169/168
| 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]) |
~2.82268 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].