gamelismic]], [[Hemimean_family|hemimean]] and [[Trimyna_family|trimyna]] temperaments among others.  In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and [[Quartisma|117440512/117406179]].  In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, [[4096/4095]], 4225/4224 and 59535/59488.
{{Harmonics in equal|267}}
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Gravity]]
[[Category:Gravity]]
[[Category:Luna]]
[[Category:Luna]]
[[Category:Quartismic]]
[[Category:Quartismic]]

Revision as of 03:26, 24 June 2023

← 266edo 267edo 268edo →
Prime factorization 3 × 89
Step size 4.49438 ¢ 
Fifth 156\267 (701.124 ¢) (→ 52\89)
Semitones (A1:m2) 24:21 (107.9 ¢ : 94.38 ¢)
Consistency limit 5
Distinct consistency limit 5

267edo is the equal division of the octave into 267 parts of 4.494382 cents each.

In the 5-limit, it tempers out both 129140163/128000000 and 274877906944/274658203125, enabling it to support both gravity and luna temperaments. In the 7-limit, it tempers out 1029/1024, 3136/3125, 50421/50000, 65625/65536, 9882516/9765625 and 28824005/28697814, enabling it to support gamelismic, hemimean and trimyna temperaments among others. In the 11-limit, it tempers out 243/242, 1375/1372, 4000/3993, 6144/6125, 8019/8000, 16896/16807, 30375/30184, 43923/43904 and 117440512/117406179. In the 13-limit, it tempers out 351/350, 1375/1372, 1575/1573, 2080/2079, 4096/4095, 4225/4224 and 59535/59488.


Approximation of prime harmonics in 267edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.83 +0.20 +1.96 +1.49 -0.08 -1.58 -0.88 +0.94 -0.36 +1.03
Relative (%) +0.0 -18.5 +4.5 +43.6 +33.2 -1.7 -35.3 -19.7 +20.9 -8.1 +23.0
Steps
(reduced)
267
(0)
423
(156)
620
(86)
750
(216)
924
(123)
988
(187)
1091
(23)
1134
(66)
1208
(140)
1297
(229)
1323
(255)