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.

[[~~Category:Equal divisions~~ of the ~~octave|###~~]] ~~<!-~~- 3-~~digit number -->~~

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:~~Nano~~]]

=== Prime harmonics ===

=== 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]]

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 {{Infobox ET}}
-'''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.
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+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:Nano]]
+=== 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]]