169/168

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Interval information
Ratio 169/168
Factorization 2-3 × 3-1 × 7-1 × 132
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 (log2 nd) 14.7932
Weil height (log2 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].

Notes