169/168
Ratio | 169/168 |
Factorization | 2^{-3} × 3^{-1} × 7^{-1} × 13^{2} |
Monzo | [-3 -1 0 -1 0 2⟩ |
Size in cents | 10.274416¢ |
Names | buzurgisma, dhanvantarisma |
Color name | 3oor1, thothoru 1sn, Thothoru comma |
FJS name | [math]\text{d1}^{13,13}_{7}[/math] |
Special properties | square superparticular, reduced |
Tenney height (log_{2} nd) | 14.7932 |
Weil height (log_{2} max(n, d)) | 14.8018 |
Wilson height (sopfr (nd)) | 42 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.85357 bits |
Comma size | small |
S-expression | S13 |
open this interval in xen-calc |
169/168, the buzurgisma or the dhanvantarisma is a superparticular ratio measuring about 10.3 cents. It is the difference between the neutral seconds of 13/12 and 14/13 as well as between the neutral sixths of 21/13 and 13/8.
Temperaments
Tempering out this comma in the 13-limit gives the rank-5 buzurgismic or dhanvantarismic temperament. Tempering it out in the 2.3.7.13 subgroup gives the rank-3 buzurgic or dhanvantaric temperament. In such systems, 13/12 and 14/13 are equated, enabling buzurgismic or dhanvantarismic chords. This is very comparable to tempering out of 121/120, which results in biyatismic, in which 11/10 is equated with 12/11.
Besides tempering, the interval serves as a period in the 13-limit temperament oganesson, where it is equated with 1/118th of the octave.
Etymology
The buzurgisma was named by Margo Schulter in 2012. The name comes from the buzurg aka buzurk genus by Safi al-Din Urmavi, which features a neutral second^{[1]}^{[2]}.
The dhanvantarisma was presumably named by an unknown guest in 2011 since it seems this wiki was the place where it made its first appearance^{[3]}.