686/675

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 height (log2 nd)	18.8208
Weil height (log2 max(n, d))	18.8441
Wilson height (sopfr(nd))	42
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~4.38834 bits
Comma size	small
S-expression	S13 * S142
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The interval of 686/675, the senga or sengic comma is a small 7-limit comma. It pops up as the difference between a stack of three 7/6's and a stack of two 5/4's.

Temperaments

Tempering out this comma in the 7-limit leads to the rank-3 sengic temperament. See sengic family for the rank-3 temperament family where it is tempered out.

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 ambulatory temperament.

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.