Quintile comma: Difference between revisions

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m FloraC moved page Pental comma to Quintile comma: Implement the community-anticipated rename
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The '''quintile comma''' ({{monzo|legend=1| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000) is a [[small comma|small]] [[5-limit]] [[comma]] of about 17.306 [[cent]]s.  
The '''quintile comma''' ({{monzo|legend=1| -28 25 -5 }}, [[ratio]]: 847 288 609 443 / 838 860 800 000) is a [[small comma|small]] [[5-limit]] [[comma]] of about 17.306 [[cent]]s. It is the amount by which a stack of five grave fourths of [[320/243]] falls short of two [[octave]]s, or the amount by which a stack of five acute fifths of [[243/160]] exceeds three octaves. It is also the amount by which a stack of five [[81/80|syntonic commas]] exceed a [[256/243|Pythagorean limma]].  


== Temperaments ==
Tempering out this comma leads to the [[quintile family]] of temperaments.
Tempering out this comma leads to the [[quintile family]] of temperaments.


{{todo|expand}}
[[Category:Commas named for their periods per equave]]
[[Category:Commas named for their periods per equave]]

Revision as of 12:58, 19 February 2025

Interval information
Factorization 2-28 × 325 × 5-5
Monzo [-28 25 -5
Size in cents 17.30645¢
Name Quintile comma
FJS name [math]\displaystyle{ \text{m}{-2}_{5,5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 79.2337
Weil norm (log2 max(n, d)) 79.2481
Wilson norm (sopfr(nd)) 156
Comma size small
Open this interval in xen-calc

The quintile comma (monzo[-28 25 -5, ratio: 847 288 609 443 / 838 860 800 000) is a small 5-limit comma of about 17.306 cents. It is the amount by which a stack of five grave fourths of 320/243 falls short of two octaves, or the amount by which a stack of five acute fifths of 243/160 exceeds three octaves. It is also the amount by which a stack of five syntonic commas exceed a Pythagorean limma.

Temperaments

Tempering out this comma leads to the quintile family of temperaments.