Mutt comma: Difference between revisions

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The '''mutt comma''' ({{monzo| -44 -3 21 }} = '''476837158203125/474989023199232''') of about 6.7 cents is the amount by which three [[25/24]] (chromatic semitone) exceed five [[128/125]] (diesis); in other words (25/24)<sup>3</sup>/(128/125)<sup>5</sup>. Tempering it out leads to temperaments of the [[mutt family]].
The '''mutt comma''' ({{monzo|legend=1| -44 -3 21 }}, [[ratio]]: 476837158203125/474989023199232) is a [[small comma|small]] [[5-limit]] [[comma]] of about 6.7 [[cent]]s. It is the amount by which three [[25/24|classical chromas]] exceed five [[128/125|dieses]]; in other words (25/24)<sup>3</sup>/(128/125)<sup>5</sup>.  


== See also ==
== Temperaments ==
* [[Mutt temperament]]
[[Tempering out]] this comma leads to the 5-limit version of the [[mutt]] temperament.
* [[Small comma]]
 
== Etymology ==
This comma was named by [[Gene Ward Smith]] in 2004 in terms of the corresponding temperament, mutt, for "<u>M</u>IDI <u>u</u>ni<u>t</u> <u>t</u>emperament".


[[Category:Mutt]]
[[Category:Mutt]]
[[Category:Commas with unknown etymology]]
[[Category:Commas named for their regular temperament properties]]

Revision as of 17:31, 12 November 2024

Interval information
Ratio 476837158203125/474989023199232
Factorization 2-44 × 3-3 × 521
Monzo [-44 -3 21
Size in cents 6.722989¢
Name mutt comma
Color name L3y21-6, trila-septriyo negative 6th
FJS name [math]\displaystyle{ \text{11d}{-6}^{5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney height (log2 nd) 97.5154
Weil height (log2 max(n, d)) 97.521
Wilson height (sopfr(nd)) 202
Comma size small
Open this interval in xen-calc

The mutt comma (monzo[-44 -3 21, ratio: 476837158203125/474989023199232) is a small 5-limit comma of about 6.7 cents. It is the amount by which three classical chromas exceed five dieses; in other words (25/24)3/(128/125)5.

Temperaments

Tempering out this comma leads to the 5-limit version of the mutt temperament.

Etymology

This comma was named by Gene Ward Smith in 2004 in terms of the corresponding temperament, mutt, for "MIDI unit temperament".