643edo: Difference between revisions

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~~The '''~~643 ~~equal division of the octave''' (~~643edo~~) divides the octave into 643 equal parts of 1.86625 cents each. It~~ is uniquely [[consistent]] to the 21-limit, with a generally flat tendency, but the 5th harmonic is

only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it [[support]]s [[~~Schismatic_family#Sesquiquartififths|~~sesquiquartififths ~~temperament~~]]. In the 11-limit it tempers out 3025/3024 and 151263/151250; in the 13-limit 1001/1000, 1716/1715 and 4225/4224; in the 17-limit 1089/1088, 1701/1700, 2431/2430 and 2601/2600; and in the 19-limit 1331/1330, 1521/1520, 1729/1728, 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank ~~three~~ 13-limit ~~temperament~~ [[~~Breed_family#Vili|~~vili ~~temperament~~]].

643edo is uniquely [[consistent]] to the 21-odd-limit, with a generally flat tendency, but the 5th harmonic is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], 2431/2430 and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.

643edo is the 117th [[prime edo]].

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

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-The '''643 equal division of the octave''' (643edo) divides the octave into 643 equal parts of 1.86625 cents each. It is uniquely [[consistent]] to the 21-limit, with a generally flat tendency, but the 5th harmonic is
+{{EDO intro|643}}
-only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it [[support]]s [[Schismatic_family#Sesquiquartififths|sesquiquartififths temperament]]. In the 11-limit it tempers out 3025/3024 and 151263/151250; in the 13-limit 1001/1000, 1716/1715 and 4225/4224; in the 17-limit 1089/1088, 1701/1700, 2431/2430 and 2601/2600; and in the 19-limit 1331/1330, 1521/1520, 1729/1728, 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank three 13-limit temperament [[Breed_family#Vili|vili temperament]].
+edo is uniquely [[consistent]] to the 21-odd-limit, with a generally flat tendency, but the 5th harmonic is only 0.000439 cents sharp as the denominator of a convergent to log<sub>2</sub>5, after [[146edo|146]] and before [[4004edo|4004]]. It tempers out [[32805/32768]] in the 5-limit and [[2401/2400]] in the 7-limit, so that it [[support]]s the [[sesquiquartififths]] temperament. In the 11-limit it tempers out [[3025/3024]] and 151263/151250; in the 13-limit [[1001/1000]], [[1716/1715]] and [[4225/4224]]; in the 17-limit [[1089/1088]], [[1701/1700]], 2431/2430 and [[2601/2600]]; and in the 19-limit 1331/1330, [[1521/1520]], [[1729/1728]], 2376/2375 and 2926/2925. It provides the [[optimal patent val]] for the rank-3 13-limit [[vili]] temperament.
 edo is the 117th [[prime edo]].
+{{Harmonics in equal|643|columns=11}}
 [[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->