224edo: Difference between revisions

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'''224edo''' is the [[EDO|equal division of the octave]] into 224 parts of 5.3571 [[cent]]s each. It is a very strong [[13-limit]] system, tempering out [[32805/32768]] in the [[5-limit]]; [[4375/4374]], 16875/16807 and 65625/65536 in the [[7-limit]]; 540/~~530~~, 1375/1372, 4000/3993 and [[Quartisma|117440512/117406179]] in the [[11-limit]]; and 625/624, 729/728, 1575/1573 and 2200/2197 in the [[13-limit]], leading to an abundance of precisely-tuned essentially tempered chords. It defines the [[~~Optimal_patent_val|~~optimal patent val]] for [[Ragismic_microtemperaments|octoid temperament]] in the 7-, 11- and 13-limit, and for [[Mirkwai_family|mirkwai]], the 7-limit planar temperament tempering out 16875/16807. It also provides an excellent tuning for [[Mirkwai_family|indra]] and [[Mirkwai_family|shibi]] temperaments. It is the twelfth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]].

'''224edo''' is the [[EDO|equal division of the octave]] into 224 parts of 5.3571 [[cent]]s each. It is a very strong [[13-limit]] system, tempering out [[32805/32768]] in the [[5-limit]]; [[4375/4374]], 16875/16807 and 65625/65536 in the [[7-limit]]; 540/539, 1375/1372, 4000/3993 and [[Quartisma|117440512/117406179]] in the [[11-limit]]; and 625/624, 729/728, 1575/1573 and 2200/2197 in the [[13-limit]], leading to an abundance of precisely-tuned essentially tempered chords. It defines the [[optimal patent val]] for [[Ragismic_microtemperaments #Octoid|octoid temperament]] in the 7-, 11- and 13-limit, and for [[Mirkwai_family|mirkwai]], the 7-limit planar temperament tempering out 16875/16807. It also provides an excellent tuning for [[Mirkwai_family #Indra|indra]] and [[Mirkwai_family #Shibi|shibi]] temperaments. It is the twelfth [[The_Riemann_Zeta_Function_and_Tuning #Zeta EDO lists|zeta integral edo]].

224 = 32 * 7, and has divisors 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112.

=Music=

== Music ==

[http://www.archive.org/details/Dreyfus Dreyfus] [http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] by [[~~Gene_Ward_Smith|~~Gene Ward Smith]]

[http://www.archive.org/details/Dreyfus Dreyfus] [http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] by [[Gene Ward Smith]]

[[Category:Edo]]

[[Category:Indra]]

[[Category:~~listen~~]]

[[Category:Listen]]

[[Category:Mirkwai]]

[[Category:Octoid]]

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-'''224edo''' is the [[EDO|equal division of the octave]] into 224 parts of 5.3571 [[cent]]s each. It is a very strong [[13-limit]] system, tempering out [[32805/32768]] in the [[5-limit]]; [[4375/4374]], 16875/16807 and 65625/65536 in the [[7-limit]]; 540/530, 1375/1372, 4000/3993 and [[Quartisma|117440512/117406179]] in the [[11-limit]]; and 625/624, 729/728, 1575/1573 and 2200/2197 in the [[13-limit]], leading to an abundance of precisely-tuned essentially tempered chords. It defines the [[Optimal_patent_val|optimal patent val]] for [[Ragismic_microtemperaments|octoid temperament]] in the 7-, 11- and 13-limit, and for [[Mirkwai_family|mirkwai]], the 7-limit planar temperament tempering out 16875/16807. It also provides an excellent tuning for [[Mirkwai_family|indra]] and [[Mirkwai_family|shibi]] temperaments. It is the twelfth [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta integral edo]].
+'''224edo''' is the [[EDO|equal division of the octave]] into 224 parts of 5.3571 [[cent]]s each. It is a very strong [[13-limit]] system, tempering out [[32805/32768]] in the [[5-limit]]; [[4375/4374]], 16875/16807 and 65625/65536 in the [[7-limit]]; 540/539, 1375/1372, 4000/3993 and [[Quartisma|117440512/117406179]] in the [[11-limit]]; and 625/624, 729/728, 1575/1573 and 2200/2197 in the [[13-limit]], leading to an abundance of precisely-tuned essentially tempered chords. It defines the [[optimal patent val]] for [[Ragismic_microtemperaments #Octoid|octoid temperament]] in the 7-, 11- and 13-limit, and for [[Mirkwai_family|mirkwai]], the 7-limit planar temperament tempering out 16875/16807. It also provides an excellent tuning for [[Mirkwai_family #Indra|indra]] and [[Mirkwai_family #Shibi|shibi]] temperaments. It is the twelfth [[The_Riemann_Zeta_Function_and_Tuning #Zeta EDO lists|zeta integral edo]].
 = 32 * 7, and has divisors 2, 4, 8, 16, 32, 7, 14, 28, 56, and 112.
-=Music=
+== Music ==
-[http://www.archive.org/details/Dreyfus Dreyfus] [http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] by [[Gene_Ward_Smith|Gene Ward Smith]]
+[http://www.archive.org/details/Dreyfus Dreyfus] [http://www.archive.org/download/Dreyfus/Genewardsmith-Dreyfus.mp3 play] by [[Gene Ward Smith]]
 [[Category:Edo]]
 [[Category:Indra]]
-[[Category:listen]]
+[[Category:Listen]]
 [[Category:Mirkwai]]
 [[Category:Octoid]]