Symbiotic comma: Difference between revisions

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merged the term "apotome" into the link to 2187/2048
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improved apotome link: I find it (for a wiki) crucial to have the highest possible coherence between link text and target. The problem with B links is that people tend to copy it verbatim and warp their text to match it. The best link reads just A
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'''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 [[2187/2048|apotome]] 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'''.
'''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 [[2187/2048|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'''.


== See also ==
== See also ==

Revision as of 10:11, 27 November 2020

Interval information
Ratio 19712/19683
Factorization 28 × 3-9 × 7 × 11
Monzo [8 -9 0 1 1
Size in cents 2.548841¢
Names symbiosma,
symbiotic comma
FJS name [math]\displaystyle{ \text{d2}^{7,11} }[/math]
Special properties reduced
Tenney height (log2 nd) 28.5314
Weil height (log2 max(n, d)) 28.5336
Wilson height (sopfr(nd)) 61
Open this interval in xen-calc

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 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 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.

See also