1156/1155: Difference between revisions

Line 1:

{{Infobox Interval

| Name = ~~septendecimal quartertones comma~~

| Name = quadrantonisma

| Color name =17oo1urg2, sosolurugu 2nd,<br>Sosolurugu comma

| Comma = yes

}}

'''1156/1155''' is a [[17-limit]] no-13 [[superparticular]] [[comma]] measuring about 1.41 [[cent]]s. It may be properly described as the ''septendecimal quartertones comma'', since it is the difference between [[34/33]] and [[35/34]], the two 17-limit quartertones.

'''1156/1155''', the '''quadrantonisma''', is a [[17-limit]] no-13 [[superparticular]] [[comma]] measuring about 1.41 [[cent]]s. It may be properly described as the ''septendecimal quartertones comma'', since it is the difference between [[34/33]] and [[35/34]], the two 17-limit quartertones.

== Commatic relations ==

In terms of commas, it is the difference between the following pairs:

* [[289/288]] and [[385/384]]

Line 18:

Line 19:

== Temperaments ==

Tempering out this comma results in [[35/33]] ~~being~~ split into two equal parts, each representing 34/33~35/34, and enables ~~the related essentially tempered~~ chords. If [[9801/9800]] is also added to the comma list, the quartertone above becomes literally a quarter of [[9/8]] and is ~~located right between~~ [[33/32]], the undecimal quartertone, and [[36/35]], the septimal quartertone.

Tempering out this comma in the 17-limit results in the rank-6 '''quadrantonismic temperament''', or in the 2.3.5.7.11.17 subgroup, the rank-5 '''quadrantonic temperament'''. In either case [[35/33]] is split into two equal parts, each representing 34/33~35/34, and enables [[quadrantonismic chords]]. If [[9801/9800]] is also added to the comma list, the quartertone above becomes literally a quarter of [[9/8]] and is tuned exactly middle of [[33/32]], the undecimal quartertone, and [[36/35]], the septimal quartertone.

== Etymology ==

The quadrantonisma was named by [[Flora Canou]] in 2023. It is a contraction of ''septendecimal quartertones comma'' into a single word consisting of Latin ''quadrans'' ("fourth") and ''tonus'' ("tone").

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

[[Category:Quadrantonismic]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septendecimal quartertones comma
+| Name = quadrantonisma
 | Color name =17oo1urg2, sosolurugu 2nd,<br>Sosolurugu comma
 | Comma = yes
 }}
-'''1156/1155''' is a [[17-limit]] no-13 [[superparticular]] [[comma]] measuring about 1.41 [[cent]]s. It may be properly described as the ''septendecimal quartertones comma'', since it is the difference between [[34/33]] and [[35/34]], the two 17-limit quartertones.
+'''1156/1155''', the '''quadrantonisma''', is a [[17-limit]] no-13 [[superparticular]] [[comma]] measuring about 1.41 [[cent]]s. It may be properly described as the ''septendecimal quartertones comma'', since it is the difference between [[34/33]] and [[35/34]], the two 17-limit quartertones.
+== Commatic relations ==
 In terms of commas, it is the difference between the following pairs:
 * [[289/288]] and [[385/384]]
@@ Line 18: / Line 19: @@
 == Temperaments ==
-Tempering out this comma results in [[35/33]] being split into two equal parts, each representing 34/33~35/34, and enables the related essentially tempered chords. If [[9801/9800]] is also added to the comma list, the quartertone above becomes literally a quarter of [[9/8]] and is located right between [[33/32]], the undecimal quartertone, and [[36/35]], the septimal quartertone.
+Tempering out this comma in the 17-limit results in the rank-6 '''quadrantonismic temperament''', or in the 2.3.5.7.11.17 subgroup, the rank-5 '''quadrantonic temperament'''. In either case [[35/33]] is split into two equal parts, each representing 34/33~35/34, and enables [[quadrantonismic chords]]. If [[9801/9800]] is also added to the comma list, the quartertone above becomes literally a quarter of [[9/8]] and is tuned exactly middle of [[33/32]], the undecimal quartertone, and [[36/35]], the septimal quartertone.
+== Etymology ==
+The quadrantonisma was named by [[Flora Canou]] in 2023. It is a contraction of ''septendecimal quartertones comma'' into a single word consisting of Latin ''quadrans'' ("fourth") and ''tonus'' ("tone").
 == See also ==
 * [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
+[[Category:Quadrantonismic]]