279edo: Difference between revisions

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'''279edo''' is the [[EDO|equal division of the octave]] into 279 parts of 4.3011 cents each.
{{EDO intro}}


== Theory ==
279edo is closely related to [[31edo]], but the [[patent val]]s differ on the mapping for [[3/1|3]]. It [[tempering out|tempers out]] 78732/78125 ([[sensipent comma]]) and {{monzo| -64 36 3 }} in the 5-limit, as well as {{monzo| -68 18 17 }} (vavoom comma); [[3136/3125]], [[19683/19600]], and [[823543/819200]] in the 7-limit. Using the [[patent val]], it tempers out [[441/440]], [[5632/5625]], 24057/24010, and 35937/35840 in the 11-limit; [[351/350]], [[676/675]], [[1716/1715]], [[4225/4224]], and [[6656/6655]] in the 13-limit.
 
5 steps of 279edo closely represent the syntonic comma, [[81/80]].
 
=== Prime harmonics ===
{{Harmonics in equal|279}}
{{Harmonics in equal|279}}
[[Category:Equal divisions of the octave|###]]
It is closely related to [[31edo]], but the patent vals differ on the mapping for 3. It tempers out 78732/78125 (sensipent comma) and |-64 36 3> in the 5-limit, as well as |-68 18 17> (vavoom comma); 3136/3125, 19683/19600, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 441/440, 5632/5625, 24057/24010, and 35937/35840 in the 11-limit; 351/350, 676/675, 1716/1715, 4225/4224, and 6656/6655 in the 13-limit.


5 steps of 279edo closely represent the syntonic comma, [[81/80]].<!-- 3-digit number -->
=== Subsets and supersets ===
Since 279 factors into {{factorization|279}}, 279edo has subset edos {{EDOs| 3, 9, 31, and 93 }}.

Revision as of 06:15, 8 March 2024

← 278edo 279edo 280edo →
Prime factorization 32 × 31
Step size 4.30108 ¢ 
Fifth 163\279 (701.075 ¢)
Semitones (A1:m2) 25:22 (107.5 ¢ : 94.62 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

279edo is closely related to 31edo, but the patent vals differ on the mapping for 3. It tempers out 78732/78125 (sensipent comma) and [-64 36 3 in the 5-limit, as well as [-68 18 17 (vavoom comma); 3136/3125, 19683/19600, and 823543/819200 in the 7-limit. Using the patent val, it tempers out 441/440, 5632/5625, 24057/24010, and 35937/35840 in the 11-limit; 351/350, 676/675, 1716/1715, 4225/4224, and 6656/6655 in the 13-limit.

5 steps of 279edo closely represent the syntonic comma, 81/80.

Prime harmonics

Approximation of prime harmonics in 279edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.88 +0.78 -1.08 -0.78 -1.82 -1.73 -0.74 -0.32 -1.62 -0.95
Relative (%) +0.0 -20.5 +18.2 -25.2 -18.1 -42.3 -40.2 -17.2 -7.4 -37.7 -22.1
Steps
(reduced)
279
(0)
442
(163)
648
(90)
783
(225)
965
(128)
1032
(195)
1140
(24)
1185
(69)
1262
(146)
1355
(239)
1382
(266)

Subsets and supersets

Since 279 factors into 32 × 31, 279edo has subset edos 3, 9, 31, and 93.