Delta centauri: Difference between revisions
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| Generators tuning = 883.9 | | Generators tuning = 883.9 | ||
| Optimization method = CWE | | Optimization method = CWE | ||
| 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. | ||
This temperament was | 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). | ||
{{Todo|inline=1|complete page|cleanup|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. Format the intervals section. }} | |||
{{Todo|inline=1|complete page|comment= Document the technical data in [[No-twos subgroup temperaments]]. Complete the infobox. | |||
== 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 | ||
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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 | ||
|- | |||
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| [[33/17]] | |||
| 883.328 | |||
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|[[99edt|46\99]] | |[[99edt|46\99]] | ||
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| 884.630 | | 884.630 | ||
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