Maximal evenness: Difference between revisions

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Consider the resulting binary word of "|" and "$". The "|"s form chunks of sizes that differ by 1 and are distributed in a MOS way by (*). The desired complement, occupied by the "$"'s, thus forms a maximally even subset.

~~== Concoctic scales ==~~

The generator of a maximally even scale is a modular multiplicative inverse of it's number of notes and the EDO size. A maximal even scale whose generator is equal to it's note amount is called [[concoctic]]. Major and minor scales in standard Western music are such—the generator is a perfect fifth of 7 semitones, as inferred through Pythagorean tuning, and the scale has 7 notes in it.

== Sound perception ==

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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 ==~~

* Maximally even heptatonic scale of [[19edo]] is the leap year arrangement of the {{w|Hebrew calendar}}.

* Maximally even octatonic scale of [[33edo]] is a leap year arrangement of the Dee calendar and the tabular, evened version of the {{w|Iranian calendars|Persian calendar}}.

[[Category:Scale]]

[[Category:Todo:cleanup]]

@@ Line 26: / Line 26: @@
 Consider the resulting binary word of "|" and "$". The "|"s form chunks of sizes that differ by 1 and are distributed in a MOS way by (*). The desired complement, occupied by the "$"'s, thus forms a maximally even subset.
-== Concoctic scales ==
-The generator of a maximally even scale is a modular multiplicative inverse of it's number of notes and the EDO size. A maximal even scale whose generator is equal to it's note amount is called [[concoctic]]. Major and minor scales in standard Western music are such—the generator is a perfect fifth of 7 semitones, as inferred through Pythagorean tuning, and the scale has 7 notes in it.
 == Sound perception ==
@@ Line 67: / Line 64: @@
 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 ==
-* Maximally even heptatonic scale of [[19edo]] is the leap year arrangement of the {{w|Hebrew calendar}}.
-* Maximally even octatonic scale of [[33edo]] is a leap year arrangement of the Dee calendar and the tabular, evened version of the {{w|Iranian calendars|Persian calendar}}.
 [[Category:Scale]]
 [[Category:Todo:cleanup]]