Olympia: Difference between revisions

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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) 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.

== 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 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.

== Etymology ==

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

== See also ==

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-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) 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.
 == 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 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.
+== Etymology ==
+The olympia was named by [[Flora Canou]] in 2021, referring to the Olympian level of Sagittal notation.
 == See also ==