742edo: Difference between revisions

m Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"
Regular temperament properties: note what it's after in the 19-limit
 
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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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* 742et has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any previous equal temperaments. It is only bettered by [[935edo|935]] in terms of absolute error, and by [[1178edo|1178]] in terms of relative error.  
* 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 [[581edo|581]] and is bettered by [[764edo|764]]; in the 23-limit it beats [[718edo|718]] and is bettered by [[814edo|814]].  
* 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 ===