Symbiotic comma: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 19712/19683

~~| Monzo = 8 -9 0 1 1~~

| Name = symbiotic comma, symbiosis, symbiosma

~~| Cents = 2.54884~~

| Color name = s1oz2, Salozo comma

| Name = ~~symbiosis~~ comma, ~~<br> symbiotic comma~~, ~~<br>~~ symbiosma

| Comma = yes

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup|2.3.7.11-subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048|apotome (2187/2048)]] and an [[77/72|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].

~~'''19712/19683''', the '''symbiosis comma''', also known as the '''symbiotic comma''' or '''symbiosma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 2.55 cents.~~ It ~~gets its names from the fact that it is tempered out in such notable temperaments as~~ [[~~Vishnuzmic family #Vishnu|vishnu~~]], [[~~Breedsmic temperaments #Newt|newt~~]], ~~[[Mirkwai clan #Kwai|kwai]]~~, [[~~Hemifamity temperaments #Supers|supers]], [[Schismatic family #Guiron|guiron~~]] and ~~[[Amity family|amity]], and, from~~ the ~~fact that it also makes a good extension to a number of other temperaments such as~~ [[~~Canou family|canou~~]]. ~~It is~~ the ~~difference between an~~ [[~~2187/2048|apotome (2187/2048)]] and an [[77/72|undecimal secor (77/72)~~]] ~~– the latter of which can be broken down into a [[33/32]] quartertone stacked on top of [[28/27]]. Alternatively stated~~, it ~~identifies~~ [[11/8]] ~~by an apotome over~~ [[9/~~7]]. Moreover, it is the sum of the [[quartisma]] and the [[nexisma~~]].

It factors into ([[4375/4374]])⋅([[5632/5625]]), and moreover, into the [[quartisma]] and the [[nexus comma]]. In the [[19-limit]], it factors neatly into ([[1216/1215]])⋅([[1540/1539]]).

== Temperaments ==

Tempering out this comma in the 11-limit results in the rank-4 '''symbiotic ~~temperament~~''' (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]).

[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, it identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243|limma]] below 9/7.

== ~~See also~~ ==

=== Symbiotian ===

* [[~~Unnoticeable~~ comma]]

[[Subgroup]]: 2.3.7.11

[[Comma list]]: 19712/19683

: mapping generators: ~2, ~3, ~7

[[Optimal tuning]]s:

* [[WE]]: ~2 = 1199.9290{{c}}, ~3/2 = 702.2265{{c}}, ~7/4 = 968.8979{{c}}

: [[error map]]: {{val| -0.071 +0.201 -0.070 -0.106 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2440{{c}}, ~7/4 = 968.8593{{c}}

: error map: {{val| 0.000 +0.289 +0.033 +0.019 }}

{{Optimal ET sequence|legend=1| 41, 58, 77, 94, 118, 135, 716, 733, 851, 868, 1003, 1138, 1273, 1449, 1584, 1719, 1854 }}

[[Badness]] (Sintel): 0.336

== Etymology ==

This comma was named by [[Aura]] in 2020, from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[cathartic]].

~~[[Category:11-limit]]~~

~~[[Category:Unnoticeable commas]]~~

[[Category:Symbiotic]]

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

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
 | Ratio = 19712/19683
-| Monzo = 8 -9 0 1 1
+| Name = symbiotic comma, symbiosis, symbiosma
-| Cents = 2.54884
+| Color name = s1oz2, Salozo comma
-| Name = symbiosis comma, <br> symbiotic comma, <br> symbiosma
+| Comma = yes
-| Color name =
-| FJS name =
-| Sound =
 }}
+'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup|2.3.7.11-subgroup]]) [[comma]] measuring about 2.55 [[cent]]s. It is the difference between an [[2187/2048|apotome (2187/2048)]] and an [[77/72|undecimal secor (77/72)]] – the latter of which can be broken down into a quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].
-'''19712/19683''', the '''symbiosis comma''', also known as the '''symbiotic comma''' or '''symbiosma''', is an [[11-limit]] [[unnoticeable comma]] measuring about 2.55 cents.  It gets its names from the fact that it is tempered out in such notable temperaments as [[Vishnuzmic family #Vishnu|vishnu]], [[Breedsmic temperaments #Newt|newt]], [[Mirkwai clan #Kwai|kwai]], [[Hemifamity temperaments #Supers|supers]], [[Schismatic family #Guiron|guiron]] and [[Amity family|amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[Canou family|canou]].  It is the difference between an [[2187/2048|apotome (2187/2048)]] and an [[77/72|undecimal secor (77/72)]] – the latter of which can be broken down into a [[33/32]] quartertone stacked on top of [[28/27]].  Alternatively stated, it identifies [[11/8]] by an apotome over [[9/7]].  Moreover, it is the sum of the [[quartisma]] and the [[nexisma]].
+It factors into ([[4375/4374]])⋅([[5632/5625]]), and moreover, into the [[quartisma]] and the [[nexus comma]]. In the [[19-limit]], it factors neatly into ([[1216/1215]])⋅([[1540/1539]]).
 == Temperaments ==
-Tempering out this comma in the 11-limit results in the rank-4 '''symbiotic temperament''' (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]).
+[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic''' temperament (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]), or in the 2.3.7.11 subgroup, the '''symbiotian''' temperament. In either case, it identifies [[11/8]] by an apotome over [[9/7]], [[11/6]] by an apotome over [[12/7]], and [[11/9]] by an apotome over [[8/7]]. Finally, it identifies 11/9 by a [[256/243|limma]] below 9/7.
-== See also ==
+=== Symbiotian ===
-* [[Unnoticeable comma]]
+[[Subgroup]]: 2.3.7.11
+[[Comma list]]: 19712/19683
+{{Mapping|legend=2| 1 0 0 -8 | 0 1 0 9 | 0 0 1 -1 }}
+: mapping generators: ~2, ~3, ~7
+[[Optimal tuning]]s:
+* [[WE]]: ~2 = 1199.9290{{c}}, ~3/2 = 702.2265{{c}}, ~7/4 = 968.8979{{c}}
+: [[error map]]: {{val| -0.071 +0.201 -0.070 -0.106 }}
+* [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2440{{c}}, ~7/4 = 968.8593{{c}}
+: error map: {{val| 0.000 +0.289 +0.033 +0.019 }}
+{{Optimal ET sequence|legend=1| 41, 58, 77, 94, 118, 135, 716, 733, 851, 868, 1003, 1138, 1273, 1449, 1584, 1719, 1854 }}
+[[Badness]] (Sintel): 0.336
+== Etymology ==
+This comma was named by [[Aura]] in 2020, from the fact that it is tempered out in such notable temperaments as [[vishnu]], [[newt]], [[kwai]], [[supers]], [[guiron]] and [[amity]], and, from the fact that it also makes a good extension to a number of other temperaments such as [[cathartic]].
-[[Category:11-limit]]
-[[Category:Unnoticeable commas]]
 [[Category:Symbiotic]]
+[[Category:Commas named for their regular temperament properties]]