159th-octave temperaments - Revision history

ArrowHead294 at 04:00, 14 February 2025

2025-02-14T04:00:03Z

← Older revision		Revision as of 04:00, 14 February 2025
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	{{~~Fractional~~-octave ~~navigation~~\|159}}		{{Infobox fractional-octave\|159}}
	[[159edo]] is a notable [[17-limit]] system. It first contains [[53edo]], tempering out Mercator's comma.		[[159edo]] is a notable [[17-limit]] system. It first contains [[53edo]], tempering out Mercator's comma.

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	This page collects temperaments that are of theoretical interest specific to 159edo, beyond just [[53edo]].		This page collects temperaments that are of theoretical interest specific to 159edo, beyond just [[53edo]].

	== Auric ==		== Auric ==
	''Auric'', named after [[Aura]], is defined by setting the 2.3.5.11 mapping to that of 159edo and the generator for the prime 7 being independent.		''Auric'', named after [[Aura]], is defined by setting the 2.3.5.11 mapping to that of 159edo and the generator for the prime 7 being independent.
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	=== 11-limit ===		=== 11-limit ===

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	=== 13-limit ===		=== 13-limit ===

	[[Subgroup]]: 2.3.5.7.11		[[Subgroup]]: 2.3.5.7.11

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	=== 17-limit ===		=== 17-limit ===

	[[Subgroup]]: 2.3.5.7.11.13.17		[[Subgroup]]: 2.3.5.7.11.13.17

BudjarnLambeth: navbox

2024-12-05T07:44:19Z

navbox

← Older revision		Revision as of 07:44, 5 December 2024
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	[[Support]]ing [[ET]]s: {{EDOs\|159, 795g, 954}}		[[Support]]ing [[ET]]s: {{EDOs\|159, 795g, 954}}

			{{Navbox fractional-octave}}

Eliora: reasoning for temp placement

2024-01-05T02:02:08Z

reasoning for temp placement

← Older revision		Revision as of 02:02, 5 January 2024
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	159edo has attracted a lot of attention from prominent microtonalists like [[Ozan Yarman]], [[Dawson Berry]] (also known as [[Aura]]), [[Gene Ward Smith]]. In addition, some of its multiples have large consistency limits as well, and this naturally commends itself to 159th-octave temperaments.		159edo has attracted a lot of attention from prominent microtonalists like [[Ozan Yarman]], [[Dawson Berry]] (also known as [[Aura]]), [[Gene Ward Smith]]. In addition, some of its multiples have large consistency limits as well, and this naturally commends itself to 159th-octave temperaments.

			This page collects temperaments that are of theoretical interest specific to 159edo, beyond just [[53edo]].
	== Auric ==		== Auric ==
	''Auric'', named after [[Aura]], is defined by setting the 2.3.5.11 mapping to that of 159edo and the generator for the prime 7 being independent.		''Auric'', named after [[Aura]], is defined by setting the 2.3.5.11 mapping to that of 159edo and the generator for the prime 7 being independent.

Eliora: /* Aemilic */ full

2024-01-05T01:52:34Z

Aemilic: full

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 == Aemilic ==
 ''Aemilic'' is described as the 159 & 954 temperament in the 17-limit and is named after the minor planet [[wikipedia:159 Aemilia|159 Aemilia]].
 [[Subgroup]]: 2.3.5.7.11.13.17

Eliora: /* Aemic (rank-3) */ facepalm

2023-12-30T01:43:04Z

Aemic (rank-3): facepalm

← Older revision		Revision as of 01:43, 30 December 2023
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	: mapping generators: ~243/242 = 1\159, ~5, ~7		: mapping generators: ~243/242 = 1\159, ~5, ~7

	[[Support]]ing [[ET]]s: {{EDOs\|159, ~~398~~, 477, 636, 795, 954, 1113, 1272, 1431, 1590}}		[[Support]]ing [[ET]]s: {{EDOs\|159, 318, 477, 636, 795, 954, 1113, 1272, 1431, 1590}}

	== Aemilic ==		== Aemilic ==

Eliora: create page, move auric here, style

2023-12-29T02:39:01Z

create page, move auric here, style

New page

{{Fractional-octave navigation|159}}
[[159edo]] is a notable [[17-limit]] system. It first contains [[53edo]], tempering out Mercator's comma.

159edo has attracted a lot of attention from prominent microtonalists like [[Ozan Yarman]], [[Dawson Berry]] (also known as [[Aura]]), [[Gene Ward Smith]]. In addition, some of its multiples have large consistency limits as well, and this naturally commends itself to 159th-octave temperaments.
== Auric ==
''Auric'', named after [[Aura]], is defined by setting the 2.3.5.11 mapping to that of 159edo and the generator for the prime 7 being independent.

Subgroup: 2.3.5.7.11

[[Comma list]]: 4000/3993, 15625/15552, 32805/32768

{{Mapping|legend=1|159 252 369 0 550|0 0 0 1 0}}

: mappping generators: ~243/242 = 1\159, ~7

[[Optimal tuning]] ([[CTE]]): ~7/4 = 968.726

{{Optimal ET sequence|legend=1|159, 318, 477c, 636c, 795cd}}

== Aemic (rank-3) ==
''Aemic'', a shortening of aemilic (see below) tempers out the [[frameshift comma]] and the [[nexus comma]]. Aemic is alternately defined by setting the 2.3.11 mapping to that of 159edo and the rest being independent generators. On the patent val it is supported by first 10 multiples of 159edo.

[[Subgroup]]: 2.3.5.7.11

[[Comma list]]: 1771561/1769472, 22876792454961/22866405883904

{{Mapping|legend=1|159 252 0 0 550|0 0 1 0 0|0 0 0 1 0}}

: mapping generators: ~243/242 = 1\159, ~5, ~7

[[Support]]ing [[ET]]s: {{EDOs|159, 398, 477, 636, 795, 954, 1113, 1272, 1431, 1590}}

== Aemilic ==
''Aemilic'' is described as the 159 & 954 temperament in the 17-limit and is named after the minor planet [[wikipedia:159 Aemilia|159 Aemilia]].

[[Subgroup]]: 2.3.5.7.11.13.17

[[Comma list]]: 2431/2430, 3025/3024, 57375/57344, 123201/123200, 160083/160000

{{Mapping|legend=1|159 252 0 -292 550 -150 1019|0 0 1 2 0 2 -1}}

: mapping generators: ~225/224 = 1\159, ~5

[[Optimal tuning]] ([[CTE]]): ~5/4 = 386.263

[[Support]]ing [[ET]]s: {{EDOs|159, 795g, 954}}