Delta centauri

Delta centauri

Subgroups	3.5.11, 3.5.11.17
Comma basis	1953125/1948617 (3.5.11);1377/1375, 265625/264627 (3.5.11.17)
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, 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.

Extensions

There is a clear strong extension to 3.5.11.17, by tempering out 1377/1375 and mapping 17/9 to 12 generators up. This provides a simpler interpretation of several intervals in the MOS scales.

One might want to extend this temperament to 3.5.11.13 to complete the 9:11:13:15 isoharmonic chord, however most extensions in that subgroup aren't very good because they seem to sacrifice either the high accuracy or low complexity that the 3.5.11 version has. Probably the best strong extension is b15 & b28, which maps 13/9 to 5 generators up, but this will make 13/9 very flat (18 cents of damage in CWE tuning). There is also the high-complexity weak extension b15 & b99 (which has a period of 13/9 and tempers out 2197/2187) and the high-complexity strong extension b15 & b71 (which splits 5/1 into two 739/325s).

Interval chain

Prime harmonics and subharmonics are bold

Number of generators	Cents*	Approximate ratios	Additional ratios in 3.5.11.17 extension
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	Additional ratios in 3.5.11.17 extension
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