936/935: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = ainisma, ainic comma

~~| Ratio = 936/935~~

| Color name = 17u3o1ug1, sutholugu unison

~~| Monzo = 3 2 -1 0 -1 1 -1~~

| Comma = yes

~~| Cents = 1.8506~~

| Name =

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

'''936/935''', the '''ainisma''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.

~~'''936/935'''~~ is an [[~~unnoticeable comma|unnoticeable~~]] [[~~17-limit~~]] ~~comma with a size of roughly 1.85 cents. It forms the interval between the interval between~~ [[18/17]] and [[55/52]] ~~as well as the interval between~~ [[13/11]] and [[85/72]]~~, the interval between the~~ [[~~273~~/~~272|tannisma (~~273/272)]] and ~~the~~ [[385/384~~|keenanisma (385~~/~~384)~~]], and~~, the interval between the~~ [[~~256~~/~~255|septendecimal kleisma (256~~/~~255)~~]] and ~~the~~ [[~~352~~/~~351|minthma (352~~/~~351)~~]]~~. Thus, tempering out this comma is a good way to extend Keenanismic, Neo-Gothic~~ and ~~Minthmic harmonies to the 17-limit. Furthermore, it is also the interval that differentiates~~ [[17/13]] ~~from~~ [[72/55]], [[24/17]] ~~from~~ [[55/39]], and [[~~117~~/64]] ~~from~~ [[~~935~~/~~512~~]].

== Commatic relations ==

This comma is the difference between the following superparticular pairs:

* [[78/77]] and [[85/84]]

* [[144/143]] and [[170/169]]

* [[221/220]] and [[289/288]]

* [[256/255]] and [[352/351]]

* [[273/272]] and [[385/384]]

* [[351/350]] and [[561/560]]

* [[364/363]] and [[595/594]]

* [[375/374]] and [[625/624]]

* [[441/440]] and [[833/832]]

* [[540/539]] and [[1275/1274]]

* [[676/675]] and [[2431/2430]]

* [[715/714]] and [[3025/3024]]

[[~~Category~~:17-limit]]

It factors into the following superparticular pairs:

[[~~Category:~~Unnoticeable comma]]

* [[1716/1715]] and [[2058/2057]]

[[Category:~~Superparticular~~]]

* [[1701/1700]] and [[2080/2079]]

[[Category:~~todo~~]]

* [[1156/1155]] and [[4914/4913]]

* [[1089/1088]] and [[6656/6655]]

* [[1001/1000]] and [[14400/14399]]

== Temperaments ==

When tempered out in the full 17-limit, the resulting rank-6 temperament is called the '''ainismic temperament''', or in the 2.3.5.11.13.17 subgroup, the rank-5 '''ainic temperament'''. Both are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called [[ainismic chords]].

=== Ainic ===

[[Subgroup]]: 2.3.5.11.13.17

[[Comma list]]: 936/935

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

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 3 || ],

|-

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

|-

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

|-

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

|-

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

|}

: sval mapping generators: ~2, ~3, ~5, ~11, ~13

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1\1, ~3/2 = 701.7942, ~5/4 = 386.4863, ~11/8 = 551.7011, ~13/8 = 840.0893

* [[CWE]]: ~2 = 1\1, ~3/2 = 701.8763, ~5/4 = 386.5772, ~11/8 = 551.8274, ~13/8 = 840.2857

{{Optimal ET sequence|legend=1| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }}

=== Ainismic ===

[[Subgroup]]: 2.3.5.7.11.13.17

[[Comma list]]: 936/935

[[Mapping]]:<br>

{| class="right-all"

|-

| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 3 || ],

|-

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

|-

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

|-

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

|-

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

|-

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

|}

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

[[Optimal tuning]]s:

* [[CTE]]: ~2 = 1\1, ~3/2 = 701.7942, ~5/4 = 386.4863, ~7/4 = 968.8259, ~11/8 = 551.7011, ~13/8 = 840.0893

* [[CWE]]: ~2 = 1\1, ~3/2 = 701.8763, ~5/4 = 386.5773, ~7/4 = 968.9509, ~11/8 = 551.8275, ~13/8 = 840.2857

{{Optimal ET sequence|legend=1| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }}

== Etymology ==

This comma was named by [[Aura]] in 2020. Its names come from the Ancient Greek word [[Wiktionary: αἶνος #Ancient Greek|''aînos'']] ("tale", "story" or "fable"), which is fitting due to the comma serving as a viable 17-limit extension to minthmic temperaments, among others. Funny enough, this same Greek word is the source of the Ancient Greek word [[Wiktionary: αἴνιγμα #Ancient Greek|''aínigma'']] ("riddle"), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time.

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

[[Category:Ainismic]]

[[Category:Commas named by translating something into another language]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = ainisma, ainic comma
-| Ratio = 936/935
+| Color name = 17u3o1ug1, sutholugu unison
-| Monzo = 3 2 -1 0 -1 1 -1
+| Comma = yes
-| Cents = 1.8506
-| Name =
-| Color name =
-| FJS name =
-| Sound =
 }}
+'''936/935''', the '''ainisma''' or '''ainic comma''', is a [[17-limit]] [[unnoticeable comma]] with a size of roughly 1.85 [[cent]]s. It arises as the amount by which a stack consisting of [[18/17]] and [[13/11]] exceeds [[5/4]], as well as the amount by which a stack consisting of [[10/9]] and [[17/16]] falls short of 13/11. Moreover, it is also the interval that differentiates the [[273/272|tannisma (273/272)]] from the [[385/384|keenanisma (385/384)]], and the [[256/255|septendecimal kleisma (256/255)]] from the [[352/351|minthma (352/351)]]. Thus, tempering out this comma is a good way to extend minthmic and gentle harmonies to the 17-limit, as well as a good way to bring keenanismic and tannismic harmonies together. See [[#Commatic relations]] for more.
-'''936/935''' is an [[unnoticeable comma|unnoticeable]] [[17-limit]] comma with a size of roughly 1.85 cents.  It forms the interval between the interval between [[18/17]] and [[55/52]] as well as the interval between [[13/11]] and [[85/72]], the interval between the [[273/272|tannisma (273/272)]] and the [[385/384|keenanisma (385/384)]], and, the interval between the [[256/255|septendecimal kleisma (256/255)]] and the [[352/351|minthma (352/351)]].  Thus, tempering out this comma is a good way to extend Keenanismic, Neo-Gothic and Minthmic harmonies to the 17-limit.  Furthermore, it is also the interval that differentiates [[17/13]] from [[72/55]], [[24/17]] from [[55/39]], and [[117/64]] from [[935/512]].
+== Commatic relations ==
+This comma is the difference between the following superparticular pairs:
+* [[78/77]] and [[85/84]]
+* [[144/143]] and [[170/169]]
+* [[221/220]] and [[289/288]]
+* [[256/255]] and [[352/351]]
+* [[273/272]] and [[385/384]]
+* [[351/350]] and [[561/560]]
+* [[364/363]] and [[595/594]]
+* [[375/374]] and [[625/624]]
+* [[441/440]] and [[833/832]]
+* [[540/539]] and [[1275/1274]]
+* [[676/675]] and [[2431/2430]]
+* [[715/714]] and [[3025/3024]]
-[[Category:17-limit]]
+It factors into the following superparticular pairs:
-[[Category:Unnoticeable comma]]
+* [[1716/1715]] and [[2058/2057]]
-[[Category:Superparticular]]
+* [[1701/1700]] and [[2080/2079]]
-[[Category:todo]]
+* [[1156/1155]] and [[4914/4913]]
+* [[1089/1088]] and [[6656/6655]]
+* [[1001/1000]] and [[14400/14399]]
+== Temperaments ==
+When tempered out in the full 17-limit, the resulting rank-6 temperament is called the '''ainismic temperament''', or in the 2.3.5.11.13.17 subgroup, the rank-5 '''ainic temperament'''. Both are characterized by the presence of [[Dyadic chord|essentially tempered chord]]s called [[ainismic chords]].
+=== Ainic ===
+[[Subgroup]]: 2.3.5.11.13.17
+[[Comma list]]: 936/935
+[[Sval]] [[mapping]]:<br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 3 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 1 || ]]
+|}
+: sval mapping generators: ~2, ~3, ~5, ~11, ~13
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~3/2 = 701.7942, ~5/4 = 386.4863, ~11/8 = 551.7011, ~13/8 = 840.0893
+* [[CWE]]: ~2 = 1\1, ~3/2 = 701.8763, ~5/4 = 386.5772, ~11/8 = 551.8274, ~13/8 = 840.2857
+{{Optimal ET sequence|legend=1| 22, 24, 31, 34, 46, 53, 58, 65, 72, 87, 111, 137, 183, 304, 320, 354, 400, 407, 441, 537, 552g, 624 }}
+=== Ainismic ===
+[[Subgroup]]: 2.3.5.7.11.13.17
+[[Comma list]]: 936/935
+[[Mapping]]:<br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 0 || 3 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || 0 || 2 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || 0 || 0 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 0 || 1 || 1 || ]]
+|}
+: mapping generators: ~2, ~3, ~5, ~7, ~11, ~13
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1\1, ~3/2 = 701.7942, ~5/4 = 386.4863, ~7/4 = 968.8259, ~11/8 = 551.7011, ~13/8 = 840.0893
+* [[CWE]]: ~2 = 1\1, ~3/2 = 701.8763, ~5/4 = 386.5773, ~7/4 = 968.9509, ~11/8 = 551.8275, ~13/8 = 840.2857
+{{Optimal ET sequence|legend=1| 22, 26, 31, 38df, 41, 46, 58, 72, 103, 111, 121, 149, 159, 171, 183, 217, 224, 270, 354, 400, 441, 552g, 624, 1393ceegg, 1576cdegg }}
+== Etymology ==
+This comma was named by [[Aura]] in 2020. Its names come from the Ancient Greek word [[Wiktionary: αἶνος #Ancient Greek|''aînos'']] ("tale", "story" or "fable"), which is fitting due to the comma serving as a viable 17-limit extension to minthmic temperaments, among others. Funny enough, this same Greek word is the source of the Ancient Greek word [[Wiktionary: αἴνιγμα #Ancient Greek|''aínigma'']] ("riddle"), from which we ultimately get our word "enigma", and this is also fitting due to the sheer difficulty that was involved in the initial process of working out both the name and the uses of this comma in a short span of time.
+== See also ==
+* [[Unnoticeable comma]]
+* [[List of superparticular intervals]]
+[[Category:Ainismic]]
+[[Category:Commas named by translating something into another language]]