742edo: Difference between revisions
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=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|742}} | {{Harmonics in equal|742|columns=11}} | ||
{{Harmonics in equal|742|columns=11|start=12|collapsed=1|title=Approximation of prime harmonics in 742edo (continued)}} | |||
=== Subsets and supersets === | === Subsets and supersets === | ||
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| 4.32 | | 4.32 | ||
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* 742et has a lower 19-limit [[ | * 742et has a lower 19-limit [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] than any previous equal temperaments, being the first to beat [[581edo|581]], before getting bettered by [[935edo|935]] in absolute error and by [[1178edo|1178]] in relative error. | ||
* 742et (742i val) is also notable in the 17- and 23-limit, where it has lower absolute errors than any previous equal temperaments. In the 17-limit it beats | * 742et (742i val) is also notable in the 17- and 23-limit, where it has lower absolute errors than any previous equal temperaments. In the 17-limit it beats 581 and is bettered by [[764edo|764]]; in the 23-limit it beats [[718edo|718]] and is bettered by [[814edo|814]]. | ||
=== Rank-2 temperaments === | === Rank-2 temperaments === | ||
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| [[Iodine]] | | [[Iodine]] | ||
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<nowiki/>* [[Normal forms|Octave-reduced form]], reduced to the first half-octave, and [[normal forms|minimal form]] in parentheses if distinct | <nowiki/>* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct | ||
== Scales == | == Scales == | ||
* Silicon[28]: 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 | * Silicon[28]: 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 10 43 | ||