Quinticular comma: Difference between revisions

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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))5 = (S(''n''+1)×S(''n''+2)2) / (S(''n''+3)2×S(''n''+4)).

== Temperaments ==

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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 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 ==

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]]

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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 ==
@@ Line 12: / Line 13: @@
 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 ==
-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]]