97ed9: Difference between revisions

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== Theory ==

97ed9 corresponds to 30.6001…edo. Each step of 97ed9 corresponds closely to five steps of [[153edo]].

97ed9 ~~is an [[Equal-step tuning|equal-step]] [[tuning system]] created by dividing the interval of [[9/1]] into 97 equal parts.~~

97ed9 features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50 (see table below). It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.

~~This system can be approximated as 30.6001 [[EDO]], meaning each step of 97ed9 corresponds closely to five steps of [[153edo]].~~

~~This non-octave, non-tritave scale~~ features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.

97ed9 sets a height record on the [[The Riemann zeta function and tuning|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes|primes 2 and 3 removed]], approximating 30.~~59745 EDO~~. This record remains unbeaten until approximately 41.~~3478 EDO~~.

97ed9 sets a height record on the [[The Riemann zeta function and tuning|Riemann zeta function]] with [[The Riemann zeta function and tuning #Removing primes|primes 2 and 3 removed]], approximating 30.59745…edo. This record remains unbeaten until approximately 41.3478…edo.

Additionally, 97ed9 is close to [[125zpi]].

Additionally, 97ed9 is close to [[125zpi]] (see [[Zeta peak index]]).

== ~~Harmonic series~~ ==

=== Harmonics ===

{{Harmonics in equal|97|9|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 97ed9 (continued)}}

{{Harmonics in equal|97|9|1|intervals=integer|columns=12|start=38|collapsed=true|title=Approximation of harmonics in 97ed9 (39–50)}}

~~{{Harmonics in equal|97|9|1|prec~~=~~1|columns~~=~~15}}~~

== Intervals ==

~~{{Harmonics in equal|97|9|1|prec~~=~~1|columns~~=~~16|start=16}}~~

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+{{Infobox ET}}
+{{ED intro}}
 == Theory ==
+ed9 corresponds to 30.6001…edo. Each step of 97ed9 corresponds closely to five steps of [[153edo]].
-ed9 is an [[Equal-step tuning|equal-step]] [[tuning system]] created by dividing the interval of [[9/1]] into 97 equal parts.
+ed9 features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50 (see table below). It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.
-This system can be approximated as 30.6001 [[EDO]], meaning each step of 97ed9 corresponds closely to five steps of [[153edo]].
-This non-octave, non-tritave scale features a well-balanced [[harmonic series segment]] from 4 to 9 and another from 39 to 50. It performs well across all [[prime harmonics]] from 5 to 19, with the exception of 13, which is slightly flat.
-ed9 sets a height record on the [[The Riemann zeta function and tuning|Riemann zeta function]] with [[The Riemann zeta function and tuning#Removing primes|primes 2 and 3 removed]], approximating 30.59745 EDO. This record remains unbeaten until approximately 41.3478 EDO.
+ed9 sets a height record on the [[The Riemann zeta function and tuning|Riemann zeta function]] with [[The Riemann zeta function and tuning #Removing primes|primes 2 and 3 removed]], approximating 30.59745…edo. This record remains unbeaten until approximately 41.3478…edo.
-Additionally, 97ed9 is close to [[125zpi]].
+Additionally, 97ed9 is close to [[125zpi]] (see [[Zeta peak index]]).
-== Harmonic series ==
+=== Harmonics ===
+{{Harmonics in equal|97|9|1|intervals=integer|columns=11}}
+{{Harmonics in equal|97|9|1|intervals=integer|columns=12|start=12|collapsed=true|title=Approximation of harmonics in 97ed9 (continued)}}
+{{Harmonics in equal|97|9|1|intervals=integer|columns=12|start=38|collapsed=true|title=Approximation of harmonics in 97ed9 (39–50)}}
-{{Harmonics in equal|97|9|1|prec=1|columns=15}}
+== Intervals ==
-{{Harmonics in equal|97|9|1|prec=1|columns=16|start=16}}
+{{Interval table}}
-{{Harmonics in equal|97|9|1|prec=1|columns=18|start=32}}