Olympia: Difference between revisions
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The '''olympia''' ([[monzo]]: {{monzo| 17 -5 0 -2 -1 }}, [[ratio]]: 131072/130977), otherwise known as the '''olympic comma''', 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>). Even more interesting is the factorization 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''' , with a very natural 13-limit extension {2080/2079, 4096/4095} (→ [[Rank-4 temperament #Olympic (131072/130977)]]). | [[Tempering out]] this comma in the full 11-limit results in the rank-4 '''olympic temperament''' , with a very natural 13-limit extension {2080/2079, 4096/4095} (→ [[Rank-4 temperament #Olympic (131072/130977)]]). As its order of 11 is one, any 7-limit temperament can be extended to the 11-limit by tempering out this comma. To make practical sense, however, it requires low complexity and high accuracy of the septimal comma, which is less common. | ||
As its order of 11 is one, any 7-limit temperament can be | |||
== Etymology == | == Etymology == | ||
The olympia was named by [[Flora Canou]] in 2021, referring to the Olympian level of Sagittal notation. | 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]] | [[Category:Commas named after musical traditions]] | ||
Revision as of 19:22, 5 February 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). Even more interesting is the factorization 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 , with a very natural 13-limit extension {2080/2079, 4096/4095} (→ Rank-4 temperament #Olympic (131072/130977)). As its order of 11 is one, any 7-limit temperament can be extended to the 11-limit by tempering out this comma. To make practical sense, however, it requires low complexity and high accuracy of the septimal comma, which is less common.
Etymology
The olympia was named by Flora Canou in 2021, referring to the Olympian level of Sagittal notation.