96ed5: Difference between revisions

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== Theory ==

~~96ed5 is an [[Equal-step tuning|equal-step]] [[tuning system]] created by dividing the interval of [[5/1]] into 96 equal parts.~~

This non-octave, non-tritave scale features a well-balanced [[harmonic series segment]] from 5 to 9, and performs exceptionally well across all [[prime harmonics]] from 5 to 23, with the exception of 19.

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== Optimization ==

In the ~~32-integer-limit and~~ 5.7.11.13.17.23 ~~subgroup, the lowest relative error~~ is ~~41.346437627379-edo, or 41<1189.94532112775>, or~~ 29.~~023056612872~~ cents.

{{Harmonics in cet|29.~~023056612872~~|columns=15|title=Approximation of harmonics in optimized 96ed5}}

The local maxima for the finite Euler product over the primes 5.7.11.13.17.23 is 29.0283 cents.

{{Harmonics in cet|29.~~023056612872~~|columns=16|start=16|title=Approximation of harmonics in optimized 96ed5}}

{{Harmonics in cet|29.0283|columns=15|title=Approximation of harmonics in optimized 96ed5}}

{{Harmonics in cet|29.0283|columns=16|start=16|title=Approximation of harmonics in optimized 96ed5}}

== Intervals ==

~~[[Category:Ed5]]~~

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+{{Infobox ET}}
+{{ED intro}}
 == Theory ==
-ed5 is an [[Equal-step tuning|equal-step]] [[tuning system]] created by dividing the interval of [[5/1]] into 96 equal parts.
 This non-octave, non-tritave scale features a well-balanced [[harmonic series segment]] from 5 to 9, and performs exceptionally well across all [[prime harmonics]] from 5 to 23, with the exception of 19.
@@ Line 16: / Line 17: @@
 == Optimization ==
-In the 32-integer-limit and 5.7.11.13.17.23 subgroup, the lowest relative error is 41.346437627379-edo, or 41<1189.94532112775>, or 29.023056612872 cents.
-{{Harmonics in cet|29.023056612872|columns=15|title=Approximation of harmonics in optimized 96ed5}}
+The local maxima for the finite Euler product over the primes 5.7.11.13.17.23 is 29.0283 cents.
-{{Harmonics in cet|29.023056612872|columns=16|start=16|title=Approximation of harmonics in optimized 96ed5}}
+{{Harmonics in cet|29.0283|columns=15|title=Approximation of harmonics in optimized 96ed5}}
+{{Harmonics in cet|29.0283|columns=16|start=16|title=Approximation of harmonics in optimized 96ed5}}
 == Intervals ==
 {{Interval table}}
-[[Category:Ed5]]
+{{todo|expand}}