Symbiotic comma

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, symbiosis, symbiosma
Color name	s1oz2, Salozo comma
FJS name	[math]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~1.2595 bits
Comma size	unnoticeable
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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.

Temperaments

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

See also

• Unnoticeable comma