686/675: Difference between revisions

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Senga = sengic comma
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The interval of '''686/675''', the '''senga''' or '''sengic comma''' is a [[Small comma|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. It is tempered out in temperaments of the [[sengic family]].
The interval of '''686/675''', the '''senga''' or '''sengic comma''' is a [[small comma|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]]''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12900.html Yahoo! Tuning Group | ''Seven limit comma names from pairs of temperament names'']</ref>.  
 
== Notes ==


[[Category:Sengic]]
[[Category:Sengic]]

Revision as of 10:54, 2 January 2024

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
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