Symbiotic comma: Difference between revisions

(21 intermediate revisions by 8 users not shown)

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 = ~~symbiosma, <br>~~symbiotic comma

| 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]]) [[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]]. It is also the difference between a [[septischisma]] and a [[olympia]].

'''19712/19683''', the '''symbiosma''' or '''symbiotic comma''', 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 apotome [[2187/2048]] and [[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 ~~[[nexuma]]. Tempering out this comma in a linearly independent fashion results in '''symbiotic temperament'''.~~

It factors into the following commas:

~~== See also ==~~

*[[2.3.7.11 subgroup]]:

* [[~~Unnoticeable~~ comma]]

:* ([[olympia]])⋅([[argyria]])

:* ([[quartisma]])⋅([[nexus comma]])

* [[11-limit]]:

:* ([[3025/3024]])⋅([[reef comma]])

:*([[4375/4374]])⋅([[5632/5625]])

* [[13-limit]]

:* ([[676/675]])⋅([[chalmersia]])

:* ([[1001/1000]])⋅([[phaotic comma]])

:* ([[4096/4095]])⋅([[35035/34992]])

* [[2.3.5.7.11.13.19 subgroup]]

:* ([[1216/1215]])⋅([[1540/1539]])

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

== Temperaments ==

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

[[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.

=== Symbiotian ===

[[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: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 = symbiosma, <br>symbiotic comma
+| 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]]) [[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]]. It is also the difference between a [[septischisma]] and a [[olympia]].
-'''19712/19683''', the '''symbiosma''' or '''symbiotic comma''', 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 apotome [[2187/2048]] and [[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 [[nexuma]]. Tempering out this comma in a linearly independent fashion results in '''symbiotic temperament'''.
+It factors into the following commas:
-== See also ==
+*[[2.3.7.11 subgroup]]:
-* [[Unnoticeable comma]]
+:* ([[olympia]])⋅([[argyria]])
+:* ([[quartisma]])⋅([[nexus comma]])
+* [[11-limit]]:
+:* ([[3025/3024]])⋅([[reef comma]])
+:*([[4375/4374]])⋅([[5632/5625]])
+* [[13-limit]]
+:* ([[676/675]])⋅([[chalmersia]])
+:* ([[1001/1000]])⋅([[phaotic comma]])
+:* ([[4096/4095]])⋅([[35035/34992]])
+* [[2.3.5.7.11.13.19 subgroup]]
+:* ([[1216/1215]])⋅([[1540/1539]])
-[[Category:11-limit]]
+== Temperaments ==
-[[Category:Unnoticeable comma]]
+[[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.
+=== Symbiotian ===
+[[Subgroup]]: 2.3.7.11
+[[Comma list]]: 19712/19683
+{{Mapping|legend=3| 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:Symbiotic]]
+[[Category:Commas named for their regular temperament properties]]