742edo: Difference between revisions
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{{EDO intro|742}} | |||
== Theory == | |||
742edo is a very strong 19-limit system and a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak tuning]], and is uniquely [[consistent]] in the [[21-odd-limit]]. It has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any edo until [[1178edo|1178]]. It tempers out [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], 2058/2057, [[2601/2600]], 4914/4913, [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit. | |||
742 = 2 × 7 × 53, so it notably contains [[53edo]] and [[14edo]]. | 742 = 2 × 7 × 53, so it notably contains [[53edo]] and [[14edo]]. | ||
Revision as of 17:12, 28 August 2022
Theory
742edo is a very strong 19-limit system and a zeta peak tuning, and is uniquely consistent in the 21-odd-limit. It has a lower 19-limit relative error than any edo until 1178. It tempers out 2401/2400 in the 7-limit, 9801/9800 in the 11-limit, 4096/4095, 6656/6655, 10648/10647 in the 13-limit, 1701/1700, 2058/2057, 2601/2600, 4914/4913, 5832/5831 in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.
742 = 2 × 7 × 53, so it notably contains 53edo and 14edo.
Prime harmonics
Script error: No such module "primes_in_edo".