Symbiotic comma: Difference between revisions
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'''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 | '''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]]. | ||
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]]). | 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 == | == Temperaments == | ||
[[Tempering out]] this comma in the 11-limit results in the rank-4 '''symbiotic | [[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. | ||
== 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 [[canou family|canou]]. | |||
[[Category:Symbiotic]] | [[Category:Symbiotic]] | ||
[[Category:Commas named for their regular temperament properties]] | [[Category:Commas named for their regular temperament properties]] | ||
Latest revision as of 10:10, 19 May 2026
| Interval information |
symbiosis,
symbiosma
19712/19683, the symbiotic comma, also known as the symbiosis or symbiosma, is an unnoticeable 11-limit (specifically 2.3.7.11-subgroup) comma measuring about 2.55 cents. 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)), 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 limma below 9/7.
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 canou.