99/80: Difference between revisions

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{{interwiki
| ro = 99/80 (ro)
| de =
| es =
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{{Infobox Interval
{{Infobox Interval
| Name = undecimal submajor third,<br>cake third
| Name = undecimal submajor third,<br>cake third
| Color name = logu 3rd, 1og3
| Color name = logu 3rd, 1og3
}}
}}
'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is [[45/44]] flat of the [[81/64|Pythagorean major third (81/64)]], and also [[100/99]] flat of the [[5/4|classical major third (5/4)]], while being [[8019/8000]] sharp of the [[100/81|grave major third (100/81)]]. The alternate name, ''cake third'', refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]'s). It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second. It is also [[2080/2079]] flat of [[26/21]].


'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''', is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good 7, of which the first truly good example is [[26edo]]. The alternate name, ''cake third'', refers to the fact that tempering out [[45/44]], the cake comma, leads to a temperament that slices 99/80 exactly in half (into two [[11/10]]s).
== Approximation ==
This interval is exactly [[8/7]] flat of the very accurate half-octave of [[99/70]], and so is accurately represented in any even edo with a good [[7/1|7]], such as [[26edo]].  


It is the sum of a [[9/8]] whole tone and an [[11/10]] submajor second, and so is [[8019/8000]] sharp of [[100/81]].
== See also ==
* [[160/99]] – its [[octave complement]]
* [[40/33]] – its [[fifth complement]]
* [[320/297]] – its [[fourth complement]]
* [[Gallery of just intervals]]


[[Category:Third]]
[[Category:Third]]
[[Category:Submajor third]]
[[Category:Submajor third]]

Latest revision as of 23:10, 24 September 2025

Interval information
Ratio 99/80
Factorization 2-4 × 32 × 5-1 × 11
Monzo [-4 2 -1 0 1
Size in cents 368.9142¢
Names undecimal submajor third,
cake third
Color name logu 3rd, 1og3
FJS name [math]\displaystyle{ \text{m3}^{11}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 12.9513
Weil norm (log2 max(n, d)) 13.2587
Wilson norm (sopfr(nd)) 30
Open this interval in xen-calc

99/80, the undecimal submajor third, also known as the cake third, is 45/44 flat of the Pythagorean major third (81/64), and also 100/99 flat of the classical major third (5/4), while being 8019/8000 sharp of the grave major third (100/81). The alternate name, cake third, refers to the fact that tempering out 45/44, the cake comma, leads to a temperament that slices 99/80 exactly in half (into two 11/10's). It arises in just intonation as the sum of a 9/8 whole tone and an 11/10 submajor second. It is also 2080/2079 flat of 26/21.

Approximation

This interval is exactly 8/7 flat of the very accurate half-octave of 99/70, and so is accurately represented in any even edo with a good 7, such as 26edo.

See also