284edo: Difference between revisions
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'''284 EDO''' divides the octave into 284 equal parts of size 4.225 [[cent]]s each. It 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 three temperaments [[agni]] and [[enlil]] and keenanismic, the 385/384 rank-four temperament. | '''284 EDO''' divides the octave into 284 equal parts of size 4.225 [[cent]]s each. It 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 three temperaments [[agni]] and [[enlil]] and keenanismic, the 385/384 rank-four temperament. | ||
{{Harmonics in equal|284}} | |||
[[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | [[Category:Equal divisions of the octave|###]] <!-- 3-digit number --> | ||
[[Category:Nano]] | [[Category:Nano]] | ||
Revision as of 03:20, 24 June 2023
| ← 283edo | 284edo | 285edo → |
284 EDO divides the octave into 284 equal parts of size 4.225 cents each. It 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 three temperaments agni and enlil and keenanismic, the 385/384 rank-four temperament.
| 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) | |