Catalog of MOS as circulating temperaments

Below is a list of MOS with number of elements from 5 to 31, plus sample EDOs where they are circulating temperaments to within ±1 comma.

MOS	EDO	Cents
Pentatonic MOS
1L 4s	41edo	234¢8’47”-468¢17’34”-702¢26’20”-936¢35’7”
2L 3s	42edo	228¢34’17”-457¢8’34”-714¢17’9”-942¢51’26”
3L 2s	43edo	251¢9’46”-502¢19’32”-725¢34’53”-976¢44’39”
4L 1s	44edo	245.4545-490.909-736.364-981.818
Hexatonic MOS
1L 5s	43edo	195¢20’56”-390¢41’53”-586¢2’48”-781¢23’43”-976¢44’39”
2L 4s	44edo	190.909-381.818-600-790.909-981.818
3L 3s	45edo	213.333-400-613.333-800-1013.333
4L 2s	40edo	210-420-600-810-1020
5L 1s	41edo	204¢52’41”-409¢45’22”-614¢38’3”-819¢30’44”-1024¢23’25”
Heptatonic MOS
1L 6s	43edo	167¢26’31”-334¢53’1”-502¢19’32”-669¢46’3”-837¢12’33”-1004¢39’4”
2L 5s	44edo	163.636-327.273-490.909-654.5455-845.4545-1009.091
3L 4s	45edo	160-320-506.667-666.667-853.333-1013.333
4L 3s	46edo	182¢36’31”-365¢13’3”-521¢44’21”-704¢20’52”-860¢52’10”-1043¢28’42”
5L 2s	40edo	180-360-540-690-870-1050
6L 1s	41edo	175¢36’35”-351¢13’10”-526¢49’45”-702¢26’20.5”-878¢2’56”-1053¢27’41”
Octatonic MOS
1L 7s	41edo	146¢20’29”-292¢40’59”-439¢1’27”-585¢21’57”-731¢42’26”-878¢2’56”-1024¢23’25”
2L 6s	42edo	142¢51’26”-285¢42’52”-428¢34’17”-600-742¢51’26”-885¢42’52”-1028¢34’17”
3L 5s	43edo	139¢32’6”-279¢4’11”-446¢30’42”-586¢2’48”-725¢34’53”-893¢1’24”-1032¢33’29”
4L 4s	44edo	136.364-300-436.364-600-736.364-900-1036.364
5L 3s	45edo	160-320-453.333-613.333-773.333-906.667-1066.667
6L 2s	46edo	156¢31’18”-313¢2’37”-469¢33’55”-600-756¢31’18”-913¢2’37”-1069¢33’55”
7L 1s	47edo	153¢11’29”-306¢22’59”-459¢34’28”-612¢45’57”-765¢57’27”-919¢8’56”-1072¢20’26”
Nonatonic MOS
1L 8s	46edo	130¢26’5”-260¢52’10”-391¢18’16”-521¢44’21”-652¢10’26”-782¢36’31”-913¢2’37”-1043¢28’42”
2L 7s	47edo	127¢39’34”-255¢19’9”-382¢58’43”-510¢38’18”-663¢49’47”-791¢29’22”-919¢8’56”-1046¢48’31”
3L 6s	48edo	125-250-400-525-650-800-925-1050
4L 5s	40edo	120-240-390-510-660-780-930-1050
5L 4s	41edo	146¢20’29”-292¢40’58.5”-409¢45’22”-526¢49’45”-673¢10’15”-790¢14’38”-936¢35’7”-1082¢55’37”
6L 3s	42edo	142.857-285.714-400-542.857-685.714-800-942.857-1085.714
7L 2s	43edo	139¢32’6”-279¢4’12”-418¢36’18”-558¢8’22”-669¢46’3”-809¢18’8”-948¢50’14”-1088¢22’20”
8L 1s	44edo	136.364-272.727-409.091-545.4545-681.818-818.182-954.5455-1090.909
Decatonic MOS
1L 9s	41edo	117¢4’23”-234¢8’46”-351¢13’10”-468¢17’34”-585¢21’57”-702¢26’20”-819¢30’44”-936¢35’7”-1053¢39’31”
2L 8s	42edo	114¢17’9”-228¢34’17”-342¢51”26”-457¢8’34”-600-714¢17’9”-828¢34’17”-942¢51”26”-1057¢8’34”
3L 7s	43edo	111¢37’40”-222¢15’21”-334¢53’1”-474¢25’6”-586¢2’47”-697¢40’28”-809¢18’8”-948¢50’14”
4L 6s	44edo	109.091-218.182-327.273-463.636-600-709.091-818.182-927.273-1063.636
5L 5s	45edo	106.667-240-346.667-480-586.667-720-826.667-960-1066.667
6L 4s	46edo	130¢26’5”-260¢52’10”-365¢13’3”-495¢39’8”-600-730¢26’5”-860¢52’10”-965¢13’3”-1095¢39’8”
7L 3s	47edo	127¢39’34”-255¢19’9”-382¢58’43”-485¢6’23”-612¢45’57”-740¢25’32”-842¢33’12”-970¢12’46”-1097¢52’20”
8L 2s	48edo	125-250-375-500-600-725-850-975-1100
9L 1s	49edo	122¢26’56”-244¢53’53”-367¢20’49-489¢47’45”-612¢14’42”-734¢41’38”-857¢8’34”-979¢35’31”-1102¢2’27”
Hendecatonic MOS
1L 10s	45edo	106.667-213.333-320-426.667-533.333-640-746.667-853.333-960-1066.667
2L 9s	46edo	130¢26’5”, 104¢28’52”
3L 8s	47edo	127¢39’34.5”, 102¢7’40”
4L 7s	48edo	100-200-325-425-525-650-750-850-975-1075-1175
5L 6s	49edo	122¢26’56”, 97¢57’33”
6L 5s	50edo	120-240-336-456-552-672-768-888-984-1104
7L 4s	40edo	120-240-330-450-570-660-780-900-990-1110
8L 3s	41edo	117¢4’23”, 87¢48’18”
9L 2s	42edo	114.286-228.571-342.857-457.143-571.429-657.143-771.429-885.714-1000-1114.286
10L 1s	43edo	111¢37’40.5”, 83¢43’15”
Dodecatonic MOS
1L 11s	49edo	122¢22’56”, 97¢57’33”
2L 10s	50edo	96-192-288-384-480-600-696-792-888-984-1080
3L 9s	51edo	117¢38’49”, 94¢7’3.5”
4L 8s	40edo	90-180-300-390-480-600-690-780-900-990-1080
5L 7s	41edo	117¢4’23”, 87¢48’18”
6L 6s	42edo	114.286-200-314.286-400-514.286-600-714.286-800-914.286-1000-1114.286
7L 5s	43edo	111¢37’40.5”, 83¢43’15”
8L 4s	44edo	109.091-218.182-300-409.091-518.182-600-709.091-818.182-900-1009.091-1118.182
9L 3s	45edo	106.667-213.333-320-400-506.667-613.333-720-800-906.667-1013.333-1120
10L 2s	46edo	104¢28’52”, 78¢15’39”
11L 1s	47edo	102¢7’40”, 76¢35’45”
Tridecatonic MOS
1L 12s	40edo	90-180-270-360-450-540-630-720-810-900-990-1080
2L 11s	41edo	117¢4’23”, 87¢48’18”
3L 10s	42edo	85.714-171.429-257.143-342.857-457.143-542.857-628.571-714.286-828.571-914.286-1000-1085.714
4L 9s	43edo	111¢37’40.5”, 83¢43’15”
5L 8s	44edo	81.818-163.636-272.727-354.5455-436.364-545.4545-654.5455-736.364-818.182-900-1009.091-1090.909
6L 7s	45edo	80-160-266.667-346.667-453.333-533.333-640-720-826.667-906.667-1013.333-1120
7L 6s	46edo	104¢28’52”, 78¢15’39”
8L 5s	47edo	102¢7’40”, 76¢35’45”
9L 4s	48edo	100-200-300-375-475-575-650-750-850-925-1025-1125
10L 3s	49edo	97¢57’33”, 73¢28’10”
11L 2s	50edo	96-192-288-384-480-576-648-744-840-936-1032-1128
12L 1s	51edo	94¢7’3.5”, 70¢17’18”
Tetradecatonic MOS
1L 13s	43edo	111¢37’40.5”, 83¢43’15”
2L 12s	44edo	109.091, 81.818
3L 11s	45edo	106.667, 80
4L 10s	46edo	104¢28’52”, 78¢15’39”
5L 9s	47edo	102¢7’40”, 76¢35’45”
6L 8s	48edo	75-150-250-325-425-500-600-675-750-850-925-1025-1100
7L 7s	49edo	97¢57’33”, 73¢28’10”
8L 6s	50edo	96-192-264-360-432-528-600-696-792-864-960-1032-1128
9L 5s	51edo	94¢7’3.5”, 70¢17’18”
10L 4s	52edo	92¢18’28”, 69¢13’51”
11L 3s	53edo	90¢33’58”, 67¢55’28”
12L 2s	40edo	90-180-270-360-450-540-600-690-780-870-960-1050-1140
13L 1s	41edo	87¢48’18”, 58¢32’12”
Pentadecatonic MOS
1L 14s	46edo	104¢28’52”, 78¢15’39”
2L 13s	47edo	102¢7’40”, 76¢35’45”
3L 12s	48edo	75-150-225-300-400-475-550-625-700-800-875-950-1025-1100
4L 11s	49edo	97¢57’33”, 73¢28’10”
5L 10s	50edo	72-144-240-312-384-480-552-624-720-792-864-960-1032-1104
6L 9s	51edo	94¢7’3.5”, 70¢17’18”
7L 8s	52edo	92¢18’28”, 69¢13’51”
8L 7s	53edo	90¢33’58”, 67¢55’28”
9L 6s	54edo	88.889, 66.667
10L 5s	40edo	90-180-240-330-420-480-570-660-720-810-900-960-1050-1140
11L 4s	41edo	87¢48’18”, 58¢32’12”
12L 3s	42edo	85.714-171.429-257.143-342.857-400-485.714-571.429-657.143-742.857-800-885.714-971.429-1057.143-1142.857
13L 2s	43edo	83¢43’15”, 55¢40’53”
14L 1s	44edo	81.818, 54.5455