Quinticular comma - Revision history

Xenllium: Quintic-particular is an idiosyncratic term

2025-05-23T12:43:54Z

Quintic-particular is an idiosyncratic term

← Older revision		Revision as of 12:43, 23 May 2025
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	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]]. It is a quintic-particular interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).		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]]. It is a quintic-particular{{idiosyncratic}} interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).

	== Temperaments ==		== Temperaments ==

Xenllium at 13:25, 20 May 2025

2025-05-20T13:25:03Z

@@ Line 7: / Line 7: @@
 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]]. It is a quintic-particular interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).
 == Temperaments ==
@@ Line 42: / Line 41: @@
 | 12''n''+11 ||{{Optimal ET sequence|2507, 2519, 2531, 2543, 2555}}
 |}
 == Etymology ==

Xenllium: Xenllium moved page 1419857/1417176 to Quinticular comma: 14-digit ratios

2025-05-20T12:38:18Z

Xenllium moved page 1419857/1417176 to Quinticular comma: 14-digit ratios

← Older revision	Revision as of 12:38, 20 May 2025
(No difference)

Xenllium at 12:35, 20 May 2025

2025-05-20T12:35:09Z

← Older revision		Revision as of 12:35, 20 May 2025
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	}}		}}

	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]].		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]]. It is a quintic-particular interval, that is, of the form ((''n''+5)/''n'') / ((''n''+3)/(''n''+2))<sup>5</sup> = (S(''n''+1)×S(''n''+2)<sup>2</sup>) / (S(''n''+3)<sup>2</sup>×S(''n''+4)).


	== Temperaments ==		== Temperaments ==
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	This comma is tempered out in following EDOs:		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		{\| class="wikitable center-1"
	* 12''n''+1 ~~family: between [[109edo~~\|109~~]] and [[337edo~~\|~~337]]~~		\|-
	* 12''n''+2 ~~family: between~~ 326 ~~and~~ 554		! EDO <br>group
	* 12''n''+3 ~~family: between~~ 555 ~~and~~ 783		! Quinticular EDOs
	* 12''n''+4 ~~family: between~~ 772 ~~and~~ 1000		\|-
	* 12''n''+5 ~~family: between~~ 1001 ~~and~~ 1229		\| 12''n'' \|\|{{Optimal ET sequence\|12, 24, 36, 48, 60, 72, 84, 96, 108, 120, 2772, 2784}}
	* 12''n''+6 ~~family: between~~ 1230 ~~and~~ 1446		\|-
	* 12''n''+7 ~~family: between~~ 1495 ~~and~~ 1663		\| 12''n''+1 \|\|{{Optimal ET sequence\|109, 121, 133, 145, 157, 169, 181, 193, 205, 217, 229, 241, 253, 265, 277, 289, 301, 313, 325, 337}}
	* 12''n''+8 ~~family: between~~ 1748 ~~and~~ 1892		\|-
	* 12''n''+9 ~~family: between~~ 2001 ~~and~~ 2109		\| 12''n''+2 \|\|{{Optimal ET sequence\|326, 338, 350, 362, 374, 386, 398, 410, 422, 434, 446, 458, 470, 482, 494, 506, 518, 530, 542, 554}}
	* 12''n''+10 ~~family: between~~ 2254 ~~and~~ 2338		\|-
	* 12''n''+11 ~~family: between~~ 2507 ~~and~~ 2555		\| 12''n''+3 \|\|{{Optimal ET sequence\|555, 567, 579, 591, 603, 615, 627, 639, 651, 663, 675, 687, 699, 711, 723, 735, 747, 759, 771, 783}}
			\|-
			\| 12''n''+4 \|\|{{Optimal ET sequence\|772, 784, 796, 808, 820, 832, 844, 856, 868, 880, 892, 904, 916, 928, 940, 952, 964, 976, 988, 1000}}
			\|-
			\| 12''n''+5 \|\|{{Optimal ET sequence\|1001, 1013, 1025, 1037, 1049, 1061, 1073, 1085, 1097, 1109, 1121, 1133, 1145, 1157, 1169, 1181, 1193, 1205, 1217, 1229}}
			\|-
			\| 12''n''+6 \|\|{{Optimal ET sequence\|1230, 1242, 1254, 1266, 1278, 1290, 1302, 1314, 1326, 1338, 1350, 1362, 1374, 1386, 1398, 1410, 1422, 1434, 1446}}
			\|-
			\| 12''n''+7 \|\|{{Optimal ET sequence\|1495, 1507, 1519, 1531, 1543, 1555, 1567, 1579, 1591, 1603, 1615, 1627, 1639, 1651, 1663}}
			\|-
			\| 12''n''+8 \|\|{{Optimal ET sequence\|1748, 1760, 1772, 1784, 1796, 1808, 1820, 1832, 1844, 1856, 1868, 1880, 1892}}
			\|-
			\| 12''n''+9 \|\|{{Optimal ET sequence\|2001, 2013, 2025, 2037, 2049, 2061, 2073, 2085, 2097, 2109}}
			\|-
			\| 12''n''+10 \|\|{{Optimal ET sequence\|2254, 2266, 2278, 2290, 2302, 2314, 2326, 2338}}
			\|-
			\| 12''n''+11 \|\|{{Optimal ET sequence\|2507, 2519, 2531, 2543, 2555}}
			\|}

	== Etymology ==		== Etymology ==
	The word ''quinticular'' was introduced by [[User:Xenllium\|Xenllium]] in 2025.		The word ''quinticular'' was introduced by [[User:Xenllium\|Xenllium]] in 2025. It is a contraction of ''quintans'' (Latin for "one fifth", splitting a fourth in five) and ''particular'' into a single word.

			== See also ==
			* [[Glacier comma]] – another example of quintic-particular comma

	[[Category:Commas named for their regular temperament properties]]		[[Category:Commas named for their regular temperament properties]]

Xenllium at 09:12, 20 May 2025

2025-05-20T09:12:58Z

← Older revision		Revision as of 09:12, 20 May 2025
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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 ==

Xenllium: Created page with "{{Infobox interval |Ratio = 1419857/1417176 |Name = quinticular comma |Color name = s17o⁵4, 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..."

2025-05-19T23:57:39Z

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..."

New page

{{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 [[18/17]]s 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 [[User:Xenllium|Xenllium]] in 2025.

[[Category:Commas named for their regular temperament properties]]