284edo: Difference between revisions

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The ~~''284~~ equal ~~division'' 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 [[~~Kleismic_family|~~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|~~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 [[~~Breed_family#Agni|~~agni]] and [[~~Kleismic_rank_three_family#Enlil|~~enlil]] and keenanismic, the 385/384 rank ~~four~~ temperament.

[[Category:~~edo~~]]

[[Category:~~nano~~]]

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.

=== 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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-The ''284 equal division'' 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 [[Kleismic_family|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|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 [[Breed_family#Agni|agni]] and [[Kleismic_rank_three_family#Enlil|enlil]] and keenanismic, the 385/384 rank four temperament.
+{{Infobox ET}}
-[[Category:edo]]
+{{ED intro}}
-[[Category:nano]]
+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.
+=== 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]]