Olympia: Difference between revisions
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S-expressions are encodings of interval relations. They don't make the interval relations trivial! Also don't discuss temps outside the Temperaments section! 1089/1024 is (33/32)^2 so it's always split in two, and it's split in four since 33/32 is split in two |
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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. | 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 | 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 olympic temperament (→ [[Rank-4 temperament #Olympic (131072/130977)]]), or in the 2.3.7.11 subgroup, the rank-3 olympian temperament. 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. | [[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. | |||
== Etymology == | == Etymology == | ||
Latest revision as of 18:59, 12 May 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.
Etymology
The olympia was named by Flora Canou in 2021, referring to the Olympian level of Sagittal notation.