Scala analysis: graileq
56% RMS grail + 44% JI grail
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 85.293 cents 85.293194 2: 196.245 cents 196.244721 3: 307.196 cents 307.196247 4: 392.489 cents 392.489441 5: 505.785 cents 505.784825 6: 579.663 cents 579.663091 7: 697.953 cents 697.953206 8: 796.245 cents 796.244721 9: 894.536 cents 894.536236 10: 1012.826 cents 1012.826350 11: 1086.705 cents 1086.704616 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 113.2954 cents 113.2954 1: 85.2932 cents 85.2932 2: 110.9515 cents 110.9515 3: 110.9515 cents 110.9515 4: 85.2932 cents 85.2932 5: 113.2954 cents 113.2954 6: 73.8783 cents 73.8783 7: 118.2901 cents 118.2901 8: 98.2915 cents 98.2915 9: 98.2915 cents 98.2915 10: 118.2901 cents 118.2901 11: 73.8783 cents 73.8783 12: 113.2954 cents 113.2954
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 73.87827 cents 1: 2 85.29319 cents 1: 2 98.29151 cents 1: 2 110.95153 cents 1: 2 113.29538 cents 1: 2 118.29011 cents 2: 2 187.17365 cents 2: 2 192.16838 cents 2: 2 196.24472 cents 2: 1 196.58303 cents 2: 2 198.58858 cents 2: 2 216.58163 cents 2: 1 221.90305 cents 3: 2 272.46684 cents 3: 2 290.45990 cents 3: 2 305.46376 cents 3: 2 307.19625 cents 3: 2 309.54010 cents 3: 2 314.87314 cents 4: 2 383.41837 cents 4: 2 388.75141 cents 4: 2 390.75696 cents 4: 1 392.48944 cents 4: 2 403.75528 cents 4: 2 420.49163 cents 4: 1 433.16326 cents 5: 2 489.04847 cents 5: 2 494.36990 cents 5: 2 501.70849 cents 5: 2 502.04679 cents 5: 2 505.78483 cents 5: 2 507.04153 cents 6: 2 579.66309 cents 6: 1 580.91979 cents 6: 2 587.33999 cents 6: 2 600.00000 cents 6: 2 612.66001 cents 6: 1 619.08021 cents 6: 2 620.33691 cents 7: 2 692.95847 cents 7: 2 694.21517 cents 7: 2 697.95321 cents 7: 2 698.29152 cents 7: 2 705.63010 cents 7: 2 710.95153 cents 8: 1 766.83674 cents 8: 2 779.50837 cents 8: 2 796.24472 cents 8: 1 807.51056 cents 8: 2 809.24304 cents 8: 2 811.24859 cents 8: 2 816.58163 cents 9: 2 885.12686 cents 9: 2 890.45990 cents 9: 2 892.80375 cents 9: 2 894.53624 cents 9: 2 909.54010 cents 9: 2 927.53316 cents 10: 1 978.09695 cents 10: 2 983.41837 cents 10: 2 1001.41142 cents 10: 1 1003.41697 cents 10: 2 1003.75528 cents 10: 2 1007.83162 cents 10: 2 1012.82635 cents 11: 2 1081.70989 cents 11: 2 1086.70462 cents 11: 2 1089.04847 cents 11: 2 1101.70849 cents 11: 2 1114.70681 cents 11: 2 1126.12173 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.45455 = 71/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 85.3 196.2 307.2 392.5 505.8 579.7 698.0 796.2 894.5 1012.8 1086.7 1200.0 85.3 : 111.0 221.9 307.2 420.5 494.4 612.7 711.0 809.2 927.5 1001.4 1114.7 1200.0 196.2 : 111.0 196.2 309.5 383.4 501.7 600.0 698.3 816.6 890.5 1003.8 1089.0 1200.0 307.2 : 85.3 198.6 272.5 390.8 489.0 587.3 705.6 779.5 892.8 978.1 1089.0 1200.0 392.5 : 113.3 187.2 305.5 403.8 502.0 620.3 694.2 807.5 892.8 1003.8 1114.7 1200.0 505.8 : 73.9 192.2 290.5 388.8 507.0 580.9 694.2 779.5 890.5 1001.4 1086.7 1200.0 579.7 : 118.3 216.6 314.9 433.2 507.0 620.3 705.6 816.6 927.5 1012.8 1126.1 1200.0 698.0 : 98.3 196.6 314.9 388.8 502.0 587.3 698.3 809.2 894.5 1007.8 1081.7 1200.0 796.2 : 98.3 216.6 290.5 403.8 489.0 600.0 711.0 796.2 909.5 983.4 1101.7 1200.0 894.5 : 118.3 192.2 305.5 390.8 501.7 612.7 698.0 811.2 885.1 1003.4 1101.7 1200.0 1012.8: 73.9 187.2 272.5 383.4 494.4 579.7 693.0 766.8 885.1 983.4 1081.7 1200.0 1086.7: 113.3 198.6 309.5 420.5 505.8 619.1 693.0 811.2 909.5 1007.8 1126.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.8783 .. 118.2901 cents 44.41185 cents 73.87827 cents 2: 187.1736 .. 221.9031 cents 34.72940 cents 68.88354 cents 3: 272.4668 .. 314.8731 cents 42.40630 cents 50.56379 cents 4: 383.4184 .. 433.1633 cents 49.74489 cents 68.54523 cents 5: 489.0485 .. 507.0415 cents 17.99305 cents 55.88521 cents 6: 579.6631 .. 620.3369 cents 40.67382 cents 72.62157 cents 7: 692.9585 .. 710.9515 cents 17.99305 cents 72.62157 cents 8: 766.8367 .. 816.5816 cents 49.74489 cents 55.88521 cents 9: 885.1269 .. 927.5332 cents 42.40630 cents 68.54523 cents 10: 978.0969 .. 1012.8264 cents 34.72940 cents 50.56379 cents 11: 1081.7099 .. 1126.1217 cents 44.41185 cents 68.88354 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 73.87827 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 118.29011 cents Average / Smallest step : 1.353578 Largest / Average step : 1.182901 Largest / Smallest step : 1.601149 Median interval of one step : 104.62152 cents, amount: 0 Least squares average step : 99.63800 cents, oct.: 1195.65604 cents Scale is strictly proper Step pattern alph. order: ABBACDEFFEDC Step pattern size order : BDDBEAFCCFAE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 50.56379 cents Scale diversity : 1.303378 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.650629 Rothenberg efficiency : 0.243687 redundancy: 0.756313 Efficiency x scale size : 2.924242 Number of different interval sizes : 71 = 6.45455 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.45455 = 71/11 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 0.33831 cents Number of recognisable fifths : 12, average 700.0000 cents Best fifths form a closed circle Formal octave complements present : 1 = 8.3333% Limited transpositions with margin 40.6738 cents: 7 Limited inverse transpositions : 4 Inversional symmetry on degrees : 2 8 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 9.8956 c. M:-20.3369 c. Twelve-tone Chromatic (1/11-comma) 27: 2 2 3 2 2 2 3 2 2 3 1 3 SP D3 SD: 10.8921 c. M: 20.0379 c. 31: 2 3 3 2 3 2 3 3 2 3 2 3 SP M ME SD: 6.1734 c. M:-16.6585 c. 33: 2 3 3 3 3 2 3 3 3 3 2 3 SP D3 SD: 9.2430 c. M: 16.2872 c. 36: 3 3 3 3 3 2 4 3 3 3 3 3 SP T3 SD: 8.8052 c. M:-14.7068 c. 39: 3 3 4 3 3 3 4 3 3 4 2 4 SP D3 SD: 7.4353 c. M: 13.4771 c. 42: 3 4 4 3 4 2 4 4 3 4 3 4 SP D3 SD: 7.4623 c. M: 12.8264 c. 43: 3 4 4 3 4 3 4 4 3 4 3 4 SP M ME SD: 5.0144 c. M:-13.0576 c. 45: 3 4 5 3 4 3 4 4 4 4 3 4 SP D3 SD: 7.1689 c. M:-12.8038 c. 47: 3 5 4 3 5 3 4 4 4 5 3 4 SP SD: 7.1017 c. M:-11.1677 c. 50: 3 5 5 3 5 3 5 4 4 5 3 5 SP D3 S SD: 6.0503 c. M: 13.2932 c. 54: 4 5 5 4 5 3 5 5 4 6 3 5 SP SD: 5.4153 c. M:-9.3959 c. 56: 4 5 5 4 6 3 6 4 5 5 4 5 SP SD: 5.6179 c. M:-9.1897 c. 60: 4 6 5 5 5 4 6 5 5 6 3 6 SP SD: 5.2317 c. M:-7.5106 c. 62: 4 6 6 4 6 4 6 5 5 6 4 6 SP D3 S SD: 3.9486 c. M: 7.8738 c. 74: 5 7 7 5 7 5 7 6 6 7 5 7 SP D3 S SD: 3.2137 c. M: 7.4209 c. 76: 5 7 7 6 7 5 7 6 7 7 5 7 SP SD: 4.6807 c. M: 7.1962 c. 77: 5 8 7 5 7 5 8 6 6 8 5 7 SP SD: 4.5852 c. M: 7.3711 c. 79: 6 7 7 6 7 5 8 6 7 8 5 7 SP SD: 4.0425 c. M:-6.9663 c. 82: 6 7 8 6 8 5 8 6 7 8 5 8 SP SD: 4.1447 c. M:-6.4103 c. 83: 6 8 7 6 8 5 8 7 7 8 5 8 SP SD: 2.6761 c. M:-6.1649 c. 95: 7 9 8 7 9 6 9 8 8 9 6 9 SP SD: 2.6580 c. M:-5.8605 c. 97: 7 9 9 7 9 6 9 8 8 10 6 9 SP SD: 2.7907 c. M: 5.1697 c. 98: 7 9 9 7 9 6 10 8 8 10 6 9 SP S SD: 2.1501 c. M: 4.1529 c. 110: 8 10 10 8 10 7 11 9 9 11 7 10 SP S SD: 1.9504 c. M:-4.2045 c. 118: 8 11 11 9 11 7 12 9 10 12 7 11 SP SD: 2.8234 c. M:-4.1228 c. 122: 9 11 11 9 11 8 12 10 10 12 7 12 SP SD: 2.1911 c. M: 4.7374 c. 126: 9 12 11 9 12 8 12 11 10 12 8 12 SP SD: 2.2513 c. M:-3.7553 c. 128: 9 12 12 9 12 8 12 11 10 13 8 12 SP SD: 1.9238 c. M: 4.2032 c. 137: 10 12 13 10 13 8 14 11 11 14 8 13 SP SD: 2.0188 c. M: 3.5440 c. 140: 10 13 13 10 13 9 13 12 11 14 9 13 SP SD: 1.9507 c. M: 3.6675 c. 141: 10 13 13 10 13 9 14 12 11 14 9 13 SP SD: 1.7847 c. M:-3.7553 c. 149: 11 13 14 11 14 9 15 12 12 15 9 14 SP SD: 1.8495 c. M:-3.2974 c. 160: 11 15 15 11 15 10 16 13 13 16 10 15 SP S SD: 1.7736 c. M: 3.2848 c. 168: 12 15 16 12 16 10 17 13 14 17 10 16 SP SD: 1.7422 c. M: 3.3876 c. 169: 12 16 15 12 16 11 16 14 14 17 10 16 SP SD: 1.7162 c. M:-2.5854 c. 172: 12 16 16 12 16 11 17 14 14 17 11 16 SP S SD: 1.4787 c. M: 3.4592 c. 184: 13 17 17 13 18 11 18 15 15 18 12 17 SP SD: 1.3766 c. M:-2.9108 c. 192: 14 17 18 14 18 12 19 15 16 19 12 18 SP SD: 1.5298 c. M: 2.4947 c. 196: 14 18 18 14 19 12 19 16 16 19 12 19 SP S SD: 1.5276 c. M: 3.0311 c. 199: 14 19 18 14 19 12 20 16 16 20 12 19 SP SD: 1.2354 c. M:-2.7503 c. 200: 14 19 18 14 19 13 19 17 16 20 12 19 SP SD: 1.5834 c. M: 2.4894 c. 201: 14 19 18 15 19 12 20 16 17 20 12 19 SP SD: 1.5006 c. M: 2.7186 c. 208: 15 19 19 15 20 12 21 17 17 21 12 20 SP S SD: 1.4663 c. M: 2.7400 c. 211: 15 20 19 15 20 13 21 17 17 21 13 20 SP SD: 1.0747 c. M:-2.8074 c. 220: 16 20 20 16 21 13 22 18 18 22 13 21 SP S SD: 1.1553 c. M:-1.9795 c. 223: 16 20 21 16 21 14 22 18 18 22 14 21 SP SD: 1.1266 c. M: 2.5227 c. 225: 16 21 21 16 21 14 22 18 19 22 14 21 SP SD: 1.3272 c. M:-2.1772 c. 226: 16 21 21 16 21 14 22 19 18 23 14 21 SP SD: 1.3083 c. M: 2.5008 c. 232: 16 22 21 17 22 14 23 19 19 23 14 22 SP SD: 1.0730 c. M: 2.5346 c. 244: 17 23 22 18 23 15 24 20 20 24 15 23 SP SD: 0.9581 c. M: 2.2782 c. 250: 18 23 23 18 23 16 24 21 20 25 15 24 SP SD: 1.2251 c. M: 1.9532 c. 251: 18 23 23 18 24 15 25 21 20 25 15 24 SP SD: 1.0099 c. M:-2.1617 c. 256: 18 24 24 18 24 16 25 21 21 25 16 24 SP S SD: 1.0118 c. M:-2.1788 c. 263: 19 24 24 19 25 16 26 22 21 26 16 25 SP SD: 0.9298 c. M:-2.2344 c. 271: 19 25 25 20 25 17 27 22 22 27 16 26 SP SD: 1.2274 c. M: 1.8338 c. 275: 20 25 25 20 26 17 27 22 23 27 17 26 SP SD: 1.0091 c. M: 2.0629 c. 282: 20 26 26 20 27 17 28 23 23 28 17 27 SP S SD: 0.7554 c. M: 1.5982 c. 294: 21 27 27 21 28 18 29 24 24 29 18 28 SP S SD: 0.5658 c. M: 1.0738 c. 437: 31 40 41 31 41 27 43 36 36 43 27 41 SP SD: 0.5424 c. M: 1.2790 c. 466: 33 43 43 33 44 29 46 38 38 46 29 44 SP S SD: 0.6593 c. M: 1.0731 c. 468: 33 44 43 33 44 29 46 39 38 46 29 44 SP SD: 0.6221 c. M:-1.1912 c. 470: 33 44 43 34 44 29 46 39 38 47 29 44 SP SD: 0.6952 c. M: 1.0379 c. 476: 34 44 44 34 45 29 47 39 39 47 29 45 SP S SD: 0.4889 c. M:-0.9379 c. 488: 35 45 45 35 46 30 48 40 40 48 30 46 SP S SD: 0.5485 c. M:-0.9532 c. 495: 35 46 46 35 47 30 49 40 41 49 30 47 SP SD: 0.5403 c. M: 1.0932 c. 507: 36 47 47 36 48 31 50 41 42 50 31 48 SP SD: 0.4302 c. M: 0.9784 c. 519: 37 48 48 37 49 32 51 42 43 51 32 49 SP SD: 0.4386 c. M: 0.8690 c. 538: 38 50 50 38 51 33 53 44 44 53 33 51 SP S SD: 0.3312 c. M:-0.6104 c. 550: 39 51 51 39 52 34 54 45 45 54 34 52 SP S SD: 0.3240 c. M:-0.7005 c. 636: 45 59 59 45 60 39 63 52 52 63 39 60 SP S SD: 0.2385 c. M: 0.4178 c. 648: 46 60 60 46 61 40 64 53 53 64 40 61 SP S SD: 0.1585 c. M:-0.3324 c. 930: 66 86 86 66 88 57 92 76 76 92 57 88 SP S SD: 0.1832 c. M: 0.3427 c. 942: 67 87 87 67 89 58 93 77 77 93 58 89 SP S SD: 0.1209 c. M: 0.2687 c. 1480: 105 137 137 105 140 91 146 121 121 146 91 140 SP S SD: 0.1298 c. M: 0.2181 c. 1492: 106 138 138 106 141 92 147 122 122 147 92 141 SP S SD: 0.1253 c. M:-0.2297 c. 1578: 112 146 146 112 149 97 156 129 129 156 97 149 SP S SD: 0.1165 c. M: 0.2397 c. 1590: 113 147 147 113 150 98 157 130 130 157 98 150 SP S SD: 0.0875 c. M: 0.1966 c. 1602: 114 148 148 114 151 99 158 131 131 158 99 151 SP S SD: 0.1136 c. M:-0.1868 c. 1706: 121 158 158 121 161 105 168 140 140 168 105 161 SP S SD: 0.1117 c. M:-0.1895 c. 1718: 122 159 159 122 162 106 169 141 141 169 106 162 SP S SD: 0.1086 c. M:-0.2251 c. 1929: 137 178 179 137 182 119 190 158 158 190 119 182 SP SD: 0.1043 c. M: 0.2883 c. 1988: 141 184 184 141 188 122 196 163 163 196 122 188 SP S SD: 0.1176 c. M: 0.1862 c. 2000: 142 185 185 142 189 123 197 164 164 197 123 189 SP S SD: 0.0731 c. M: 0.1532 c. 2012: 143 186 186 143 190 124 198 165 165 198 124 190 SP S SD: 0.0634 c. M: 0.1401 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x x 4 S SD: 2.0009 cents 3 x x x x 4 x x x 5 x x 6 S SD: 4.2621 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.1529 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 4.0319 cents 6 x x 7 x 8 x 9 x 10:11 x 12 S SD: 9.3401 cents 7 x 8 x 9 x 10 x 11:12 x 13:14 S SD: 11.4006 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 8.6745 cents 9 x 10:11 x 12:13 x 14:15:16:17:18 S SD: 9.0834 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 7.2381 cents 11 x 12:13:14:15 x 16:17:18:20:21:22 S SD: 10.7553 cents 12:13 x 14:15:16:17:18:19:20:22 x 24 S SD: 8.1009 cents 13:14:15 x 16:17:18:19:21:22:23:24:26 SD: 9.9312 cents 14:15:16:17:18:19:20:21:22:23:25:26:28 SD: 7.7888 cents 15:16:17:18:19:20:21:22:24:25:27:28:30 SD: 4.7313 cents 20:21:22:24:25:27:28:30:32:34:36:37:40 SD: 4.3121 cents 24:25:27:29:30:32:34:36:38:40:43:45:48 SD: 3.1902 cents 32:34:36:38:40:43:45:48:51:54:57:60:64 SD: 2.8390 cents 35:37:39:42:44:47:49:52:55:59:63:66:70 SD: 2.5040 cents 36:38:40:43:45:48:50:54:57:60:65:67:72 SD: 2.3989 cents 40:42:45:48:50:54:56:60:63:67:72:75:80 SD: 1.8757 cents 50:53:56:60:63:67:70:75:79:84:90:94:100 SD: 1.8445 cents 55:58:62:66:69:74:77:82:87:92:99:103:110 SD: 1.6611 cents 56:59:63:67:70:75:78:84:89:94:101:105:112 SD: 1.4273 cents 58:61:65:69:73:78:81:87:92:97:104:109:116 SD: 1.2002 cents 77:81:86:92:97:103:108:115:122:129:138:144:154 SD: 1.0355 cents 82:86:92:98:103:110:115:123:130:137:147:154:164 SD: 1.0008 cents 83:87:93:99:104:111:116:124:131:139:149:155:166 SD: 0.8708 cents 98:103:110:117:123:131:137:147:155:164:176:184:196 SD: 0.7223 cents 103:108:115:123:129:138:144:154:163:173:185:193:206 SD: 0.6741 cents 118:124:132:141:148:158:165:177:187:198:212:221:236 SD: 0.4444 cents 176:185:197:210:221:236:246:263:279:295:316:330:352 SD: 0.3967 cents 200:210:224:239:251:268:280:299:317:335:359:375:400 SD: 0.3810 cents 201:211:225:240:252:269:281:301:318:337:361:377:402 SD: 0.3363 cents 216:227:242:258:271:289:302:323:342:362:388:405:432 SD: 0.2746 cents 259:272:290:309:325:347:362:388:410:434:465:485:518 SD: 0.2527 cents 274:288:307:327:344:367:383:410:434:459:492:513:548 SD: 0.2292 cents 334:351:374:399:419:447:467:500:529:560:600:626:668 SD: 0.2017 cents 377:396:422:450:473:505:527:564:597:632:677:706:754 SD: 0.1497 cents 433:455:485:517:543:580:605:648:686:726:777:811:866 SD: 0.1069 cents