Maximal evenness: Difference between revisions

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Let's say we want to see what would repeatedly stacking 11th harmonic do well in all of 11-limit, in an EDO that presents it well.

11/8 amounts to 17 steps of 37edo, and the solution to the problem {{nowrap|17*''x'' (mod 1) {{=}} 37}} is 24, meaning if the generator is 11/8, we are dealing with a 24 tone maximally even scale. As such, the temperament we are looking for is 24 & 37, which can be interpreted as [[freivald]] or [[emka]].

11/8 amounts to 17 steps of 37edo, and the solution to the problem {{nowrap|17*''x'' (mod 1) {{=}} 37}} is 24, meaning if the generator is 11/8, we are dealing with a 24 tone maximally even scale. As such, the temperament we are looking for is {{nowrap|24 & 37}}, which can be interpreted as [[freivald]] or [[emka]].

=== Example 3: On-request maximum evenness scales ===

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We simply merge {{nowrap|52 & 293}} in a selected limit to get our answer. Let's say 17 limit, we get a {{nowrap|52 & 243c}} temperament with a comma list 225/224, 715/714, 2880/2873, 22750/22627 and 60112/60025.

Let's see what temperament does the Tabular Persian or Dee calendar offer {{nowrap|(29 & 33)}}. In the 5-limit, we get a contorted Lala-Quinyo (553584375:536870912).

== Sonifications ==

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 Let's say we want to see what would repeatedly stacking 11th harmonic do well in all of 11-limit, in an EDO that presents it well.
-/8 amounts to 17 steps of 37edo, and the solution to the problem {{nowrap|17*''x'' (mod 1) {{=}} 37}} is 24, meaning if the generator is 11/8, we are dealing with a 24 tone maximally even scale. As such, the temperament we are looking for is 24 & 37, which can be interpreted as [[freivald]] or [[emka]].
+/8 amounts to 17 steps of 37edo, and the solution to the problem {{nowrap|17*''x'' (mod 1) {{=}} 37}} is 24, meaning if the generator is 11/8, we are dealing with a 24 tone maximally even scale. As such, the temperament we are looking for is {{nowrap|24 &amp; 37}}, which can be interpreted as [[freivald]] or [[emka]].
 === Example 3: On-request maximum evenness scales ===
@@ Line 68: / Line 68: @@
 We simply merge {{nowrap|52 &amp; 293}} in a selected limit to get our answer. Let's say 17 limit, we get a {{nowrap|52 &amp; 243c}} temperament with a comma list 225/224, 715/714, 2880/2873, 22750/22627 and 60112/60025.
 Let's see what temperament does the Tabular Persian or Dee calendar offer {{nowrap|(29 &amp; 33)}}. In the 5-limit, we get a contorted Lala-Quinyo (553584375:536870912).
 == Sonifications ==