Olympia: Difference between revisions

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{{Infobox Interval

| Ratio = 131072/130977

| Name = olympia

| Name = olympia, olympic comma

| Color name = salururu unison, s1urr1

| Comma = yes

}}

The '''olympia''' ([[monzo]]: {{monzo| 17 -5 0 -2 -1 }}, [[ratio]]: 131072/130977) is an 11-limit (~~also~~ 2.3.7.11 subgroup) [[~~unnoticeable~~ 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]]). ~~Even more interesting~~ is the ~~possible factorization~~ into two [[13-limit]] [[superparticular]] ~~ratios~~: [[2080/2079]] × [[4096/4095]]. ~~In fact,~~ the olympia is the default ~~interval~~ represented by three [[mina]]s in the Olympian level of [[Sagittal notation]], from which it gets its name.

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]])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 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 ==

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 (→ [[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)2]] to become equidistant.

As ~~its~~ order of 11 is one, any 7-limit temperament can be ~~immediately~~ extended to the 11-limit ~~in theory~~ by tempering out this comma~~. To make practical sense, however~~, it ~~requires~~ low complexity and high accuracy ~~of 64/63, which is less common~~.

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.

== ~~See also~~ ==

== Etymology ==

* [[~~Unnoticeable comma~~]]

The olympia was named by [[Flora Canou]] in 2021, referring to the Olympian level of Sagittal notation.

[[Category:Olympic]]

[[Category:Commas named after musical traditions]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
 | Ratio = 131072/130977
-| Name = olympia
+| Name = olympia, olympic comma
 | Color name = salururu unison, s1urr1
 | Comma = yes
 }}
-The '''olympia''' ([[monzo]]: {{monzo| 17 -5 0 -2 -1 }}, [[ratio]]: 131072/130977) is an 11-limit (also 2.3.7.11 subgroup) [[unnoticeable 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]]). Even more interesting is the possible factorization into two [[13-limit]] [[superparticular]] ratios: [[2080/2079]] × [[4096/4095]]. In fact, the olympia is the default interval represented by three [[mina]]s in the Olympian level of [[Sagittal notation]], from which it gets its name.
+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 ==
-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 (→ [[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.
-As its order of 11 is one, any 7-limit temperament can be immediately extended to the 11-limit in theory by tempering out this comma. To make practical sense, however, it requires low complexity and high accuracy of 64/63, which is less common.
+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.
-== See also ==
+== Etymology ==
-* [[Unnoticeable comma]]
+The olympia was named by [[Flora Canou]] in 2021, referring to the Olympian level of Sagittal notation.
 [[Category:Olympic]]
+[[Category:Commas named after musical traditions]]