List of 31et rank two temperaments by badness

Below are listed rank-2 temperaments supported by the 31edo patent val, below the indicated cutoff in TE badness.

5-limit temperaments

Listed is the TE logflat badness times 1000 for four temperaments with badness less than 0.1.

#	Name	Badness	Comma list
1	Meantone	7.381	81/80
2	Luna	20.576	274877906944/274658203125
3	Würschmidt	40.603	393216/390625
4	Orson	40.807	2109375/2097152

7-limit temperaments

Listed is the TE badness times 1000 for 19 temperaments with badness less than 0.06.

#	Name	Badness	Comma list
1	Tertiaseptal	12.995	2401/2400 65625/65536
2	Meantone	13.707	81/80 126/125
3	Miracle	16.742	225/224 1029/1024
4	Hemiwürschmidt	20.307	2401/2400 3136/3125
5	Orwell	20.735	225/224 1728/1715
6	Myna	27.044	126/125 1728/1715
7	Valentine	31.056	126/125 1029/1024
8	Quasiorwell	35.832	2401/2400 29360128/29296875
9	Mothra	37.146	81/80 1029/1024
10	Hemithirds	44.284	1029/1024 3136/3125
11	Subneutral	45.792	2401/2400 274877906944/274658203125
12	Squares	45.993	81/80 2401/2400
13	Tritonic	47.578	225/224 50421/50000
14	Nusecond	50.389	126/125 2430/2401
15	Semisept	50.472	1728/1715 3136/3125
16	Würschmidt	50.776	225/224 8748/8575
17	Grendel	51.834	6144/6125 16875/16807
18	Mohajira	55.714	81/80 6144/6125
19	Slender	56.934	225/224 589824/588245

11-limit temperaments

Listed is the TE badness times 1000 for 68 temperaments with badness less than 0.05.

#	Name	Badness	Comma list
1	Miracle	10.684	225/224 243/242 441/440
2	Orwell	15.231	99/98 121/120 176/175
3	Hemitert	15.633	2401/2400 3025/3024 65625/65536
4	Valentine	16.687	121/120 126/125 176/175
5	Myna	16.842	126/125 176/175 243/242
6	Meantone	17.027	81/80 99/98 126/125
7	Quasiorwell	17.540	2401/2400 3025/3024 5632/5625
8	Hemithirds	19.003	385/384 441/440 3136/3125
9	Grendel	19.845	540/539 1375/1372 5632/5625
10	Hemiwürschmidt	21.069	243/242 441/440 3136/3125
11	Meanpop	21.543	81/80 126/125 540/539
12	Squares	21.636	81/80 99/98 121/120
13	Semisept	22.476	176/175 540/539 1331/1323
14	Tritonic	23.659	121/120 225/224 441/440
15	Würschmidt	24.413	99/98 176/175 243/242
16	Slender	25.342	225/224 385/384 1331/1323
17	Migration	25.516	81/80 121/120 126/125
18	Nusecond	25.621	99/98 121/120 126/125
19	Mothra	25.642	81/80 99/98 385/384
20	Mohajira	26.064	81/80 121/120 176/175
21	Eris	27.621	540/539 1375/1372 65625/65536
22	Hemiwur	29.270	121/120 176/175 1375/1372
23	Triwell	29.807	385/384 441/440 456533/455625
24	Tertia	30.171	385/384 1331/1323 1375/1372
25		30.609	2401/2400 3025/3024 369140625/369098752
26	Mosura	31.334	81/80 540/539 1029/1024
27	Newspeak	31.438	225/224 441/440 1728/1715
28		32.121	3025/3024 180224/180075 703125/702464
29	Revelation	32.946	99/98 176/175 1029/1024
30	Myno	33.434	99/98 126/125 385/384
31	Worschmidt	33.436	126/125 243/242 385/384
32		34.814	2401/2400 3025/3024 3136/3125
33	Tertiaseptal	35.576	243/242 441/440 703125/702464
34	Quadrawell	36.493	385/384 1375/1372 14641/14580
35	Borwell	38.377	225/224 243/242 2420/2401
36		39.162	441/440 3388/3375 6144/6125
37	Sentinel	39.595	99/98 243/242 385/384
38	Birds	39.921	441/440 3136/3125 41503/41472
39		40.217	99/98 121/120 1029/1024
40	Marrakesh	40.539	126/125 176/175 14641/14580
41		41.496	2401/2400 5632/5625 46656/46585
42		41.680	126/125 176/175 14641/14406
43		42.204	126/125 540/539 1029/1024
44	Oracle	42.687	121/120 225/224 1029/1024
45	Cypress	42.719	99/98 126/125 243/242
46		42.869	81/80 99/98 2541/2500
47	Prajapati	42.959	81/80 126/125 1029/1024
48		44.005	225/224 441/440 9317/9216
49		44.041	126/125 176/175 2430/2401
50	Diesic	44.186	121/120 441/440 891/875
51		44.660	176/175 1331/1323 2401/2400
52		44.729	3025/3024 5632/5625 825000/823543
53		44.888	2401/2400 46656/46585 172032/171875
54		45.168	225/224 385/384 585640/583443
55	Tritoni	45.456	225/224 385/384 27783/27500
56		45.466	81/80 540/539 1375/1372
57		45.509	81/80 176/175 1331/1323
58		45.795	176/175 243/242 1375/1372
59		45.928	540/539 5632/5625 151263/151250
60		46.181	243/242 441/440 1815/1792
61		46.462	225/224 243/242 1617/1600
62		47.885	121/120 225/224 891/875
63		48.088	540/539 3136/3125 15488/15435
64		48.150	121/120 441/440 3136/3125
65		48.186	225/224 385/384 891/875
66		48.798	2401/2400 3025/3024 1265625/1261568
67		49.572	121/120 126/125 2079/2048
68		49.917	121/120 126/125 1728/1715

13-limit temperaments

Listed is the TE badness times 1000 for 64 temperaments with badness less than 0.04.

#	Name	Badness	Comma list
1	Benediction	15.715	225/224 243/242 351/350 441/440
2	Myna	17.125	126/125 144/143 176/175 196/195
3	Meantone	18.048	66/65 81/80 99/98 105/104
4	Miraculous	18.669	105/104 144/143 196/195 275/273
5	Orwell	19.718	99/98 121/120 176/175 275/273
6	Winston	19.931	66/65 99/98 105/104 121/120
7	Valentino	20.665	121/120 126/125 176/175 196/195
8	Meanpop	20.883	81/80 105/104 144/143 196/195
9	Lupercalia	21.328	66/65 105/104 121/120 126/125
10	Hemithirds	21.738	196/195 352/351 1001/1000 1029/1024
11	Tritonic	22.993	105/104 121/120 196/195 275/273
12	Hemiwürschmidt	23.074	243/242 351/350 441/440 3584/3575
13	Nusecond	23.323	66/65 99/98 121/120 126/125
14	Mohajira	23.388	66/65 105/104 121/120 512/507
15	Würschmidt	23.593	99/98 144/143 176/175 275/273
16	Mothra	23.954	81/80 99/98 105/104 144/143
17	Agora	24.522	81/80 99/98 105/104 121/120
18	Grendel	24.839	352/351 540/539 625/624 1375/1372
19	Semisept	25.204	176/175 351/350 540/539 1375/1372
20	Gallium	25.484	81/80 99/98 121/120 126/125
21	Squares	25.514	66/65 81/80 99/98 121/120
22	Grosstone	25.899	81/80 99/98 126/125 144/143
23	Slender	25.913	225/224 275/273 385/384 1331/1323
24		27.405	385/384 441/440 625/624 13720/13689
25		27.835	81/80 105/104 121/120 196/195
26	Migration	28.071	66/65 121/120 126/125 1215/1183
27		28.384	352/351 385/384 625/624 1331/1323
28	Semishly	28.408	144/143 176/175 196/195 275/273
29	Hemiwur	28.432	121/120 176/175 196/195 275/273
30		29.207	66/65 81/80 105/104 1001/1000
31	Revelation	29.452	66/65 99/98 105/104 1001/1000
32	Maneh	29.868	66/65 105/104 126/125 540/539
33		30.237	144/143 225/224 351/350 441/440
34	Hemithir	31.199	144/143 196/195 243/242 625/624
35		31.732	352/351 1001/1000 1716/1715 3025/3024
36		31.850	66/65 99/98 126/125 385/384
37		31.990	351/350 385/384 441/440 3146/3125
38		32.359	351/350 540/539 1375/1372 5632/5625
39		33.007	66/65 81/80 126/125 385/384
40		33.451	225/224 243/242 441/440 1875/1859
41		34.382	66/65 99/98 105/104 243/242
42		34.458	105/104 126/125 144/143 243/242
43		35.530	99/98 105/104 121/120 640/637
44		35.585	126/125 196/195 385/384 1575/1573
45		36.239	66/65 81/80 99/98 385/384
46		36.331	66/65 105/104 126/125 512/507
47		36.533	121/120 225/224 351/350 441/440
48		36.656	99/98 105/104 126/125 144/143
49		36.857	81/80 144/143 176/175 1029/1024
50		36.876	243/242 441/440 625/624 3584/3575
51		37.382	66/65 81/80 99/98 1001/1000
52		37.408	99/98 105/104 144/143 243/242
53		37.732	225/224 351/350 385/384 1331/1323
54		37.849	66/65 99/98 126/125 243/242
55		37.885	81/80 105/104 196/195 512/507
56		38.116	66/65 121/120 343/338 441/440
57		38.811	126/125 176/175 243/242 1573/1568
58		38.812	105/104 196/195 275/273 648/637
59		39.221	126/125 144/143 196/195 1029/1024
60		39.271	196/195 352/351 1001/1000 6144/6125
61		39.531	225/224 243/242 351/350 2420/2401
62		39.576	99/98 105/104 121/120 126/125
63		39.707	126/125 176/175 196/195 648/637
64		39.907	121/120 176/175 351/350 1375/1372