169/168

Interval information

Ratio	169/168
Factorization	2-3 × 3-1 × 7-1 × 132
Monzo	[-3 -1 0 -1 0 2⟩
Size in cents	10.27442¢
Names	buzurgisma, dhanvantarisma
Color name	3oor1, thothoru 1sn, Thothoru comma
FJS name	[math]\displaystyle{ \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
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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 buzurg or dhanvantari 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.

169/168 is tempered out in the 1-16/13-4/3-64/39 chord, with the steps 16/13-13/12-16/13-39/32, which is symmetrical (it is the same when inverted). It intertwines two 4/3's between the 1st and 3rd, and 2nd and 4th notes. Tempering out 169/168 means that 14/13 can appear in this chord as well as 13/12.

Etymology

The buzurgisma was presumably named by Gene Ward Smith in 2012 since it seems this wiki was the place where it made its first appearance. The name seems to come from the buzurk genus by Safi al-Din Urmavi, which features a neutral second.

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.