Sensipent comma: Difference between revisions

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78732/78125 = |2 9 -7>, the sensipent comma or medium semicomma, is an interval of 13.399 cents which is the amount by which the difference between seven minor thirds and two fourths exceeds an octave, in other words (6/5)^7/(4/3)^2/2. Tempering it out leads to [[Sensipent_family#Sensipent|sensipent temperament]].
{{Infobox Interval
| Ratio = 78732/78125
| Name = sensipent comma, medium semicomma
| Color name = g<sup>7</sup>2, Sepgu comma
| Comma = yes
}}
The '''sensipent comma''' ([[ratio]]: 78732/78125, {{monzo|legend=1| 2 9 -7 }}), also known as the '''medium semicomma''', is [[small comma|small]] [[5-limit]] [[comma]] of about 13.4 [[cent]]s. It is the amount by which a stack of seven [[6/5|classical minor thirds]] exceeds two [[4/3|perfect fourths]] and an [[octave]], in other words ([[6/5]])<sup>7</sup>/(([[4/3]])<sup>2</sup>×[[2/1|2]]). Equivalently, it is also equal to ([[6/5]])<sup>5</sup>/(([[10/9]])<sup>2</sup>×[[2/1|2]]). It is also the difference between [[5/4]] and a stack of three [[27/25]] large limmas.  
 
== Temperaments ==
[[Tempering out]] this comma in the 5-limit leads to the [[sensipent]] temperament.
 
See [[Sensipent family]] for the [[family of temperaments]] where it is tempered out.  
 
== See also ==
* [[Syntonic–kleismic equivalence continuum]]
 
[[Category:Sensipent]]
[[Category:Commas named for the generator of their temperament]]

Latest revision as of 16:36, 1 October 2026

Interval information
Ratio 78732/78125
Factorization 22 × 39 × 5-7
Monzo [2 9 -7⟩
Size in cents 13.39901 ¢
Names sensipent comma,
medium semicomma
Color name g72, Sepgu comma
FJS name [math]\displaystyle{ \text{dd2}_{5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 32.5182
Weil norm (log2 max(n, d)) 32.5293
Wilson norm (sopfr(nd)) 66
Comma size small
Open this interval in xen-calc

The sensipent comma (ratio: 78732/78125, monzo: [2 9 -7⟩), also known as the medium semicomma, is small 5-limit comma of about 13.4 cents. It is the amount by which a stack of seven classical minor thirds exceeds two perfect fourths and an octave, in other words (6/5)7/((4/3)2×2). Equivalently, it is also equal to (6/5)5/((10/9)2×2). It is also the difference between 5/4 and a stack of three 27/25 large limmas.

Temperaments

Tempering out this comma in the 5-limit leads to the sensipent temperament.

See Sensipent family for the family of temperaments where it is tempered out.

See also

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