Symbiotic comma: Difference between revisions

19712/19683, the symbiotic comma, also known as the symbiosis or symbiosma, is an unnoticeable 11-limit comma measuring about 2.55 cents. It gets its names 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 canou. It is the difference between an apotome (2187/2048) and an 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 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)). This temperament 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 limma below 9/7.

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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 '''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]]. Tempering out this comma in a linearly independent fashion results in '''symbiotic temperament'''.
+'''19712/19683''', the '''symbiotic comma''', also known as the '''symbiosis''' or '''symbiosma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] [[comma]] measuring about 2.55 [[cent]]s. It gets its names 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 [[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 quartertone of [[33/32]] stacked on top of a third-tone of [[28/27]].
-== See also ==
+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]]).
-* [[Unnoticeable comma]]
+== Temperaments ==
+[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic temperament''' (→ [[Rank-4 temperament #Symbiotic (19712/19683)]]). This temperament 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.
-[[Category:11-limit]]
-[[Category:Unnoticeable commas]]
 [[Category:Symbiotic]]
+[[Category:Commas named for their regular temperament properties]]

Symbiotic comma: Difference between revisions

Latest revision as of 08:18, 20 February 2025

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