Symbiotic comma
Ratio | 19712/19683 |
Factorization | 2^{8} × 3^{-9} × 7 × 11 |
Monzo | [8 -9 0 1 1⟩ |
Size in cents | 2.548841¢ |
Names | symbiotic comma, symbiosis, symbiosma |
FJS name | [math]\text{d2}^{7,11}[/math] |
Special properties | reduced |
Tenney height (log_{2} 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.
Temperaments
Tempering out this comma in the 11-limit results in the rank-4 symbiotic temperament (→ Rank-4 temperament #Symbiotic (19712/19683)).