742edo: Difference between revisions
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== Theory == | == 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 tempers out the vishnuzma and the fortune comma in the 5-limit, supporting [[vishnu]] and [[fortune]]; [[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. | 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 tempers out the vishnuzma and the fortune comma in the 5-limit, supporting [[vishnu]] and [[fortune]]; [[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. | ||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|742}} | {{Harmonics in equal|742}} | ||
=== Subsets and supersets === | |||
742 = 2 × 7 × 53, so it notably contains [[53edo]] and [[14edo]]. It supports [[Fractional-octave temperaments#Silicon|silicon]] temperament (224 & 742) with period 14 in the 13-limit, and [[iodine]] temperament (159 & 742) with period 53 in the 17-limit. | |||
== Regular temperament properties == | == Regular temperament properties == | ||
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| [[Iodine]] | | [[Iodine]] | ||
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