284edo: Difference between revisions
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{{Infobox ET}} | |||
{{ED intro}} | |||
[[ | The equal temperament [[tempering out|tempers out]] the kleisma, [[15625/15552]], and the breedsma, [[2401/2400]], and is a good tuning for [[quadritikleismic]] temperament which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out [[385/384]], for which it provides the [[optimal patent val]]. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank-3 temperaments [[agni]] and [[enlil]] and keenanismic, the 385/384 rank-4 temperament. | ||
[[Category: | |||
=== Prime harmonics === | |||
{{Harmonics in equal|284}} | |||
=== Subsets and supersets === | |||
Since 284 factors into {{factorization|284}}, 284edo has subset edos {{EDOs| 2, 4, 71, and 142 }}. | |||
[[Category:Keenanismic]] | |||
[[Category:Agni]] | |||
[[Category:Enlil]] | |||
[[Category:Quadritikleismic]] | |||
Latest revision as of 14:28, 20 February 2025
| ← 283edo | 284edo | 285edo → |
284 equal divisions of the octave (abbreviated 284edo or 284ed2), also called 284-tone equal temperament (284tet) or 284 equal temperament (284et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 284 equal parts of about 4.23 ¢ each. Each step represents a frequency ratio of 21/284, or the 284th root of 2.
The equal temperament tempers out the kleisma, 15625/15552, and the breedsma, 2401/2400, and is a good tuning for quadritikleismic temperament which tempers out both. This is particularly true for the 11-limit version of quadritikleismic, which also tempers out 385/384, for which it provides the optimal patent val. In fact, if 385/384 is tempered out essentially the same tuning accuracy can be obtained using quadritikleismic, since 284 provides the optimal patent val for quadritikleismic, the rank-3 temperaments agni and enlil and keenanismic, the 385/384 rank-4 temperament.
Prime harmonics
| Harmonic | 3 | 5 | 7 | 9 | 11 | 13 | 15 | 17 | 19 | 21 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.55 | -1.81 | -1.22 | -1.09 | -2.02 | +0.32 | +1.87 | +0.68 | -1.74 | -1.77 | +1.30 |
| Relative (%) | -12.9 | -42.8 | -28.9 | -25.9 | -47.9 | +7.5 | +44.3 | +16.1 | -41.1 | -41.8 | +30.8 | |
| Steps (reduced) |
450 (166) |
659 (91) |
797 (229) |
900 (48) |
982 (130) |
1051 (199) |
1110 (258) |
1161 (25) |
1206 (70) |
1247 (111) |
1285 (149) | |
Subsets and supersets
Since 284 factors into 22 × 71, 284edo has subset edos 2, 4, 71, and 142.