Delta centauri - Revision history

FloraC: Re-organize a bit. Update todo

2026-10-09T08:59:29Z

Re-organize a bit. Update todo

← Older revision		Revision as of 08:59, 9 October 2026
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	'''Delta centauri''' is the [[non-octave]] [[regular temperament\|temperament]] of the [[3.5.11 subgroup]] that [[tempering out\|tempers out]] the 4-cent comma, [[1953125/1948617]]. This temperament is generated by an almost-just [[5/3]] and stacking it nine times and tritave-reducing reaches the representation of [[11/9]]. Basically it is a slightly-tempered [[3.5 subgroup]]. The best tuning is to flatten 5/3 by around half a cent, though just 5/3 or slightly sharp 5/3 will work fine too. It is a [[microtemperament]] with sub-cent error on the 5th and 11th harmonics in optimal tunings, and fairly low [[complexity]] as far as microtemperaments go.		'''Delta centauri''' is the [[non-octave]] [[regular temperament\|temperament]] of the [[3.5.11 subgroup]] that [[tempering out\|tempers out]] the 4-cent comma, [[1953125/1948617]]. This temperament is generated by an almost-just [[5/3]] and stacking it nine times and tritave-reducing reaches the representation of [[11/9]]. Basically it is a slightly-tempered [[3.5 subgroup]]. The best tuning is to flatten 5/3 by around half a cent, though just 5/3 or slightly sharp 5/3 will work fine too. It is a [[microtemperament]] with sub-cent error on the 5th and 11th harmonics in optimal tunings, and fairly low [[complexity]] as far as microtemperaments go.

	This temperament was seemingly first discovered by ~~[[User:MisterShafXen~~\|MisterShafXen]] in 2025<ref>https://en.xen.wiki/index.php?title=4-cent_comma&diff=prev&oldid=183697</ref>, and was named by {{u\|CompactStar}} in 2026 after the star {{w\|Delta Centauri}}, following a series of non-octave temperaments that are named after stars, and as a reference to the 4-cent comma (delta being the 4th letter of the Greek alphabet).		This temperament was seemingly first discovered by {{u\|MisterShafXen}} in 2025<ref>[https://en.xen.wiki/index.php?title=4-cent_comma&diff=prev&oldid=183697 Xenharmonic Wiki \| ''4-cent comma'' (Revision as of 11:56, 28 February 2025 by MisterShafXen)]</ref>, and was named by {{u\|CompactStar}} in 2026 after the star {{w\|Delta Centauri}}, following a series of non-octave temperaments that are named after stars, and as a reference to the 4-cent comma (delta being the 4th letter of the Greek alphabet).

	~~== Scales ==~~		{{Todo\|inline=1\|complete page\|cleanup\|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. Format the intervals section. }}
	The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]]

	{{Todo\|inline=1\|complete page\|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. ~~Make~~ the intervals ~~and tunings~~ section. }}

	== Extensions ==		== Extensions ==
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	<nowiki/>* In 3.5.11 CWE tuning, tritave-reduced		<nowiki/>* In 3.5.11 CWE tuning, tritave-reduced

	== Tuning spectrum ==		== Scales ==
			The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]]

			== Tunings ==
			=== Tuning spectrum ===
	{\| class="wikitable center-all left-4"		{\| class="wikitable center-all left-4"
	! Edt<br>generator		! Edt<br>generator

FloraC: - trivial mos scales, + manual newline in the infobox

2026-10-09T08:28:55Z

- trivial mos scales, + manual newline in the infobox

← Older revision		Revision as of 08:28, 9 October 2026
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	\| Generators tuning = 883.9		\| Generators tuning = 883.9
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = ~~[[2L 1s (3/1-equivalent)\|2L 1s<3/1>]],[[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]],~~ [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]]		\| MOS scales = [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], <br>[[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]]

	}}		}}
	'''Delta centauri''' is the [[non-octave]] [[regular temperament\|temperament]] of the [[3.5.11 subgroup]] that [[tempering out\|tempers out]] the 4-cent comma, [[1953125/1948617]]. This temperament is generated by an almost-just [[5/3]] and stacking it nine times and tritave-reducing reaches the representation of [[11/9]]. Basically it is a slightly-tempered [[3.5 subgroup]]. The best tuning is to flatten 5/3 by around half a cent, though just 5/3 or slightly sharp 5/3 will work fine too. It is a [[microtemperament]] with sub-cent error on the 5th and 11th harmonics in optimal tunings, and fairly low [[complexity]] as far as microtemperaments go.		'''Delta centauri''' is the [[non-octave]] [[regular temperament\|temperament]] of the [[3.5.11 subgroup]] that [[tempering out\|tempers out]] the 4-cent comma, [[1953125/1948617]]. This temperament is generated by an almost-just [[5/3]] and stacking it nine times and tritave-reducing reaches the representation of [[11/9]]. Basically it is a slightly-tempered [[3.5 subgroup]]. The best tuning is to flatten 5/3 by around half a cent, though just 5/3 or slightly sharp 5/3 will work fine too. It is a [[microtemperament]] with sub-cent error on the 5th and 11th harmonics in optimal tunings, and fairly low [[complexity]] as far as microtemperaments go.

CompactStar at 01:22, 9 October 2026

2026-10-09T01:22:53Z

← Older revision		Revision as of 01:22, 9 October 2026
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	\| Generators tuning = 883.9		\| Generators tuning = 883.9
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]],[[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s~~<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s~~<3/1>]]		\| MOS scales = [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]],[[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]]

	}}		}}
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	== Scales ==		== Scales ==
	The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]]~~, [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]~~		The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]]


	{{Todo\|inline=1\|complete page\|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. Make the intervals and tunings section. }}		{{Todo\|inline=1\|complete page\|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. Make the intervals and tunings section. }}

CompactStar at 01:22, 9 October 2026

2026-10-09T01:22:45Z

← Older revision		Revision as of 01:22, 9 October 2026
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	\| Generators tuning = 883.9		\| Generators tuning = 883.9
	\| Optimization method = CWE		\| Optimization method = CWE
			\| MOS scales = [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]],[[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]

	}}		}}
	'''Delta centauri''' is the [[non-octave]] [[regular temperament\|temperament]] of the [[3.5.11 subgroup]] that [[tempering out\|tempers out]] the 4-cent comma, [[1953125/1948617]]. This temperament is generated by an almost-just [[5/3]] and stacking it nine times and tritave-reducing reaches the representation of [[11/9]]. Basically it is a slightly-tempered [[3.5 subgroup]]. The best tuning is to flatten 5/3 by around half a cent, though just 5/3 or slightly sharp 5/3 will work fine too. It is a [[microtemperament]] with sub-cent error on the 5th and 11th harmonics in optimal tunings, and fairly low [[complexity]] as far as microtemperaments go.		'''Delta centauri''' is the [[non-octave]] [[regular temperament\|temperament]] of the [[3.5.11 subgroup]] that [[tempering out\|tempers out]] the 4-cent comma, [[1953125/1948617]]. This temperament is generated by an almost-just [[5/3]] and stacking it nine times and tritave-reducing reaches the representation of [[11/9]]. Basically it is a slightly-tempered [[3.5 subgroup]]. The best tuning is to flatten 5/3 by around half a cent, though just 5/3 or slightly sharp 5/3 will work fine too. It is a [[microtemperament]] with sub-cent error on the 5th and 11th harmonics in optimal tunings, and fairly low [[complexity]] as far as microtemperaments go.

CompactStar: /* Tuning spectrum */

2026-10-09T01:18:02Z

Tuning spectrum

← Older revision		Revision as of 01:18, 9 October 2026
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	\| 883.051		\| 883.051
	\| Smallest EDT with a reasonable tuning of this temperament		\| Smallest EDT with a reasonable tuning of this temperament
			\|-
			\|
			\| [[33/17]]
			\| 883.328
			\|
	\|-		\|-
	\|[[99edt\|46\99]]		\|[[99edt\|46\99]]

CompactStar at 01:16, 9 October 2026

2026-10-09T01:16:37Z

← Older revision		Revision as of 01:16, 9 October 2026
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	== Scales ==		== Scales ==
	The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]		The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]


			{{Todo\|inline=1\|complete page\|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. Make the intervals and tunings section. }}

	== Extensions ==		== Extensions ==

CompactStar: /* Scales */

2026-10-09T01:16:31Z

Scales

← Older revision		Revision as of 01:16, 9 October 2026
Line 15:		Line 15:
	== Scales ==		== Scales ==
	The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]		The same small [[MOS scale]]s as the 3.5 subgroup are produced: [[2L 1s (3/1-equivalent)\|2L 1s<3/1>]], [[2L 3s (3/1-equivalent)\|2L 3s<3/1>]], [[2L 5s (3/1-equivalent))\|2L 5s<3/1>]], [[2L 7s (3/1-equivalent)\|2L 7s<3/1>]], [[2L 9s (3/1-equivalent)\|2L 9s<3/1>]], [[2L 11s (3/1-equivalent)\|2L 11s<3/1>]], [[13L 2s (3/1-equivalent)\|13L 2s<3/1>]], [[15L 13s (3/1-equivalent)\|15L 13s<3/1>]], [[28L 15s (3/1-equivalent)\|28L 15s<3/1>]]


	~~{{Todo\|inline=1\|complete page\|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. Make the intervals and tunings section. }}~~

	== Extensions ==		== Extensions ==

CompactStar: /* Tuning spectrum */

2026-10-09T01:16:23Z

Tuning spectrum

← Older revision		Revision as of 01:16, 9 October 2026
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	\|		\|
	\| 884.630		\| 884.630
			\|
	\|-		\|-
	\|		\|

CompactStar: /* Tuning spectrum */

2026-10-09T01:16:10Z

Tuning spectrum

← Older revision		Revision as of 01:16, 9 October 2026
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	\|		\|
	\| 884.007		\| 884.007
			\|
	\|-		\|-
	\|		\|

CompactStar: /* Tuning spectrum */

2026-10-09T01:15:44Z

Tuning spectrum

← Older revision		Revision as of 01:15, 9 October 2026
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	\|		\|
	\| 884.007		\| 884.007
			\|-
			\|
			\| [[25/17]]
			\| 884.210
			\|
	\|-		\|-
	\|		\|
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	\| 884.224		\| 884.224
	\|		\|
	\|
	\|-		\|-
	\|		\|
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	\| 884.235		\| 884.235
	\|		\|
	\|
	\|-		\|-
	\| [[114edt\|53\114]]		\| [[114edt\|53\114]]