User:BudjarnLambeth/311edo MOS scales

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This list was calculated by xenoindex for the Xenharmonic Alliance Discord server; I am posting it here so that readers can access the information, however it shouldn't be moved the main space until a wiki editor (possibly future me) rewrites it in a more wiki-friendly format --BudjarnLambeth (talk) 02:37, 11 October 2025 (UTC)

Scales have 5 to 13 tones.
L:s hardness ratios are between 6:5 and 5:1.
No nL 1s or 1L ns MOSes included.
Sorted by generator size.

Key:

Notes & pattern, hardness, generator, 311edo-step pattern

13 7L 6s, 35:11, [46 265], [ 35 35 11 35 11 35 11 35 11 35 11 35 11 ]

13 7L 6s, 29:18, [47 264], [ 29 29 18 29 18 29 18 29 18 29 18 29 18 ]

13 6L 7s, 32:17, [49 262], [ 32 17 32 17 32 17 32 17 32 17 32 17 17 ]

13 6L 7s, 39:11, [50 261], [ 39 11 39 11 39 11 39 11 39 11 39 11 11 ]

11 6L 5s, 41:13, [54 257], [ 41 41 13 41 13 41 13 41 13 41 13 ]

11 6L 5s, 36:19, [55 256], [ 36 36 19 36 19 36 19 36 19 36 19 ]

11 6L 5s, 31:25, [56 255], [ 31 31 25 31 25 31 25 31 25 31 25 ]

11 5L 6s, 37:21, [58 253], [ 37 21 37 21 37 21 37 21 37 21 21 ]

11 5L 6s, 43:16, [59 252], [ 43 16 43 16 43 16 43 16 43 16 16 ]

11 5L 6s, 49:11, [60 251], [ 49 11 49 11 49 11 49 11 49 11 11 ]

9 5L 4s, 51:14, [65 246], [ 51 51 14 51 14 51 14 51 14 ]

9 5L 4s, 47:19, [66 245], [ 47 47 19 47 19 47 19 47 19 ]

9 5L 4s, 43:24, [67 244], [ 43 43 24 43 24 43 24 43 24 ]

9 5L 4s, 39:29, [68 243], [ 39 39 29 39 29 39 29 39 29 ]

9 4L 5s, 39:31, [70 241], [ 39 31 39 31 39 31 39 31 31 ] 13 9L 4s, 31:8, [70 241], [ 31 31 31 8 31 31 8 31 31 8 31 31 8 ]

9 4L 5s, 44:27, [71 240], [ 44 27 44 27 44 27 44 27 27 ] 13 9L 4s, 27:17, [71 240], [ 27 27 27 17 27 27 17 27 27 17 27 27 17 ]

9 4L 5s, 49:23, [72 239], [ 49 23 49 23 49 23 49 23 23 ]

9 4L 5s, 54:19, [73 238], [ 54 19 54 19 54 19 54 19 19 ] 13 4L 9s, 35:19, [73 238], [ 35 19 19 35 19 19 35 19 19 35 19 19 19 ]

9 4L 5s, 59:15, [74 237], [ 59 15 59 15 59 15 59 15 15 ] 13 4L 9s, 44:15, [74 237], [ 44 15 15 44 15 15 44 15 15 44 15 15 15 ]

13 4L 9s, 53:11, [75 236], [ 53 11 11 53 11 11 53 11 11 53 11 11 11 ]

11 4L 7s, 55:13, [81 230], [ 55 13 55 13 13 55 13 13 55 13 13 ]

7 4L 3s, 65:17, [82 229], [ 65 65 17 65 17 65 17 ] 11 4L 7s, 48:17, [82 229], [ 48 17 48 17 17 48 17 17 48 17 17 ]

7 4L 3s, 62:21, [83 228], [ 62 62 21 62 21 62 21 ] 11 4L 7s, 41:21, [83 228], [ 41 21 41 21 21 41 21 21 41 21 21 ]

7 4L 3s, 59:25, [84 227], [ 59 59 25 59 25 59 25 ] 11 4L 7s, 34:25, [84 227], [ 34 25 34 25 25 34 25 25 34 25 25 ]

7 4L 3s, 56:29, [85 226], [ 56 56 29 56 29 56 29 ]

7 4L 3s, 53:33, [86 225], [ 53 53 33 53 33 53 33 ] 11 7L 4s, 33:20, [86 225], [ 33 33 20 33 33 20 33 33 20 33 20 ]

7 4L 3s, 50:37, [87 224], [ 50 50 37 50 37 50 37 ] 11 7L 4s, 37:13, [87 224], [ 37 37 13 37 37 13 37 37 13 37 13 ]

7 3L 4s, 53:38, [91 220], [ 53 38 53 38 53 38 38 ] 10 7L 3s, 38:15, [91 220], [ 38 38 38 15 38 38 15 38 38 15 ]

7 3L 4s, 57:35, [92 219], [ 57 35 57 35 57 35 35 ] 10 7L 3s, 35:22, [92 219], [ 35 35 35 22 35 35 22 35 35 22 ]

7 3L 4s, 61:32, [93 218], [ 61 32 61 32 61 32 32 ]

7 3L 4s, 65:29, [94 217], [ 65 29 65 29 65 29 29 ] 10 3L 7s, 36:29, [94 217], [ 36 29 29 36 29 29 36 29 29 29 ] 13 10L 3s, 29:7, [94 217], [ 29 29 29 29 7 29 29 29 7 29 29 29 7 ]

7 3L 4s, 69:26, [95 216], [ 69 26 69 26 69 26 26 ] 10 3L 7s, 43:26, [95 216], [ 43 26 26 43 26 26 43 26 26 26 ] 13 10L 3s, 26:17, [95 216], [ 26 26 26 26 17 26 26 26 17 26 26 26 17 ]

7 3L 4s, 73:23, [96 215], [ 73 23 73 23 73 23 23 ] 10 3L 7s, 50:23, [96 215], [ 50 23 23 50 23 23 50 23 23 23 ]

7 3L 4s, 77:20, [97 214], [ 77 20 77 20 77 20 20 ] 10 3L 7s, 57:20, [97 214], [ 57 20 20 57 20 20 57 20 20 20 ] 13 3L 10s, 37:20, [97 214], [ 37 20 20 20 37 20 20 20 37 20 20 20 20 ]

7 3L 4s, 81:17, [98 213], [ 81 17 81 17 81 17 17 ] 10 3L 7s, 64:17, [98 213], [ 64 17 17 64 17 17 64 17 17 17 ] 13 3L 10s, 47:17, [98 213], [ 47 17 17 17 47 17 17 17 47 17 17 17 17 ]

13 3L 10s, 57:14, [99 212], [ 57 14 14 14 57 14 14 14 57 14 14 14 14 ]

8 3L 5s, 77:16, [109 202], [ 77 16 77 16 16 77 16 16 ] 11 3L 8s, 61:16, [109 202], [ 61 16 16 61 16 16 16 61 16 16 16 ]

5 3L 2s, 91:19, [110 201], [ 91 91 19 91 19 ] 8 3L 5s, 72:19, [110 201], [ 72 19 72 19 19 72 19 19 ] 11 3L 8s, 53:19, [110 201], [ 53 19 19 53 19 19 19 53 19 19 19 ]

5 3L 2s, 89:22, [111 200], [ 89 89 22 89 22 ] 8 3L 5s, 67:22, [111 200], [ 67 22 67 22 22 67 22 22 ] 11 3L 8s, 45:22, [111 200], [ 45 22 22 45 22 22 22 45 22 22 22 ]

5 3L 2s, 87:25, [112 199], [ 87 87 25 87 25 ] 8 3L 5s, 62:25, [112 199], [ 62 25 62 25 25 62 25 25 ] 11 3L 8s, 37:25, [112 199], [ 37 25 25 37 25 25 25 37 25 25 25 ]

5 3L 2s, 85:28, [113 198], [ 85 85 28 85 28 ] 8 3L 5s, 57:28, [113 198], [ 57 28 57 28 28 57 28 28 ]

5 3L 2s, 83:31, [114 197], [ 83 83 31 83 31 ] 8 3L 5s, 52:31, [114 197], [ 52 31 52 31 31 52 31 31 ] 11 8L 3s, 31:21, [114 197], [ 31 31 31 21 31 31 31 21 31 31 21 ]

5 3L 2s, 81:34, [115 196], [ 81 81 34 81 34 ] 8 3L 5s, 47:34, [115 196], [ 47 34 47 34 34 47 34 34 ] 11 8L 3s, 34:13, [115 196], [ 34 34 34 13 34 34 34 13 34 34 13 ]

5 3L 2s, 79:37, [116 195], [ 79 79 37 79 37 ]

5 3L 2s, 77:40, [117 194], [ 77 77 40 77 40 ]

5 3L 2s, 75:43, [118 193], [ 75 75 43 75 43 ] 8 5L 3s, 43:32, [118 193], [ 43 43 32 43 43 32 43 32 ] 13 8L 5s, 32:11, [118 193], [ 32 32 11 32 32 11 32 11 32 32 11 32 11 ]

5 3L 2s, 73:46, [119 192], [ 73 73 46 73 46 ] 8 5L 3s, 46:27, [119 192], [ 46 46 27 46 46 27 46 27 ] 13 8L 5s, 27:19, [119 192], [ 27 27 19 27 27 19 27 19 27 27 19 27 19 ]

5 3L 2s, 71:49, [120 191], [ 71 71 49 71 49 ] 8 5L 3s, 49:22, [120 191], [ 49 49 22 49 49 22 49 22 ] 13 5L 8s, 27:22, [120 191], [ 27 22 27 22 22 27 22 27 22 22 27 22 22 ]

5 3L 2s, 69:52, [121 190], [ 69 69 52 69 52 ] 8 5L 3s, 52:17, [121 190], [ 52 52 17 52 52 17 52 17 ] 13 5L 8s, 35:17, [121 190], [ 35 17 35 17 17 35 17 35 17 17 35 17 17 ]

5 3L 2s, 67:55, [122 189], [ 67 67 55 67 55 ] 8 5L 3s, 55:12, [122 189], [ 55 55 12 55 55 12 55 12 ] 13 5L 8s, 43:12, [122 189], [ 43 12 43 12 12 43 12 43 12 12 43 12 12 ]

5 2L 3s, 70:57, [127 184], [ 70 57 70 57 57 ] 7 5L 2s, 57:13, [127 184], [ 57 57 57 13 57 57 13 ] 12 5L 7s, 44:13, [127 184], [ 44 13 44 13 44 13 13 44 13 44 13 13 ]

5 2L 3s, 73:55, [128 183], [ 73 55 73 55 55 ] 7 5L 2s, 55:18, [128 183], [ 55 55 55 18 55 55 18 ] 12 5L 7s, 37:18, [128 183], [ 37 18 37 18 37 18 18 37 18 37 18 18 ]

5 2L 3s, 76:53, [129 182], [ 76 53 76 53 53 ] 7 5L 2s, 53:23, [129 182], [ 53 53 53 23 53 53 23 ] 12 5L 7s, 30:23, [129 182], [ 30 23 30 23 30 23 23 30 23 30 23 23 ]

5 2L 3s, 79:51, [130 181], [ 79 51 79 51 51 ] 7 5L 2s, 51:28, [130 181], [ 51 51 51 28 51 51 28 ] 12 7L 5s, 28:23, [130 181], [ 28 28 23 28 23 28 28 23 28 23 28 23 ]

5 2L 3s, 82:49, [131 180], [ 82 49 82 49 49 ] 7 5L 2s, 49:33, [131 180], [ 49 49 49 33 49 49 33 ] 12 7L 5s, 33:16, [131 180], [ 33 33 16 33 16 33 33 16 33 16 33 16 ]

5 2L 3s, 85:47, [132 179], [ 85 47 85 47 47 ] 7 5L 2s, 47:38, [132 179], [ 47 47 47 38 47 47 38 ] 12 7L 5s, 38:9, [132 179], [ 38 38 9 38 9 38 38 9 38 9 38 9 ]

5 2L 3s, 88:45, [133 178], [ 88 45 88 45 45 ]

5 2L 3s, 91:43, [134 177], [ 91 43 91 43 43 ]

5 2L 3s, 94:41, [135 176], [ 94 41 94 41 41 ] 7 2L 5s, 53:41, [135 176], [ 53 41 41 53 41 41 41 ] 9 7L 2s, 41:12, [135 176], [ 41 41 41 41 12 41 41 41 12 ]

5 2L 3s, 97:39, [136 175], [ 97 39 97 39 39 ] 7 2L 5s, 58:39, [136 175], [ 58 39 39 58 39 39 39 ] 9 7L 2s, 39:19, [136 175], [ 39 39 39 39 19 39 39 39 19 ]

5 2L 3s, 100:37, [137 174], [ 100 37 100 37 37 ] 7 2L 5s, 63:37, [137 174], [ 63 37 37 63 37 37 37 ] 9 7L 2s, 37:26, [137 174], [ 37 37 37 37 26 37 37 37 26 ]

5 2L 3s, 103:35, [138 173], [ 103 35 103 35 35 ] 7 2L 5s, 68:35, [138 173], [ 68 35 35 68 35 35 35 ]

5 2L 3s, 106:33, [139 172], [ 106 33 106 33 33 ] 7 2L 5s, 73:33, [139 172], [ 73 33 33 73 33 33 33 ] 9 2L 7s, 40:33, [139 172], [ 40 33 33 33 40 33 33 33 33 ] 11 9L 2s, 33:7, [139 172], [ 33 33 33 33 33 7 33 33 33 33 7 ]

5 2L 3s, 109:31, [140 171], [ 109 31 109 31 31 ] 7 2L 5s, 78:31, [140 171], [ 78 31 31 78 31 31 31 ] 9 2L 7s, 47:31, [140 171], [ 47 31 31 31 47 31 31 31 31 ] 11 9L 2s, 31:16, [140 171], [ 31 31 31 31 31 16 31 31 31 31 16 ]

5 2L 3s, 112:29, [141 170], [ 112 29 112 29 29 ] 7 2L 5s, 83:29, [141 170], [ 83 29 29 83 29 29 29 ] 9 2L 7s, 54:29, [141 170], [ 54 29 29 29 54 29 29 29 29 ]

5 2L 3s, 115:27, [142 169], [ 115 27 115 27 27 ] 7 2L 5s, 88:27, [142 169], [ 88 27 27 88 27 27 27 ] 9 2L 7s, 61:27, [142 169], [ 61 27 27 27 61 27 27 27 27 ] 11 2L 9s, 34:27, [142 169], [ 34 27 27 27 27 34 27 27 27 27 27 ] 13 11L 2s, 27:7, [142 169], [ 27 27 27 27 27 27 7 27 27 27 27 27 7 ]

5 2L 3s, 118:25, [143 168], [ 118 25 118 25 25 ] 7 2L 5s, 93:25, [143 168], [ 93 25 25 93 25 25 25 ] 9 2L 7s, 68:25, [143 168], [ 68 25 25 25 68 25 25 25 25 ] 11 2L 9s, 43:25, [143 168], [ 43 25 25 25 25 43 25 25 25 25 25 ] 13 11L 2s, 25:18, [143 168], [ 25 25 25 25 25 25 18 25 25 25 25 25 18 ]

7 2L 5s, 98:23, [144 167], [ 98 23 23 98 23 23 23 ] 9 2L 7s, 75:23, [144 167], [ 75 23 23 23 75 23 23 23 23 ] 11 2L 9s, 52:23, [144 167], [ 52 23 23 23 23 52 23 23 23 23 23 ] 13 2L 11s, 29:23, [144 167], [ 29 23 23 23 23 23 29 23 23 23 23 23 23 ]

7 2L 5s, 103:21, [145 166], [ 103 21 21 103 21 21 21 ] 9 2L 7s, 82:21, [145 166], [ 82 21 21 21 82 21 21 21 21 ] 11 2L 9s, 61:21, [145 166], [ 61 21 21 21 21 61 21 21 21 21 21 ] 13 2L 11s, 40:21, [145 166], [ 40 21 21 21 21 21 40 21 21 21 21 21 21 ]

9 2L 7s, 89:19, [146 165], [ 89 19 19 19 89 19 19 19 19 ] 11 2L 9s, 70:19, [146 165], [ 70 19 19 19 19 70 19 19 19 19 19 ] 13 2L 11s, 51:19, [146 165], [ 51 19 19 19 19 19 51 19 19 19 19 19 19 ]

11 2L 9s, 79:17, [147 164], [ 79 17 17 17 17 79 17 17 17 17 17 ] 13 2L 11s, 62:17, [147 164], [ 62 17 17 17 17 17 62 17 17 17 17 17 17 ]

13 2L 11s, 73:15, [148 163], [ 73 15 15 15 15 15 73 15 15 15 15 15 15 ]