Delta centauri: Difference between revisions

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|-
|-
|1
|1
|
|883.901
|[[5/3]]
|[[5/3]]
|-
|-
|2
|2
|
|1767.802
|[[25/9]]
|[[25/9]]
|-
|-
|3
|3
|
|749.748
|[[125/81]]
|[[125/81]]
|-
|-
|4
|4
|
|1633.649
|[[625/343]]
|[[625/343]]
|-
|-
|5
|5
|
|615.595
|
|[[891/625]]
|-
|-
|6
|6
|
|1499.496
|
|[[297/125]]
|-
|-
|7
|7
|
|481.442
|
|[[33/25]]
|-
|-
|8
|8
|
|1365.343
|
|[[11/5]]
|-
|-
|9
|9
|
|347.289
|[[11/9]]
|[[11/9]]
|-
|-
|10
|10
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|1231.190
|
|[[55/27]]
|-
|-
|11
|11
|
|213.136
|
|[[275/243]]
|-
|-
|12
|12

Revision as of 20:18, 8 October 2026

Delta centauri
Subgroups 3.5.11
Comma basis 1953125/1948617
Reduced mapping ⟨1; 1 9]
ET join b28 & b71
Generators (CWE) ~5/3 = 883.9 ¢
MOS scales n/a
Ploidacot mono5cleft
Minimax error -throdd-limit:  ¢
Target scale size -throdd-limit: notes

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 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
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
13
14
15

* In 3.5.11 CWE tuning

References