29th-octave temperaments - Revision history

Eliora: /* Copper */ less charged language

2026-03-22T16:55:41Z

Copper: less charged language

← Older revision		Revision as of 16:55, 22 March 2026
Line 24:		Line 24:
	Copper temperament is derived from a 5-limit comma called [[copper comma]], because it is constructed the same way towards 29edo as [[Kirnberger's atom]] is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.		Copper temperament is derived from a 5-limit comma called [[copper comma]], because it is constructed the same way towards 29edo as [[Kirnberger's atom]] is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.

	~~Surprisingly,~~ despite 29edo's fifth being closer to 3/2 than 12edo's, copper has a higher TE error than [[atomic]] and is not a [[very high accuracy temperaments\|very high accuracy temperament]].		It is worth noting that despite 29edo's fifth being closer to 3/2 than 12edo's, copper has a higher TE error than [[atomic]] and hence is not a [[very high accuracy temperaments\|very high accuracy temperament]].

	Subgroup: 2.3.5		Subgroup: 2.3.5

ArrowHead294 at 03:43, 14 February 2025

2025-02-14T03:43:10Z

← Older revision		Revision as of 03:43, 14 February 2025
Line 1:		Line 1:
	{{~~Fractional~~-octave ~~navigation~~\|29}}		{{Infobox fractional-octave\|29}}
	[[29edo]] is notable for being the first equal division to have a more precise [[3/2]] than [[12edo]], and the first tuning to be consistent in the [[15-odd-limit]]. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.		[[29edo]] is notable for being the first equal division to have a more precise [[3/2]] than [[12edo]], and the first tuning to be consistent in the [[15-odd-limit]]. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.

Line 20:		Line 20:

	[[Badness]]: 1.020556		[[Badness]]: 1.020556

	== Copper ==		== Copper ==
	Copper temperament is derived from a 5-limit comma called [[copper comma]], because it is constructed the same way towards 29edo as [[Kirnberger's atom]] is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.		Copper temperament is derived from a 5-limit comma called [[copper comma]], because it is constructed the same way towards 29edo as [[Kirnberger's atom]] is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.

BudjarnLambeth: navbox

2024-12-05T07:26:30Z

navbox

← Older revision		Revision as of 07:26, 5 December 2024
Line 36:		Line 36:

	[[Support]]ing [[ET]]s: {{EDOs\|29, 754, 783, 812, 1566, 1537, 2320, 3103, 3132}}, ...		[[Support]]ing [[ET]]s: {{EDOs\|29, 754, 783, 812, 1566, 1537, 2320, 3103, 3132}}, ...

			{{Navbox fractional-octave}}

	[[Category:29edo]]		[[Category:29edo]]
	~~[[Category:Temperament collections]]~~

	{{Todo\| review }}		{{Todo\| review }}

Eliora: Move 5-limit mystery to here as it's the most logical place for it to be

2023-08-03T23:57:37Z

Move 5-limit mystery to here as it's the most logical place for it to be

← Older revision		Revision as of 23:57, 3 August 2023
Line 2:		Line 2:
	[[29edo]] is notable for being the first equal division to have a more precise [[3/2]] than [[12edo]], and the first tuning to be consistent in the [[15-odd-limit]]. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.		[[29edo]] is notable for being the first equal division to have a more precise [[3/2]] than [[12edo]], and the first tuning to be consistent in the [[15-odd-limit]]. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.

	~~Temperaments discussed elsewhere include~~:		== Mystery (5-limit) ==
	* [[Mystery]] → [[Hemifamity temperaments#Mystery~~\|Hemifamity temperaments~~]]		: ''Main article: [[Mystery]] and for higher-limit versions see [[Hemifamity temperaments #Mystery]]''

	~~Mystery, being a notable 13~~-limit ~~temperament~~, ~~has~~ a ~~dedicated page~~.		The mystery temperament in the 5-limit is described by tempering out the comma {{monzo\| 46 -29 }}, where a circle of 29 fifths closes on 17 octaves, and it is supported by small multiples of 29edo.

			Subgroup: 2.3.5

			[[Comma]]: {{monzo\| 46 -29 }}

			[[Mapping]]: [{{val\| 29 46 0 }}, {{val\| 0 0 1 }}]

			Mapping generators: ~531441/524288, ~5

			[[POTE generator]]: ~5/4 = 387.408

			{{Optimal ET sequence\|legend=1\| 29, 58, 87, 232, 319 }}

			[[Badness]]: 1.020556
	== Copper ==		== Copper ==
	Copper temperament is derived from a 5-limit comma called [[copper comma]], because it is constructed the same way towards 29edo as [[Kirnberger's atom]] is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.		Copper temperament is derived from a 5-limit comma called [[copper comma]], because it is constructed the same way towards 29edo as [[Kirnberger's atom]] is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.

Eliora at 15:18, 7 July 2023

2023-07-07T15:18:27Z

← Older revision		Revision as of 15:18, 7 July 2023
Line 1:		Line 1:
			{{Fractional-octave navigation\|29}}
	[[29edo]] is notable for being the first equal division to have a more precise [[3/2]] than [[12edo]], and the first tuning to be consistent in the [[15-odd-limit]]. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.		[[29edo]] is notable for being the first equal division to have a more precise [[3/2]] than [[12edo]], and the first tuning to be consistent in the [[15-odd-limit]]. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.

FloraC: Mystery's notability is the cause of having a dedicated page

2023-06-15T13:15:00Z

Mystery's notability is the *cause* of having a dedicated page

← Older revision		Revision as of 13:15, 15 June 2023
Line 2:		Line 2:

	Temperaments discussed elsewhere include:		Temperaments discussed elsewhere include:
	* ''[[Mystery]]~~'',~~ → [[Hemifamity temperaments#Mystery\|Hemifamity temperaments]]		* [[Mystery]] → [[Hemifamity temperaments#Mystery\|Hemifamity temperaments]]

	Mystery is notable ~~for having~~ a ~~separate~~ page.		Mystery, being a notable 13-limit temperament, has a dedicated page.

	== Copper ==		== Copper ==
Line 25:		Line 25:
	[[Category:29edo]]		[[Category:29edo]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]

			{{Todo\| review }}

Eliora: /* Copper */ yeah not the best

2023-05-18T23:20:40Z

Copper: yeah not the best

← Older revision		Revision as of 23:20, 18 May 2023
Line 21:		Line 21:
	Optimal tuning (CTE): ~3/2 = 701.905		Optimal tuning (CTE): ~3/2 = 701.905

	[[Support]]ing [[ET]]s: {{EDOs\|23, 754, 783, 812, 1566, 1537, 2320, 3103, 3132}}, ...		[[Support]]ing [[ET]]s: {{EDOs\|29, 754, 783, 812, 1566, 1537, 2320, 3103, 3132}}, ...

	[[Category:29edo]]		[[Category:29edo]]
	[[Category:Temperament collections]]		[[Category:Temperament collections]]

Eliora: 29th octave temps are notable so I'm creating this

2023-05-18T23:20:21Z

29th octave temps are notable so I'm creating this

New page

[[29edo]] is notable for being the first equal division to have a more precise [[3/2]] than [[12edo]], and the first tuning to be consistent in the [[15-odd-limit]]. 29th-octave temperaments occur naturally when temperament-merging edos whose greatest common divisor is 29.

Temperaments discussed elsewhere include:
* ''[[Mystery]]'', → [[Hemifamity temperaments#Mystery|Hemifamity temperaments]]

Mystery is notable for having a separate page.

== Copper ==
Copper temperament is derived from a 5-limit comma called [[copper comma]], because it is constructed the same way towards 29edo as [[Kirnberger's atom]] is towards 12edo. A fifth of each of these tunings is modified by a tiny amount, then a circle of these fifths is set to close eventually at the octave.

Surprisingly, despite 29edo's fifth being closer to 3/2 than 12edo's, copper has a higher TE error than [[atomic]] and is not a [[very high accuracy temperaments|very high accuracy temperament]].

Subgroup: 2.3.5

Comma list: {{monzo|-481 261 29}}

Mapping: [{{val|29 0 481}}, {{val|0 1 -9}}]

Mapping generators: ~{{monzo|-199 12 108}} = 1\29, ~3/2 = 701.905

Optimal tuning (CTE): ~3/2 = 701.905

[[Support]]ing [[ET]]s: {{EDOs|23, 754, 783, 812, 1566, 1537, 2320, 3103, 3132}}, ...

[[Category:29edo]]
[[Category:Temperament collections]]