18edf: Difference between revisions

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~~'''18EDF''' is the [[EDF|equal division of the just perfect fifth]] into 18 parts of 38.9975 [[cents]] each, corresponding to 30.7712 [[edo]].~~

It is related to the [[regular temperament]] which [[tempers out]] 2401/2400 and 8589934592/8544921875 in the [[7-limit]]; with 5632/5625, 46656/46585, and 166698/166375 in the [[11-limit]], which is supported by [[31edo]], [[369edo]], [[400edo]], [[431edo]], and [[462edo]].

== Theory ==

18edf is related to the [[regular temperament]] which [[tempering out|tempers out]] 2401/2400 and 8589934592/8544921875 in the [[7-limit]]; with 5632/5625, 46656/46585, and 166698/166375 in the [[11-limit]], which is supported by [[31edo]], [[369edo]], [[400edo]], [[431edo]], and [[462edo]].

Lookalikes: [[31edo]], [[49edt]], [[72ed5]], [[80ed6]]

==Harmonics==

=== Harmonics ===

==Intervals==

== Intervals ==

{| class="wikitable mw-collapsible"

|+ Intervals of 18edf

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|}

==Related regular temperaments==

== Related regular temperaments ==

The rank-two regular temperament supported by 31edo and 369edo has three equal divisions of the interval which equals an octave minus the step interval of 18EDF as a generator.

===7-limit 31&369===

=== 7-limit 31&369 ===

Commas: 2401/2400, 8589934592/8544921875

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EDOs: 31, 369, 400, 431, 462

{{~~todo~~|expand|comment=say what the temperaments are like and why one would want to use them, and for what}}

{{Todo|cleanup|expand|inline=1|comment=say what the temperaments are like and why one would want to use them, and for what}}

@@ Line 1: / Line 1: @@
 {{Infobox ET}}
-'''18EDF''' is the [[EDF|equal division of the just perfect fifth]] into 18 parts of 38.9975 [[cents]] each, corresponding to 30.7712 [[edo]].
+{{ED intro}}
-It is related to the [[regular temperament]] which [[tempers out]] 2401/2400 and 8589934592/8544921875 in the [[7-limit]]; with 5632/5625, 46656/46585, and 166698/166375 in the [[11-limit]], which is supported by [[31edo]], [[369edo]], [[400edo]], [[431edo]], and [[462edo]].
+== Theory ==
+edf is related to the [[regular temperament]] which [[tempering out|tempers out]] 2401/2400 and 8589934592/8544921875 in the [[7-limit]]; with 5632/5625, 46656/46585, and 166698/166375 in the [[11-limit]], which is supported by [[31edo]], [[369edo]], [[400edo]], [[431edo]], and [[462edo]].
 Lookalikes: [[31edo]], [[49edt]], [[72ed5]], [[80ed6]]
-==Harmonics==
+=== Harmonics ===
 {{Harmonics in equal|18|3|2}}
 {{Harmonics in equal|18|3|2|start=12|collapsed=1}}
-==Intervals==
+== Intervals ==
 {| class="wikitable mw-collapsible"
 |+ Intervals of 18edf
@@ Line 204: / Line 205: @@
 |}
-==Related regular temperaments==
+== Related regular temperaments ==
 The rank-two regular temperament supported by 31edo and 369edo has three equal divisions of the interval which equals an octave minus the step interval of 18EDF as a generator.
-===7-limit 31&amp;369===
+=== 7-limit 31&amp;369 ===
 Commas: 2401/2400, 8589934592/8544921875
@@ Line 234: / Line 235: @@
 EDOs: 31, 369, 400, 431, 462
-{{todo|expand|comment=say what the temperaments are like and why one would want to use them, and for what}}
+{{Todo|cleanup|expand|inline=1|comment=say what the temperaments are like and why one would want to use them, and for what}}