7033edo: Difference between revisions

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~~The 7033 equal division divides the octave into 7033 equal parts of 0.17062 cents each. It~~ is a [[~~The_Riemann_Zeta_Function_and_Tuning~~#Zeta EDO lists|zeta peak and integral edo]]~~; it is~~ not ~~known at this time (2015) if it is~~ a gap edo~~, but it seems unlikely~~. This excellence is explained by the fact that it is very strong in the 17-limit, with a lower [[~~Tenney-Euclidean_temperament_measures~~#TE simple badness|relative error]] than any smaller division, and a lower [[~~Tenney-Euclidean_metrics~~#~~Logflat~~ TE badness| TE ~~loglfat~~ badness]] than any lower edo excepting [[72edo|72]]. A basis for its 17-limit ~~commas~~ is {28561/28560, 31213/31212, 37180/37179, 918750/918731, 1257795/1257728, 3070625/3070548}.

7033edo is a [[the Riemann zeta function and tuning #Zeta EDO lists|zeta peak and integral edo]], though not a gap edo. This excellence is partly explained by the fact that it is very strong in the [[17-limit]], with a lower [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, and a lower [[Tenney–Euclidean temperament measures #TE simple badness|TE logflat badness]] than any lower edo excepting [[72edo|72]]. It has a flat tendency, with all the lower [[harmonic]]s until [[19/1|19]] tuned flat. A [[comma basis|basis]] for its 17-limit [[comma]]s is {[[28561/28560]], [[31213/31212]], [[37180/37179]], 918750/918731, 1257795/1257728, 3070625/3070548}. It also [[tempering out|tempers out]] [[123201/123200]], [[194481/194480]], and [[336141/336140]], the three smallest 17-limit [[superparticular]]s.

Since the approximation to harmonic 19 is weak, it can be used as a no-19 system, in which it continues to be strong up to the [[37-limit]], and is [[consistent]] to the no-19 39-odd-limit.

=== Prime harmonics ===

{{Harmonics in equal|7033|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 7033edo (continued)}}

=== Subsets and supersets ===

Since 7033 factors into primes as {{nowrap| 13 × 541 }}, 7033edo contains [[13edo]] and [[541edo]] as subsets.

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-The 7033 equal division divides the octave into 7033 equal parts of 0.17062 cents each. It is a  [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak and integral edo]]; it is not known at this time (2015) if it is a gap edo, but it seems unlikely. This excellence is explained by the fact that it is very strong in the 17-limit, with a lower [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any smaller division, and a lower [[Tenney-Euclidean_metrics#Logflat TE badness| TE loglfat badness]] than any lower edo excepting [[72edo|72]]. A basis for its 17-limit commas is {28561/28560, 31213/31212, 37180/37179, 918750/918731, 1257795/1257728, 3070625/3070548}.
+{{Infobox ET}}
+{{ED intro}}
+edo is a [[the Riemann zeta function and tuning #Zeta EDO lists|zeta peak and integral edo]], though not a gap edo. This excellence is partly explained by the fact that it is very strong in the [[17-limit]], with a lower [[Tenney–Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, and a lower [[Tenney–Euclidean temperament measures #TE simple badness|TE logflat badness]] than any lower edo excepting [[72edo|72]]. It has a flat tendency, with all the lower [[harmonic]]s until [[19/1|19]] tuned flat. A [[comma basis|basis]] for its 17-limit [[comma]]s is {[[28561/28560]], [[31213/31212]], [[37180/37179]], 918750/918731, 1257795/1257728, 3070625/3070548}. It also [[tempering out|tempers out]] [[123201/123200]], [[194481/194480]], and [[336141/336140]], the three smallest 17-limit [[superparticular]]s.
+Since the approximation to harmonic 19 is weak, it can be used as a no-19 system, in which it continues to be strong up to the [[37-limit]], and is [[consistent]] to the no-19 39-odd-limit.
+=== Prime harmonics ===
+{{Harmonics in equal|7033|columns=11}}
+{{Harmonics in equal|7033|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 7033edo (continued)}}
+=== Subsets and supersets ===
+Since 7033 factors into primes as {{nowrap| 13 × 541 }}, 7033edo contains [[13edo]] and [[541edo]] as subsets.