686/675

From Xenharmonic Wiki
Jump to navigation Jump to search
Interval information
Ratio 686/675
Factorization 2 × 3-3 × 5-2 × 73
Monzo [1 -3 -2 3
Size in cents 27.985289¢
Names sengic comma,
senga
Color name z3gg3, Trizo-agugu comma
FJS name [math]\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]\sqrt{n\cdot d}[/math])
~4.29618 bits
Comma size small
S-expression S13 * S142
open this interval in xen-calc

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.

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[1].

Notes