Olympia: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 131072/130977 | | Ratio = 131072/130977 | ||
| Name = olympia, olympic comma | |||
| Name = olympia | |||
| Color name = salururu unison, s1urr1 | | Color name = salururu unison, s1urr1 | ||
| | | Comma = yes | ||
}} | }} | ||
The '''olympia''' ([[monzo]]: {{monzo| 17 -5 0 -2 -1 }}, [[ratio]]: 131072/130977) is an 11-limit ( | The '''olympia''' ([[monzo]]: {{monzo| 17 -5 0 -2 -1 }}, [[ratio]]: 131072/130977), otherwise known as the '''olympic comma''', is an [[unnoticeable comma|unnoticeable]] [[11-limit]] (specifically [[2.3.7.11 subgroup|2.3.7.11-]][[subgroup]]) [[comma]] measuring about 1.26 [[cent]]s. It is the difference between the undecimal quartertone ([[33/32]]) and a stack of two septimal commas (([[64/63]])<sup>2</sup>), which gives rise to its [[S-expression]] as S64<sup>2</sup>⋅S65. Equivalently, it is the difference between [[22/21]] and a stack of three septimal commas. | ||
It factors into two [[13-limit]] [[superparticular ratio]]s: ([[2080/2079]])⋅([[4096/4095]]). These ratios and the olympia itself are the default intervals represented by one, two, and three [[mina]]s in the Olympian level of [[Sagittal notation]], from which it gets its name. | |||
== Temperaments == | == Temperaments == | ||
Tempering out this comma in the full 11-limit results in the rank-4 | [[Tempering out]] this comma in the full 11-limit results in the rank-4 olympic temperament (→ [[Rank-4 temperament #Olympic (131072/130977)]]), or in the 2.3.7.11 subgroup, the rank-3 olympian temperament. In either case, it sets 1–64/63–33/32–22/21–[[1089/1024|(33/32)<sup>2</sup>]] to become equidistant. | ||
Olympic has a very natural 13-limit extension {[[2080/2079]], [[4096/4095]]}. As the comma's order of 11 is one, any 7-limit temperament can be extended to the 11-limit by tempering out this comma, but it works best for temperaments with low complexity and high accuracy in the septimal comma. | |||
Olympian is also very close to undecimal [[gary]], which also tempers out the symbiotic comma and makes all the 2.3.7.11 reachable through the chain of fifths, thus equating [[64/63]] with a [[pythagorean comma]]. | |||
== | == Etymology == | ||
The olympia was named by [[Flora Canou]] in 2021, referring to the Olympian level of Sagittal notation. | |||
[[Category:Olympic]] | [[Category:Olympic]] | ||
[[Category:Commas named after musical traditions]] | |||
Latest revision as of 08:11, 29 September 2026
| Interval information |
olympic comma
reduced subharmonic
The olympia (monzo: [17 -5 0 -2 -1⟩, ratio: 131072/130977), otherwise known as the olympic comma, is an unnoticeable 11-limit (specifically 2.3.7.11-subgroup) comma measuring about 1.26 cents. It is the difference between the undecimal quartertone (33/32) and a stack of two septimal commas ((64/63)2), which gives rise to its S-expression as S642⋅S65. Equivalently, it is the difference between 22/21 and a stack of three septimal commas.
It factors into two 13-limit superparticular ratios: (2080/2079)⋅(4096/4095). These ratios and the olympia itself are the default intervals represented by one, two, and three minas in the Olympian level of Sagittal notation, from which it gets its name.
Temperaments
Tempering out this comma in the full 11-limit results in the rank-4 olympic temperament (→ Rank-4 temperament #Olympic (131072/130977)), or in the 2.3.7.11 subgroup, the rank-3 olympian temperament. In either case, it sets 1–64/63–33/32–22/21–(33/32)2 to become equidistant.
Olympic has a very natural 13-limit extension {2080/2079, 4096/4095}. As the comma's order of 11 is one, any 7-limit temperament can be extended to the 11-limit by tempering out this comma, but it works best for temperaments with low complexity and high accuracy in the septimal comma.
Olympian is also very close to undecimal gary, which also tempers out the symbiotic comma and makes all the 2.3.7.11 reachable through the chain of fifths, thus equating 64/63 with a pythagorean comma.
Etymology
The olympia was named by Flora Canou in 2021, referring to the Olympian level of Sagittal notation.