Delta centauri: Difference between revisions
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| Generators = 5/3 | | Generators = 5/3 | ||
| Generators tuning = 883.9 | | Generators tuning = 883.9 | ||
| Optimization method = CWE | |||
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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. | ||
Revision as of 20:37, 6 October 2026
| Delta Centauri |
Delta Centauri is the non-octave temperament of the 3.5.11 subgroup that 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.
Etymology
This temperament was named by CompactStar in 2026 after the star 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).
MOS scales
The same small MOS scales as the 3.5 subgroup are produced:2L 1s<3/1>, 2L 3s<3/1>, 2L 5s<3/1>, 2L 7s<3/1>, 2L 9s<3/1>, 2L 11s<3/1>, 13L 2s<3/1>, 15L 13s<3/1>, 28L 15s<3/1>