Ditonma: Difference between revisions

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The '''ditonma''' is an interval of about 18.168 cents. It has the monzo [-27 -2 13⟩ and the ratio '''1220703125 / 1207959552'''.  
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]]).


It defines the [[ditonmic family]] of temperaments.
== Temperaments ==
{{stub}}
[[Tempering out]] this comma leads to the [[ditonmic family]] of temperaments, which falls between [[Magic]] and [[Würschmidt]] on the [[Father–3 equivalence continuum]].


[[Category:Commas with unknown 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>.
 
== Notes ==
<references/>
 
[[Category:Commas named for the generator of their temperament]]

Latest revision as of 14:29, 9 August 2025

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 height (log2 nd) 60.355
Weil height (log2 max(n, d)) 60.3701
Wilson height (sopfr(nd)) 125
Comma size small
Open this interval in xen-calc

The ditonma is a small 5-limit comma of about 18.168 cents. It has the 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).

Temperaments

Tempering out this comma leads to the ditonmic family of temperaments, which falls between Magic and Würschmidt on the Father–3 equivalence continuum.

Etymology

This comma was named by Petr Pařízek in 2011 in terms of the corresponding temperament, ditonic[1].

Notes

  1. See Ditonmic family for sources.