279edo: Difference between revisions
Created page with "'''279edo''' is the equal division of the octave into 279 parts of 4.3011 cents each. It is closely related to 31edo, but the patent vals differ on the mapping for..." Tags: Mobile edit Mobile web edit |
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[[ | 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 is close to the syntonic comma, [[81/80]]. Unfortunately, it is not compatible with the patent val, but the 279c val. | |||
=== Prime harmonics === | |||
{{Harmonics in equal|279}} | |||
=== Subsets and supersets === | |||
Since 279 factors into {{factorization|279}}, 279edo has subset edos {{EDOs| 3, 9, 31, and 93 }}. [[1395edo]], which divides its step into five, makes for a strong higher-limit system. | |||
Latest revision as of 19:31, 17 April 2026
| ← 278edo | 279edo | 280edo → |
279 equal divisions of the octave (abbreviated 279edo or 279ed2), also called 279-tone equal temperament (279tet) or 279 equal temperament (279et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 279 equal parts of about 4.3 ¢ each. Each step represents a frequency ratio of 21/279, or the 279th root of 2.
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 is close to the syntonic comma, 81/80. Unfortunately, it is not compatible with the patent val, but the 279c val.
Prime harmonics
| 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. 1395edo, which divides its step into five, makes for a strong higher-limit system.