Dimcomp comma: Difference between revisions

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The '''dimcomp comma''' is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 7.4 [[cent]]s. It is the amount by which a stack of four quasi-tempered minor thirds ([[25/21]]) exceeds an octave.  
The '''dimcomp comma''' is a [[small comma|small]] [[7-limit]] [[comma]] measuring about 7.4 [[cent]]s. It is the amount by which a stack of four quasi-tempered minor thirds (([[25/21]])<sup>4</sup>) exceeds an [[2/1|octave]].  


== Temperaments ==
== Temperaments ==
Tempering out this comma in the 7-limit leads to the [[dimcomp]] temperament, with the effect of splitting the octave into four equal parts, and edos that are not multiples of 4 cannot be tempering it out. Rank-2 temperaments tempering it out include [[diminished (temperament)|diminished]], [[compton]], [[bidia]], [[quadritikleismic]], [[octoid]], etc.  
[[Tempering out]] this comma in the 7-limit leads to the [[dimcomp]] temperament, with the effect of splitting the octave into four equal parts, and edos that are not multiples of 4 cannot be tempering it out. Rank-2 temperaments tempering it out include [[diminished (temperament)|diminished]], [[compton]], [[bidia]], [[quadritikleismic]], [[octoid]], etc.  


See [[Dimcomp family]] for a number of rank-3 temperaments where it is tempered out.  
See [[Dimcomp family]] for a number of rank-3 temperaments where it is tempered out.  

Revision as of 08:40, 12 February 2026

Interval information
Ratio 390625/388962
Factorization 2-1 × 3-4 × 58 × 7-4
Monzo [-1 -4 8 -4
Size in cents 7.386082¢
Name dimcomp comma
Color name quadruyoyo comma
FJS name [math]\displaystyle{ \text{5d}{-4}^{5,5,5,5,5,5,5,5}_{7,7,7,7} }[/math]
Special properties reduced
Tenney norm (log2 nd) 37.1447
Weil norm (log2 max(n, d)) 37.1508
Wilson norm (sopfr(nd)) 82
Comma size small
Open this interval in xen-calc

The dimcomp comma is a small 7-limit comma measuring about 7.4 cents. It is the amount by which a stack of four quasi-tempered minor thirds ((25/21)4) exceeds an octave.

Temperaments

Tempering out this comma in the 7-limit leads to the dimcomp temperament, with the effect of splitting the octave into four equal parts, and edos that are not multiples of 4 cannot be tempering it out. Rank-2 temperaments tempering it out include diminished, compton, bidia, quadritikleismic, octoid, etc.

See Dimcomp family for a number of rank-3 temperaments where it is tempered out.