From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 8192/8019
Factorization 213 × 3-6 × 11-1
Monzo [13 -6 0 0 -1
Size in cents 36.952052¢
Name Alpharabian inframinor second
Color name s1u2, salu 2nd
FJS name [math]\text{m2}_{11}[/math]
Special properties reduced
Tenney height (log2 nd) 25.9692
Weil height (log2 max(n, d)) 26
Wilson height (sopfr (nd)) 55
Harmonic entropy
(Shannon, [math]\sqrt{nd}[/math])
~4.51548 bits
open this interval in xen-calc

8192/8019, the Alpharabian inframinor second, is the basic inframinor second in the 2.3.11 subgroup. It differs from 4096/3993, the Alpharabian paralimma, by 243/242, it differs from 45/44, the undecimal 1/5-tone, by the schisma, and, it also differs from 64/63, the Archytas comma, by 896/891. As suggested by its name, it is reached by subtracting a 33/32 quartertone from 256/243. Conspicuously, this interval is almost exactly one third of a 16/15 diatonic semitone- a stack of three falling short of it by the triagnoshenisma.

When treated as a comma to be tempered, and thus tempered out, for instance, in undecimal superpyth temperament, the result is the obliteration of any distinction between the diatonic intervals of Pythagorean tuning and nearby paradiatonic intervals- most notably, it obliterates the distinction between 16/11 and 729/512, and this, combined with the fact that this interval is an inframinor second when not tempered, leads to the comma name dimifondisma, with "dimi" from "diminished", "f" from "fifth" and "ond" from "second".

See also