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 | 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 | 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 the 117th [[prime edo]]. | 643edo is the 117th [[prime edo]]. | ||
Revision as of 18:16, 25 January 2022
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 log25, after 146 and before 4004. It tempers out 32805/32768 in the 5-limit and 2401/2400 in the 7-limit, so that it supports 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 vili temperament.
643edo is the 117th prime edo.