Quinticular comma: Difference between revisions

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Created page with "{{Infobox interval |Ratio = 1419857/1417176 |Name = quinticular comma |Color name = s17o<sup>5</sup>4, saquinso 4th |Comma = yes }} '''1419857/1417176''', the '''quinticular comma''' is a 2.3.17 subgroup comma that is the difference between five 18/17s and one 4/3. It is tempered out in following EDOs: * 12''n'' family (up to 120) * 12''n''+1 family (between 109 and 337) == Etymology == The word ''quinticular'' was introduced by Xenllium..."
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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 ==
== Etymology ==

Revision as of 09:12, 20 May 2025

Interval information
Ratio 1419857/1417176
Subgroup monzo 2.3.17 [-3 -11 5
Size in cents 3.272038¢
Name quinticular comma
Color name s17o54, saquinso 4th
FJS name [math]\displaystyle{ \text{5d4}^{17,17,17,17,17} }[/math]
Special properties reduced
Tenney norm (log2 nd) 40.8719
Weil norm (log2 max(n, d)) 40.8746
Wilson norm (sopfr(nd)) 124
Comma size unnoticeable
Open this interval in xen-calc

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

Temperaments

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

This comma is tempered out in following EDOs:

  • 12n family: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 2772, 2784
  • 12n+1 family: between 109 and 337
  • 12n+2 family: between 326 and 554
  • 12n+3 family: between 555 and 783
  • 12n+4 family: between 772 and 1000
  • 12n+5 family: between 1001 and 1229
  • 12n+6 family: between 1230 and 1446
  • 12n+7 family: between 1495 and 1663
  • 12n+8 family: between 1748 and 1892
  • 12n+9 family: between 2001 and 2109
  • 12n+10 family: between 2254 and 2338
  • 12n+11 family: between 2507 and 2555

Etymology

The word quinticular was introduced by Xenllium in 2025.