Symbiotic comma: Difference between revisions

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


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

Revision as of 23:18, 1 September 2022

Interval information
Ratio 19712/19683
Factorization 28 × 3-9 × 7 × 11
Monzo [8 -9 0 1 1
Size in cents 2.548841¢
Names symbiosis comma,
symbiotic comma,
symbiosma
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 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 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 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.

Temperaments

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

See also