99/80: Difference between revisions
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This interval relates back to the Pythagorean major third via the cake comma |
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'''99/80''', the '''undecimal submajor third''', also known as the '''cake third''' | '''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 | It arises in [[just intonation]] as the sum of a [[9/8]] whole tone and an [[11/10]] submajor second. | ||
== 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]]. | |||
== See also == | == See also == | ||
* [[160/99]] – its [[octave complement]] | * [[160/99]] – its [[octave complement]] | ||
* [[40/33]] – its [[fifth complement]] | * [[40/33]] – its [[fifth complement]] | ||
Revision as of 16:47, 15 December 2024
| Interval information |
cake third
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 11/10s).
It arises in just intonation as the sum of a 9/8 whole tone and an 11/10 submajor second.
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
- 160/99 – its octave complement
- 40/33 – its fifth complement
- 320/297 – its fourth complement
- Gallery of just intervals