Delta centauri: Difference between revisions
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== Interval chain == | == Interval chain == | ||
<div style="display: inline-grid; margin-right: 25px;"> | <div style="display: inline-grid; margin-right: 25px;"> | ||
{|class="wikitable" | {|class="wikitable" | ||
|- | |- | ||
| Line 93: | Line 92: | ||
|[[363/125]] | |[[363/125]] | ||
|} | |} | ||
{|class="wikitable" | |||
|- | |||
!Number of generators | |||
!Cents* | |||
!Approximate ratios | |||
|- | |||
|0 | |||
|0.00 | |||
|[[1/1]] | |||
|- | |||
|1 | |||
|883.901 | |||
|'''[[5/3]]''' | |||
|- | |||
|2 | |||
|1767.802 | |||
|[[25/9]] | |||
|- | |||
|3 | |||
|749.748 | |||
|[[125/81]] | |||
|- | |||
|4 | |||
|1633.649 | |||
|[[625/343]] | |||
|- | |||
|5 | |||
|615.595 | |||
|[[891/625]], [[3125/2187]] | |||
|- | |||
|6 | |||
|1499.496 | |||
|[[297/125]] | |||
|- | |||
|7 | |||
|481.442 | |||
|[[33/25]] | |||
|- | |||
|8 | |||
|1365.343 | |||
|[[11/5]] | |||
|- | |||
|9 | |||
|347.289 | |||
|'''[[11/9]]''' | |||
|- | |||
|10 | |||
|1231.190 | |||
|[[55/27]] | |||
|- | |||
|11 | |||
|213.136 | |||
|[[275/243]] | |||
|- | |||
|12 | |||
|1097.037 | |||
|[[1375/729]] | |||
|- | |||
|13 | |||
|78.983 | |||
|[[3267/3125]], [[6875/6561]] | |||
|- | |||
|14 | |||
|962.884 | |||
|[[1089/625]] | |||
|- | |||
|15 | |||
|1846.785 | |||
|[[363/125]] | |||
|} | |||
</div> | </div> | ||
<nowiki/>* In 3.5.11 CWE tuning | <nowiki/>* In 3.5.11 CWE tuning | ||
| Line 102: | Line 170: | ||
[[Category:Rank-2 temperaments]] | [[Category:Rank-2 temperaments]] | ||
[[Category:Non-octave temperaments]] | [[Category:Non-octave temperaments]] | ||
[[Category:Subgroup temperaments]] | |||
[[Category:Microtemperaments]] | |||
Revision as of 20:24, 8 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.
This temperament was seemingly first discovered by MisterShafXen in 2025[1], and 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).
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>
|
Todo: complete page
Document the technical data in No-twos subgroup temperaments. Complete the infobox. Make the intervals and tunings section. |
Interval chain
| Number of generators | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.00 | 1/1 |
| 1 | 883.901 | 5/3 |
| 2 | 1767.802 | 25/9 |
| 3 | 749.748 | 125/81 |
| 4 | 1633.649 | 625/343 |
| 5 | 615.595 | 891/625, 3125/2187 |
| 6 | 1499.496 | 297/125 |
| 7 | 481.442 | 33/25 |
| 8 | 1365.343 | 11/5 |
| 9 | 347.289 | 11/9 |
| 10 | 1231.190 | 55/27 |
| 11 | 213.136 | 275/243 |
| 12 | 1097.037 | 1375/729 |
| 13 | 78.983 | 3267/3125, 6875/6561 |
| 14 | 962.884 | 1089/625 |
| 15 | 1846.785 | 363/125 |
| Number of generators | Cents* | Approximate ratios |
|---|---|---|
| 0 | 0.00 | 1/1 |
| 1 | 883.901 | 5/3 |
| 2 | 1767.802 | 25/9 |
| 3 | 749.748 | 125/81 |
| 4 | 1633.649 | 625/343 |
| 5 | 615.595 | 891/625, 3125/2187 |
| 6 | 1499.496 | 297/125 |
| 7 | 481.442 | 33/25 |
| 8 | 1365.343 | 11/5 |
| 9 | 347.289 | 11/9 |
| 10 | 1231.190 | 55/27 |
| 11 | 213.136 | 275/243 |
| 12 | 1097.037 | 1375/729 |
| 13 | 78.983 | 3267/3125, 6875/6561 |
| 14 | 962.884 | 1089/625 |
| 15 | 1846.785 | 363/125 |
* In 3.5.11 CWE tuning