686/675: Difference between revisions

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Created page with "{{Infobox Interval | Ratio = 686/675 | Monzo = 1 -3 -2 3 | Cents = 27.98529 | Name = sengic comma, <br>senga comma | Color name = z<sup>3</sup>gg3, ruyoyo 3rd | FJS name = dd3..."
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{{Infobox Interval
{{Infobox Interval
| Ratio = 686/675
| Name = sengic comma, senga
| Monzo = 1 -3 -2 3
| Color name = z<sup>3</sup>gg3, Trizo-agugu comma
| Cents = 27.98529
| Comma = yes
| Name = sengic comma, <br>senga comma
| Color name = z<sup>3</sup>gg3, ruyoyo 3rd
| FJS name = dd3<sup>7, 7, 7</sup><sub>25</sub>
| Sound =  
}}
}}


The interval of '''686/675''', the '''senga comma''' or '''sengic comma''' is a [[7-limit]] small 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.  


[[Category:7-limit]]
== Temperaments ==
[[Category:Interval]]
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.
[[Category:Ratio]]
 
[[Category:Small comma]]
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]]''<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:Commas named by combining multiple temperament names]]
<references />

Latest revision as of 10:33, 3 April 2025

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.

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[1].

Notes