Catalog of MOS as circulating temperaments

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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[1]
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 46edo 208¢41’45”-417¢23’29”-600-808¢41’45”-1017¢23’29”
5L 1s 47edo 204¢15’19”-408¢30’38”-612¢45’57”-817¢1’17”-1021¢16’36”
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 47edo 178¢43’24”-357¢26’49”-536¢10’13”-689¢21’42”-868¢5’7”-1046¢48’31”
6L 1s 48edo 175-350-525-700-875-1050
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 49edo 122¢26’56”-244¢53’53”-391¢50’12”-514¢17’9”-661¢13’28”-783¢40’24”-930¢36’44”-1053¢3’41”
5L 4s 50edo 144-288-408-552-672-936-1080
6L 3s 51edo 141¢10’35”-282¢21’11”-400-541¢10’35”-682¢21’11”-800-941¢10’35”-1082¢21’11”
7L 2s 52edo 138¢27’42”-276¢55’23”-415¢23’5”-553¢50’46”-669¢13’51”-807¢41’32”-946¢9’14”-1084¢36’55”
8L 1s 53edo 135¢50’57”-271¢41”53’-407¢32’50”-543¢23’46”-679¢14’43”-815¢5’40”-950¢56’36”-1086¢47’33”
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 118¢48’43”, 106¢54’50.5”
3L 8s 47edo 117¢38’50”, 105¢52’56”
4L 7s 48edo 116¢30’17”, 104¢51’16”
5L 6s 49edo 116¢7’45”, 103¢13’33”
6L 5s 50edo 114¢53’37”, 102¢7’40”
7L 4s 51edo 113¢41’1”, 101¢3’9”
8L 3s 52edo 112.5, 100
9L 2s 53edo 111¢20’25”, 98¢58’9”
10L 1s 54edo 110¢12’15”, 97¢57’33”
Dodecatonic MOS
1L 11s 49edo 111¢20’25”, 98¢58’9”
2L 10s 50edo 110¢12’15”, 97¢57’33”
3L 9s 51edo 109.091, 96.97
4L 8s 52edo 108, 96
5L 7s 53edo 106¢54’50.5”, 95¢2’58”
6L 6s 54edo 105¢52’56”, 94¢7’4”
7L 5s 103edo 104¢51’16”, 93¢12’14”
8L 4s 104edo 103¢50’46”, 92¢18’28”
9L 3s 93edo 103¢13’33”, 90¢19’21”
10L 2s 94edo 102¢7’40”, 89¢21’42”
11L 1s 95edo 101¢3’9”, 88¢25’16”
Tridecatonic MOS
1L 12s 40edo 90-180-270-360-450-540-630-720-810-900-990-1080
2L 11s 41edo 103¢13’33”, 90¢19’21”
3L 10s 42edo 102¢7’40”, 89¢21’42”
4L 9s 43edo 101¢3’9”, 88¢25’16”
5L 8s 44edo 100, 87.5
6L 7s 45edo 98¢58’9”, 86¢35’53”
7L 6s 46edo 97.959, 85.714
8L 5s 47edo 96.97, 84.8485
9L 4s 48edo 96, 84
10L 3s 49edo 95.0495, 83.168
11L 2s 50edo 94.118, 82.353
12L 1s 51edo 93.204, 81.553
Tetradecatonic MOS
1L 13s 43edo 96.97, 84.8485
2L 12s 44edo 96, 84
3L 11s 45edo 95.0495, 83.168
4L 10s 46edo 94.118, 82.353
5L 9s 47edo 93.204, 81.553
6L 8s 48edo 92.308, 80.769
7L 7s 49edo 91.571, 80
8L 6s 50edo 90.566, 79.245
9L 5s 51edo 90.323, 77.419
10L 4s 52edo 89.362, 76.596
11L 3s 53edo 88.421, 75.7895
12L 2s 54edo 87.5, 75
13L 1s 97edo 86.598, 74.227
Pentadecatonic MOS
1L 14s 46edo 90.566, 79.245
2L 13s 47edo 89.72, 78.505
3L 12s 48edo 90.323, 77.419
4L 11s 49edo 89.362, 76.596
5L 10s 50edo 88.421, 75.7895
6L 9s 51edo 87.5, 75
7L 8s 52edo 86.598, 74.227
8L 7s 53edo 85.714, 73.469
9L 6s 54edo 84.8485, 72.727
10L 5s 100edo 84, 72
11L 4s 101edo 83.168, 71.287
12L 3s 102edo 82.353, 70.588
13L 2s 103edo 81.553, 69.903
14L 1s 104edo 80.769, 69.231
  1. Repeating decimals longer than three digits given in cents ¢ min ’ sec ”