97ed9: Difference between revisions

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~~== Theory ==~~

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

~~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]].

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

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

~~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.

== Theory ==

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.

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== Harmonic series ==

=== 2 to 15 ===

=== 2 to 19 ===

=== 38 to 52 ===

=== 36 to 53 ===

{{Harmonics in equal|97|9|1|columns=7|title=(contd.)|collapsed=1|start=45}}

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

== Intervals ==

@@ Line 1: / Line 1: @@
-== Theory ==
+{{Infobox ET}}
+'''97ed9''' is an [[Equal-step tuning|equal-step]] [[tuning system]] created by dividing the interval of [[9/1]] into 97 equal parts.
-ed9 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]].
-This system can be approximated as 30.6001 [[EDO]], meaning each step of 97ed9 corresponds closely to five steps of [[153edo]].
+ed9 is a non-[[octave]], non-[[tritave]] scale.
-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.
+== Theory ==
+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.
@@ Line 13: / Line 15: @@
 == Harmonic series ==
-=== 2 to 15 ===
+=== 2 to 19 ===
-{{Harmonics in equal|97|9|1|columns=7}}
+{{Harmonics in equal|97|9|1|columns=9}}
-{{Harmonics in equal|97|9|1|columns=7|title=(contd.)|start=8}}
+{{Harmonics in equal|97|9|1|columns=9|title=(contd.)|start=10}}
-=== 38 to 52 ===
+=== 36 to 53 ===
-{{Harmonics in equal|97|9|1|columns=7|collapsed=1|start=37}}
+{{Harmonics in equal|97|9|1|columns=9|collapsed=1|start=35}}
-{{Harmonics in equal|97|9|1|columns=7|title=(contd.)|collapsed=1|start=45}}
+{{Harmonics in equal|97|9|1|columns=9|title=(contd.)|collapsed=1|start=44}}
 == Intervals ==