81/76: Difference between revisions

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CompactStar (talk | contribs)
While dog temperament is an exotemperament, we have names like "father comma" for 16/15 so I think this is acceptable.
Godtone (talk | contribs)
mNo edit summary
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| Color name = 19u1, inu 1sn, <br>Inu comma
| Color name = 19u1, inu 1sn, <br>Inu comma
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'''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).
'''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]].


== Etymology ==
== 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).
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 ==
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 ~3/2.


== See also ==
== See also ==

Revision as of 23:40, 23 August 2024

Interval information
Ratio 81/76
Subgroup monzo 2.3.19 [-2 4 -1
Size in cents 110.307¢
Name dog comma
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, the dog comma is a 19-limit interval, 110.3 cents 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.

Etymology

The word dog for this interval was introduced by Xenllium in 2023. It was translated from Japanese word (いぬ, inu), a play of its color name, inu (as the identical pronunciation).

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 ~3/2.

See also