Delta centauri
| 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>
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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 | 1018.054 | 9/5 |
| 2 | 134.153 | 27/25 |
| 3 | 1152.207 | 243/125 |
| 4 | 268.306 | 729/625 |
| 5 | 1286.360 | 625/297, 6561/3125 |
| 6 | 402.459 | 125/99 |
| 7 | 1420.513 | 25/11 |
| 8 | 536.612 | 15/11 |
| 9 | 1554.547 | 27/11 |
| 10 | 670.765 | 81/55 |
| 11 | 1688.819 | 729/275 |
| 12 | 804.918 | 2187/1375 |
| 13 | 1822.972 | 3125/1089, 19683/6875 |
| 14 | 939.071 | 625/363 |
| 15 | 55.170 | 125/121 |
* In 3.5.11 CWE tuning
Tuning spectrum
| Edt generator |
Unchanged interval (eigenmonzo) |
Generator (¢) | Comments |
|---|---|---|---|
| 6\13 | 877.823 | Flattest generator of 13L 2s<3/1> MOS This is an exo tuning as 11/9 is 292.6 cents | |
| 19\41 | 881.393 | ||
| 13\28 | 883.051 | Smallest EDT with a reasonable tuning of this temperament | |
| 46\99 | 883.737 | ||
| 33/25 | 883.787 | ||
| 11/5 | 883.859 | ||
| 11/9 | 883.914 | ||
| 55/27 | 883.959 | Error is equally distributed between 11/9 and 5/3 | |
| 33\71 | 884.007 | ||
| 53\114 | 884.242 | ||
| 5/3 | 884.359 | Trithagorean/3.5 subgroup | |
| 20\43 | 884.630 | ||
| 27\58 | 885.393 | ||
| 7\15 | 887.579 | Sharpest generator of 13L 2s<3/1> MOS This is an exo tuning as 11/9 is 380.4 cents |