97ed9: Difference between revisions

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

~~This system can be approximated as~~ 30.~~6001 [[EDO]], meaning each~~ step of 97ed9 corresponds closely to five steps of [[153edo]].

== Theory ==

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

~~97ed9 is a non-[[octave]], non-[[tritave]] scale~~.

~~== Theory ==~~

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.

97ed9 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]] (see [[Zeta peak index]]).

== ~~Harmonic series~~ ==

=== Harmonics ===

~~=== 2 to 19~~ ===

{{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|columns=9|title=(~~contd.~~)~~|start=10~~}}

~~=== 36 to 53 ===~~

{{Harmonics in equal|97|9|1|~~columns~~=9|~~collapsed~~=1|start=~~35}}~~

~~{{Harmonics in equal~~|~~97|9|1|columns~~=9|title=(~~contd.~~)~~|collapsed=1|start=44~~}}

== Intervals ==

~~{{todo|expand}}~~

~~[[Category:Ed9]][[Category:Equal-step tuning]]~~

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''97ed9''' is an [[Equal-step tuning|equal-step]] [[tuning system]] created by dividing the interval of [[9/1]] into 97 equal parts.
+{{ED intro}}
-This system can be approximated as 30.6001 [[EDO]], meaning each step of 97ed9 corresponds closely to five steps of [[153edo]].
+== Theory ==
+ed9 corresponds to 30.6001…edo. Each step of 97ed9 corresponds closely to five steps of [[153edo]].
-ed9 is a non-[[octave]], non-[[tritave]] scale.
-== Theory ==
+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.
-ed9 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]] (see [[Zeta peak index]]).
-== Harmonic series ==
+=== Harmonics ===
+{{Harmonics in equal|97|9|1|intervals=integer|columns=11}}
-=== 2 to 19 ===
+{{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|columns=9}}
+{{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|columns=9|title=(contd.)|start=10}}
-=== 36 to 53 ===
-{{Harmonics in equal|97|9|1|columns=9|collapsed=1|start=35}}
-{{Harmonics in equal|97|9|1|columns=9|title=(contd.)|collapsed=1|start=44}}
 == Intervals ==
 {{Interval table}}
-{{todo|expand}}
-[[Category:Ed9]][[Category:Equal-step tuning]]