Olympia - Revision history

FloraC: 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

2026-05-12T18:59:51Z

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

← Older revision		Revision as of 18:59, 12 May 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	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 is the difference between the undecimal quartertone ([[33/32]]) and a stack of {{nowrap\| two septimal commas (([[64/63]])<sup>2</sup>) }}, which according to its S-expression comma family categorisation as a lopsided comma (S64<sup>2</sup>⋅S65) is trivial information. Interestingly/nontrivially, tempering it out causes {{nowrap\| 1/1 - 64/63 - 33/32 - 22/21 - [[1089/1024]] }} to become equidistant, thereby splitting the [[1089/1024\|parapotome]] into four equal parts, as {{nowrap\| ([[22/21]])/([[33/32]]) {{=}} [[64/63]] }} and {{nowrap\| 1089/1024 * S64<sup>2</sup> * S65 {{=}} 22/21 * 64/63 }}. 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.		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 ==

Godtone at 18:24, 12 May 2026

2026-05-12T18:24:34Z

← Older revision		Revision as of 18:24, 12 May 2026
Line 5:		Line 5:
	\| Comma = yes		\| Comma = yes
	}}		}}
	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.		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 {{nowrap\| two septimal commas (([[64/63]])<sup>2</sup>) }}, which according to its S-expression comma family categorisation as a lopsided comma (S64<sup>2</sup>⋅S65) is trivial information. Interestingly/nontrivially, tempering it out causes {{nowrap\| 1/1 - 64/63 - 33/32 - 22/21 - [[1089/1024]] }} to become equidistant, thereby splitting the [[1089/1024\|parapotome]] into four equal parts, as {{nowrap\| ([[22/21]])/([[33/32]]) {{=}} [[64/63]] }} and {{nowrap\| 1089/1024 * S64<sup>2</sup> * S65 {{=}} 22/21 * 64/63 }}. 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 ==

FloraC: + rank-3 olympian

2026-03-20T09:40:57Z

+ rank-3 olympian

← Older revision		Revision as of 09:40, 20 March 2026
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	== 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)]]). 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~~.		[[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.

	== Etymology ==		== Etymology ==

FloraC: Cleanup

2026-02-05T19:22:51Z

Cleanup

← Older revision		Revision as of 19:22, 5 February 2026
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	\| Comma = yes		\| Comma = yes
	}}		}}
	The '''olympia''' ([[monzo]]: {{monzo\| 17 -5 0 -2 -1 }}, [[ratio]]: 131072/130977), otherwise known as the '''olympic comma''', 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>). 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 ~~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 ==		== 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.

	~~== See also ==~~
	* [[Unnoticeable comma]]

	[[Category:Olympic]]		[[Category:Olympic]]
	[[Category:Commas named after musical traditions]]		[[Category:Commas named after musical traditions]]

BudjarnLambeth at 23:50, 3 November 2024

2024-11-03T23:50:13Z

← Older revision		Revision as of 23:50, 3 November 2024
Line 19:		Line 19:

	[[Category:Olympic]]		[[Category:Olympic]]
			[[Category:Commas named after musical traditions]]

FloraC: +alt name

2024-03-31T08:17:20Z

+alt name

← Older revision		Revision as of 08:17, 31 March 2024
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	{{Infobox Interval		{{Infobox Interval
	\| Ratio = 131072/130977		\| Ratio = 131072/130977
	\| Name = olympia		\| Name = olympia, olympic comma
	\| Color name = salururu unison, s1urr1		\| Color name = salururu unison, s1urr1
	\| Comma = yes		\| 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 [[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 ==		== Temperaments ==

FloraC: +naming info

2023-04-13T04:52:41Z

+naming info

← Older revision		Revision as of 04:52, 13 April 2023
Line 5:		Line 5:
	\| Comma = yes		\| 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) 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 ==		== 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.		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 ==		== See also ==

Plumtree: Normalising usage of Infobox Interval

2022-10-25T17:53:27Z

Normalising usage of Infobox Interval

← Older revision		Revision as of 17:53, 25 October 2022
Line 1:		Line 1:
	{{Infobox Interval		{{Infobox Interval
	~~\| Icon =~~
	\| Ratio = 131072/130977		\| Ratio = 131072/130977
	~~\| Monzo = 17 -5 0 -2 -1~~
	~~\| Cents = 1.25524~~
	\| Name = olympia		\| Name = olympia
	\| Color name = salururu unison, s1urr1		\| Color name = salururu unison, s1urr1
	\| ~~FJS name =~~		\| Comma = yes
	~~\| Sound~~ =
	}}		}}
	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.
Line 19:		Line 15:
	* [[Unnoticeable comma]]		* [[Unnoticeable comma]]

	~~[[Category:11-limit]]~~
	~~[[Category:Unnoticeable commas]]~~
	[[Category:Olympic]]		[[Category:Olympic]]

Fredg999 category edits: Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

2022-03-20T22:01:55Z

Moving from Category:Unnoticeable comma to Category:Unnoticeable commas using Cat-a-lot

← Older revision		Revision as of 22:01, 20 March 2022
Line 20:		Line 20:

	[[Category:11-limit]]		[[Category:11-limit]]
	[[Category:Unnoticeable ~~comma~~]]		[[Category:Unnoticeable commas]]
	[[Category:Olympic]]		[[Category:Olympic]]

FloraC: +an important observation

2021-11-05T12:51:16Z

+an important observation

← Older revision		Revision as of 12:51, 5 November 2021
Line 13:		Line 13:
	== 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 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.

	== See also ==		== See also ==