Ditonma: Difference between revisions

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Add description of derivation and point to equvalence continuum
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{{Distinguish|Ditonic comma}}
{{Infobox Interval
{{Infobox Interval
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| Name = Ditonma
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The '''ditonma''' is a [[small comma|small]] [[5-limit]] [[comma]] of about 18.168 [[cent]]s. It has the [[monzo]] {{monzo| -27 -2 13 }} and the [[ratio]] '''1220703125 / 1207959552'''. It is the amount by which a stack of 13 classic major thirds ([[5/4]]) exceeds a stack of 3 octaves and 2 perfect fifths ([[3/2]]).
The '''ditonma''' ({{monzo|legend=1| -27 -2 13 }}, [[ratio]]: 1 220 703 125 / 1 207 959 552) is a [[small comma|small]] [[5-limit]] [[comma]] of about 18.2 [[cent]]s. It is the amount by which a stack of 13 classic major thirds ([[5/4]]) exceeds a stack of 3 [[octave]]s and 2 perfect fifths ([[3/2]]).


== Temperaments ==
== Temperaments ==
[[Tempering out]] this comma leads to the [[ditonmic family]] of temperaments, which falls between [[Magic]] and [[Würschmidt]] on the [[Father–3 equivalence continuum]].
[[Tempering out]] this comma leads to the [[ditonic]] temperament, which falls between [[magic]] and [[würschmidt]] on the [[Father–3 equivalence continuum]].
 
See [[Ditonmic family]] for the [[family of temperaments]] where it is tempered out.  


== Etymology ==
== Etymology ==
This comma was named by [[Petr Pařízek]] in 2011 in terms of the corresponding temperament, [[ditonic]]<ref>See [[Ditonmic family]] for sources. </ref>.  
This comma was named by [[Petr Pařízek]] in 2011 in terms of the corresponding temperament, [[ditonic]]<ref>See [[Ditonmic family]] for sources. </ref>. However, ''ditonic comma'' refers to the [[Pythagorean comma]], so the irregular name ''ditonma'' was coined instead.  


== Notes ==
== References ==
<references/>
<references/>


[[Category:Ditonic]]
[[Category:Commas named for the generator of their temperament]]
[[Category:Commas named for the generator of their temperament]]

Latest revision as of 07:32, 21 September 2026

Not to be confused with Ditonic comma.
Interval information
Factorization 2-27 × 3-2 × 513
Monzo [-27 -2 13
Size in cents 18.16828 ¢
Name Ditonma
Color name LLy13-4, lala-theyo negative 4th,
Lala-theyo comma
FJS name [math]\displaystyle{ \text{7d}{-4}^{5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 60.355
Weil norm (log2 max(n, d)) 60.3701
Wilson norm (sopfr(nd)) 125
Comma size small
Open this interval in xen-calc

The ditonma (monzo[-27 -2 13, ratio: 1 220 703 125 / 1 207 959 552) is a small 5-limit comma of about 18.2 cents. It is the amount by which a stack of 13 classic major thirds (5/4) exceeds a stack of 3 octaves and 2 perfect fifths (3/2).

Temperaments

Tempering out this comma leads to the ditonic temperament, which falls between magic and würschmidt on the Father–3 equivalence continuum.

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

Etymology

This comma was named by Petr Pařízek in 2011 in terms of the corresponding temperament, ditonic[1]. However, ditonic comma refers to the Pythagorean comma, so the irregular name ditonma was coined instead.

References

  1. See Ditonmic family for sources.