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.