814edo: Difference between revisions

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The '''814 equal division''' divides the octave into 814 equal parts of 1.474 ~~cents~~ each.It is uniquely [[~~consistent|~~consistent]] to the 17-limit and is a strong 17-limit system. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it [[support]]s and gives a good tuning for [[~~Schismatic_family#Sesquiquartififths|~~sesquiquartififths ~~temperament~~]]. In the 11-limit it tempers out 9801/9800, in the 13-limit ~~4224~~/4224 and 6656/6655, and in the 17-limit 1701/1700, 2058/2057, 2601/2600, 4914/4913 and 5832/5831. The 171&643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[~~Optimal_patent_val|~~optimal patent val]].

The '''814 equal division''' divides the [[octave]] into 814 [[equal]] parts of 1.474 [[cent]]s each. It is uniquely [[consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The 171&643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]].

=== Prime harmonics ===

=== Miscellany ===

Since 814 = 2 × 11 × 37, 814edo has subset edos {{EDOs| 2, 11, 22, 37, 74, and 407 }}.

[[Category:Equal divisions of the octave|###]]

[[Category:Sesquiquartififths]]

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 {{Infobox ET}}
-The '''814 equal division''' divides the octave into 814 equal parts of 1.474 cents each.It is uniquely [[consistent|consistent]] to the 17-limit and is a strong 17-limit system. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it [[support]]s and gives a good tuning for [[Schismatic_family#Sesquiquartififths|sesquiquartififths temperament]]. In the 11-limit it tempers out 9801/9800, in the 13-limit 4224/4224 and 6656/6655, and in the 17-limit 1701/1700, 2058/2057, 2601/2600, 4914/4913 and 5832/5831. The 171&amp;643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[Optimal_patent_val|optimal patent val]].
+The '''814 equal division''' divides the [[octave]] into 814 [[equal]] parts of 1.474 [[cent]]s each. It is uniquely [[consistent]] to the [[17-odd-limit]] and is a strong 17-limit system. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s and gives a good tuning for [[sesquiquartififths]]. In the 11-limit it tempers out [[9801/9800]], in the 13-limit [[4225/4224]] and [[6656/6655]], and in the 17-limit [[1701/1700]], [[2058/2057]], [[2601/2600]], [[4914/4913]] and [[5832/5831]]. The 171&amp;643 temperament gives an extension of sesquiquartififths to the 17-limit for which 814edo provides the [[optimal patent val]].
+=== Prime harmonics ===
+{{Harmonics in equal|814|columns=11}}
+=== Miscellany ===
+Since 814 = 2 × 11 × 37, 814edo has subset edos {{EDOs| 2, 11, 22, 37, 74, and 407 }}.
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
 [[Category:Sesquiquartififths]]