Symbiotic comma

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Interval information
Ratio 19712/19683
Factorization 28 × 3-9 × 7 × 11
Monzo [8 -9 0 1 1
Size in cents 2.548841¢
Names symbiotic comma,
FJS name [math]\text{d2}^{7,11}[/math]
Special properties reduced
Tenney height (log2 n⋅d) 28.5314
Weil height (max(n, d)) 19712
Benedetti height (n⋅d) 387991296
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.42656 bits
Comma size unnoticeable
open this interval in xen-calc

19712/19683, the symbiotic comma, also known as the symbiosis 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. It factors into (4375/4374)(5632/5625), and moreover, into the quartisma and the nexus comma.


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

See also