The Jacobins
The Jacobins is a collection of microtemperaments of different ranks which all temper out the jacobin comma, 6656/6655.
The main focus here will be on the 2.5.11.13 subgroup, as the jacobin comma can be entrenched in other temperaments like vidar.
Quite coincidentally, 1789edo supports an enormous amount of these temperaments.
Onzonic
Named for the French word for eleven, onze, since the generator is 11/8. Initially defined for 2.5.11.13, but it can be extended.
Pure onzonic
Pure onzonic is the temperament that was initially defined as "jacobin" before Flora Canou pointed out that the name "jacobin temperament" would refer to a rank-5 temperamnet tempering out 6656/6655. Since jacobin comma is the difference between a stack of three 11/8s and 13/10, it was natural to choose 11/8 as the generator for the rank 2 "jacobin temperament". Name "pure onzonic" is thus reserved for the pure 2.5.11.13 subgroup.
Subgroup: 2.5.11.13
Comma list: 6656/6655, [-119 -46 15 47⟩
Mapping: [⟨1 74 3 74], ⟨0 -156 1 -153]]
Optimal tuning (CTE): ~11/8 = 551.370
Estates general
Named so because it is defined as the 1789 & 3125 temperament due to 3125 providing optimal patent val for the jacobin comma, 3125 is 5 to the 5th power, and Estates General were called by Louis XVI on 5th May 1789 (05/05). Defined starting with the 2.5.11.13.19 subgroup, upwards to the 2.5.11.13.19.23.29.31 subgroup.
Subgroup: 2.5.11.13.19
Comma list: 6656/6655, 40960000000/40943078891, [-133 50 -7 18 -6⟩
Mapping: [⟨1 118 -107 -212 450], ⟨0 -266 254 496 -1025]]
Optimal tuning (CTE): ~2588443885831192576/1914932769775390625 = 521.856
2.5.11.13.19.23 subgroup
Subgroup: 2.5.11.13.19.23
Comma list: 6656/6655, 62500/62491, 190676992/190653125, [-92 23 -2 14 -10 8⟩
Mapping: [⟨1 118 -107 -212 450 579], ⟨0 -266 254 496 -1025 -1321]]
Optimal tuning (CTE): ~2592407900127232/1918105439453125 = 521.856
2.5.11.13.19.23.29 subgroup
Subgroup: 2.5.11.13.19.23.29
Comma list: 6656/6655, 62500/62491, 190676992/190653125, 7592198144/7591796875, 897740062375/897648164864
Mapping: [⟨1 118 -107 -212 450 579 251], ⟨0 -266 254 496 -1025 -1321 -566]]
Optimal tuning (CTE): ~184000/136097 = 521.856
2.5.11.13.19.23.29.31 subgroup
Subgroup: 2.5.11.13.19.23.29.31
Comma list: 6656/6655, 62500/62491, 9425/9424, 190676992/190653125, 507528125/507510784, 519411073024/519363934375
Mapping: [⟨1 118 -107 -212 450 579 251 -179], ⟨0 -266 254 496 -1025 -1321 -566 423]]
Optimal tuning (CTE): ~80275/59392 = 521.856
Sextilimeans
It's like sextilififths, but the fourth that is divided into 6 is tuned meantone, corresponding to a fifth of 1039\1789, or about 1/4.26-commma meantone. Defined as the 229 & 1789 temperament.
Subgroup: 2.5.7.11.13
Comma list: 6656/6655, 8122034375/8120172544, [-12 -29 36 -2 -4⟩
Mapping: [⟨1 36 23 -24 -45], ⟨0 -482 -289 393 697]]
Optimal tuning (CTE): ~16807/16000 = 83.846
Double Bastille
Defined as the 1789 & 2814 temperament, and named because 2814 divided in two is 1407, and Bastille storming happened on 14 July 1789. Unfortunately 1407 & 1789 temperament does not temper out the jacobin comma (at least in the patent val), so it's not possible to include it here.
Subgroup: 2.5.7.11.13
Comma list: 6656/6655, [43 -18 0 5 -5⟩, [6 -30 -3 8 12⟩
Mapping: [⟨1 26 -938 -51 -136], ⟨0 -30 1192 69 177]]
Optimal tuning (CTE): ~91750400/53094899 = 947.121
Vals: 1789, 2814, ...