81/76: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Name = dog comma
| Name = Boethius' chromatic semitone
| Color name = 19u1, inu 1sn, <br>Inu comma
| Color name = 19u1, inu 1sn, <br>Inu comma
}}
}}
'''81/76''', the '''dog comma''' is a [[19-limit]] interval, 110.3 [[cent]]s in size. It is the difference between [[19/16]] (otonal minor third) and [[81/64]] (Pythagorean major third) and thus is [[81/80]] larger than [[20/19]].
'''81/76''', '''Boethius' chromatic semitone''', is a [[19-limit]] interval of about 110.3 [[cent]]s in size. It differs from [[2187/2048]], the Pythagorean apotome, by [[513/512]], the undevicesimal schisma or Boethius' comma, hence the name. It also differs from [[16/15]] by [[1216/1215]], and is the difference between [[19/16]] (otonal minor third) and [[81/64]] (Pythagorean major third) and thus is [[81/80]] larger than [[20/19]].  
 
== Etymology ==
The word ''dog'' for this interval was introduced by [[User:Xenllium|Xenllium]] in 2023. It was translated from Japanese word <span style="font-family:san-serif" lang="ja">犬</span> (<span style="font-family:san-serif" lang="ja">いぬ</span>, inu), a play of its [[Color notation|color name]], ''inu'' (as the identical pronunciation).


== Temperaments ==
== Temperaments ==
Tempering this interval leads to a 2.3.19 version of [[mavila]] where four mavila fifths yields [[19/16]], so is potentially of relevance in [[16edo]] if one wants to interpret its fifth as a 27{{cent}} flat ~3/2.
This interval has been proposed to be used as a [[comma]] to be [[tempering out|tempered out]], though the musical utility of it is unknown yet. The name ''dog comma'' was suggested by [[Xenllium]] in 2023, translated from Japanese word 犬 (いぬ, inu), a play of its [[Kite's color notation|color name]], ''inu'' (as the identical pronunciation).


== See also ==
== See also ==
* [[Large comma]]
* [[Large comma]]
* [[No-fives subgroup temperaments #Dog|Dog temperament]]


[[Category:Semitone]]
[[Category:Semitone]]
[[Category:Commas named after their color name]]

Latest revision as of 10:24, 16 June 2026

Interval information
Ratio 81/76
Subgroup monzo 2.3.19 [-2 4 -1
Size in cents 110.307¢
Name Boethius' chromatic semitone
Color name 19u1, inu 1sn,
Inu comma
FJS name [math]\displaystyle{ \text{A1}_{19} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.5878
Weil norm (log2 max(n, d)) 12.6797
Wilson norm (sopfr(nd)) 35
Open this interval in xen-calc

81/76, Boethius' chromatic semitone, is a 19-limit interval of about 110.3 cents in size. It differs from 2187/2048, the Pythagorean apotome, by 513/512, the undevicesimal schisma or Boethius' comma, hence the name. It also differs from 16/15 by 1216/1215, and is the difference between 19/16 (otonal minor third) and 81/64 (Pythagorean major third) and thus is 81/80 larger than 20/19.

Temperaments

This interval has been proposed to be used as a comma to be tempered out, though the musical utility of it is unknown yet. The name dog comma was suggested by Xenllium in 2023, translated from Japanese word 犬 (いぬ, inu), a play of its color name, inu (as the identical pronunciation).

See also