686/675

686/675, the senga or sengic comma, is a small 7-limit comma measuring about 28.0 cents. It pops up as the difference between 7/6 and a stack of two 15/14's, or the difference between 5/4 and a stack of three 15/14's. Besides, it is the difference between the septimal minor second, 28/27, and the jubilisma, 50/49.

Interval information

Ratio	686/675
Factorization	2 × 3-3 × 5-2 × 73
Monzo	[1 -3 -2 3⟩
Size in cents	27.98529¢
Names	sengic comma, senga
Color name	z3gg3, Trizo-agugu comma
FJS name	[math]\displaystyle{ \text{dd3}^{7,7,7}_{5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	18.8208
Weil norm (log2 max(n, d))	18.8441
Wilson norm (sopfr(nd))	42
Comma size	small
S-expression	S13⋅S142
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It factors into simpler commas as (126/125)⋅(245/243), the stack of the two simplest commas to define the 7-limit sensi temperament. In the 2.3.5.7.13 subgroup, it factors into (91/90)⋅(196/195), which equals (169/168)⋅(196/195)² in turn, making it a lopsided comma with S-expression S13⋅S14².

Temperaments

Tempering out this comma in the 7-limit leads to the rank-3 sengic temperament. Rank-2 temperaments tempering out this comma include sensi, negri and liese. Tempering out this comma in the 3/2.5/4.7/4 fractional subgroup gives the ambulatory temperament.

See Sengic family for the family of rank-3 temperaments where it is tempered out. See Sengic temperaments for the collection of rank-2 temperaments where it is tempered out.

Etymology

The name senga was given by Gene Ward Smith in 2005. It is a contraction of sensi and gawel, although gawel was later renamed to liese.