Quinticular comma: Difference between revisions

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~~'''1419857/1417176''', the~~ '''quinticular comma''' is a 2.3.17 [[subgroup]] comma ~~that is~~ the difference between five [[18/17]]s and ~~one~~ [[4/3]]. It is tempered out in following EDOs:

The '''quinticular comma''' is a 2.3.17 [[subgroup]] comma of measuring 3.27 [[cent]]s, with frequency ratio of 1419857/1417176. It forms the difference between five semitones of [[18/17]] and a perfect fourth, [[4/3]].

* 12''n'' family ~~(up to~~ 120)

* 12''n''+1 family (between 109 and 337)

== Temperaments ==

Tempering out this comma in the 2.3.17 subgroup leads to the '''quinticular temperament''', which is related to a number of [[Cluster MOS|cluster temperaments]], such as [[quintaleap]], [[quindromeda]], and [[quintaschis]].

This comma is tempered out in following EDOs:

* 12''n'' family: [[12edo|12]], [[24edo|24]], [[36edo|36]], [[48edo|48]], [[60edo|60]], [[72edo|72]], [[84edo|84]], [[96edo|96]], [[108edo|108]], [[120edo|120]], 2772, 2784

* 12''n''+1 family: between [[109edo|109]] and [[337edo|337]]

* 12''n''+2 family: between 326 and 554

* 12''n''+3 family: between 555 and 783

* 12''n''+4 family: between 772 and 1000

* 12''n''+5 family: between 1001 and 1229

* 12''n''+6 family: between 1230 and 1446

* 12''n''+7 family: between 1495 and 1663

* 12''n''+8 family: between 1748 and 1892

* 12''n''+9 family: between 2001 and 2109

* 12''n''+10 family: between 2254 and 2338

* 12''n''+11 family: between 2507 and 2555

== Etymology ==

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 }}
-'''1419857/1417176''', the '''quinticular comma''' is a 2.3.17 [[subgroup]] comma that is the difference between five [[18/17]]s and one [[4/3]]. It is tempered out in following EDOs:
+The '''quinticular comma''' is a 2.3.17 [[subgroup]] comma of measuring 3.27 [[cent]]s, with frequency ratio of 1419857/1417176. It forms the difference between five semitones of [[18/17]] and a perfect fourth, [[4/3]].
-* 12''n'' family (up to 120)
-* 12''n''+1 family (between 109 and 337)
+== Temperaments ==
+Tempering out this comma in the 2.3.17 subgroup leads to the '''quinticular temperament''', which is related to a number of [[Cluster MOS|cluster temperaments]], such as [[quintaleap]], [[quindromeda]], and [[quintaschis]].
+This comma is tempered out in following EDOs:
+* 12''n'' family: [[12edo|12]], [[24edo|24]], [[36edo|36]], [[48edo|48]], [[60edo|60]], [[72edo|72]], [[84edo|84]], [[96edo|96]], [[108edo|108]], [[120edo|120]], 2772, 2784
+* 12''n''+1 family: between [[109edo|109]] and [[337edo|337]]
+* 12''n''+2 family: between 326 and 554
+* 12''n''+3 family: between 555 and 783
+* 12''n''+4 family: between 772 and 1000
+* 12''n''+5 family: between 1001 and 1229
+* 12''n''+6 family: between 1230 and 1446
+* 12''n''+7 family: between 1495 and 1663
+* 12''n''+8 family: between 1748 and 1892
+* 12''n''+9 family: between 2001 and 2109
+* 12''n''+10 family: between 2254 and 2338
+* 12''n''+11 family: between 2507 and 2555
 == Etymology ==