1156/1155: Difference between revisions

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{{Infobox Interval

| Name = ~~septendecimal quartertones comma~~

| Name = quadrantonisma

| Color name =17oo1urg2, sosolurugu 2nd

| 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]]

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== 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.

=== Quadrantonic ===

[[Subgroup]]: 2.3.5.7.11.17

[[Sval]] [[mapping]]: <br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 1 || 0 || 0 || 1 || 1 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 1 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 1 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || -2 || -1 || ]]

|}

: sval mapping generators: ~2, ~3, ~5, ~7, ~34/11

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186

{{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 27eg, 39dg, 43, 46, 65d, 68, 72, 118, 171, 183, 239, 282, 301, 311, 400, 422, 472, 494, 894, 1012g, 1205, 1388 }}

=== Quadrantonismic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Mapping]]: <br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -1 || ],

|-

| ⟨ || 0 || 1 || 0 || 0 || 1 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 1 || 0 || 1 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 1 || 1 || 0 || 1 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || -2 || 0 || -1 || ],

|-

| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]

|}

: mapping generators: ~2, ~3, ~5, ~7, ~34/11, ~13

[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186, ~13/8

{{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 26, 27eg, 29g, 39dfg, 43, 46, 65d, 68, 72, 111, 121, 140, 171, 183, 217, 282, 301, 311, 354, 400, 422, 494, 894, 1012g, 1133, 1205, 1506g, 1627e }}

== 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]]

[[Category:Commas named for the intervals they stack]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = septendecimal quartertones comma
+| Name = quadrantonisma
-| Color name =17oo1urg2, sosolurugu 2nd
+| 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.
+=== Quadrantonic ===
+[[Subgroup]]: 2.3.5.7.11.17
+[[Sval]] [[mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 1 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 1 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 1 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || -2 || -1 || ]]
+|}
+: sval mapping generators: ~2, ~3, ~5, ~7, ~34/11
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186
+{{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 27eg, 39dg, 43, 46, 65d, 68, 72, 118, 171, 183, 239, 282, 301, 311, 400, 422, 472, 494, 894, 1012g, 1205, 1388 }}
+=== Quadrantonismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 1 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 1 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 1 || 0 || 1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || -2 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~34/11, ~13
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9948, ~5/4 = 386.3991, ~7/4 = 968.9508, ~17/11 = 752.9186, ~13/8
+{{Optimal ET sequence|legend=1| 17cg, 19eg, 22, 26, 27eg, 29g, 39dfg, 43, 46, 65d, 68, 72, 111, 121, 140, 171, 183, 217, 282, 301, 311, 354, 400, 422, 494, 894, 1012g, 1133, 1205, 1506g, 1627e }}
+== 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]]
+[[Category:Commas named for the intervals they stack]]