Scala analysis: DIMENSIONEC
Dimension EC Scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 119.558 cents 119.558000 2: 196.199 cents 196.198500 3: 315.641 cents 315.641300 4: 352.751 cents 352.750800 5: 505.775 cents 505.775000 6: 620.428 cents 620.428400 7: 701.955 cents 701.955000 8: 822.859 cents 822.859120 9: 891.959 cents 891.959400 10: 1011.526 cents 1011.526340 11: 1047.158 cents 1047.158100 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 152.8419 cents 152.8419 1: 119.5580 cents 119.5580 2: 76.6405 cents 76.6405 3: 119.4428 cents 119.4428 4: 37.1095 cents 37.1095 5: 153.0242 cents 153.0242 6: 114.6534 cents 114.6534 7: 81.5266 cents 81.5266 8: 120.9041 cents 120.9041 9: 69.1003 cents 69.1003 10: 119.5669 cents 119.5669 11: 35.6318 cents 35.6318 12: 152.8419 cents 152.8419
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 35.63176 cents 1: 1 37.10950 cents 1: 1 69.10028 cents 1: 1 76.64050 cents 1: 1 81.52660 cents 1: 1 114.65340 cents 1: 1 119.44280 cents 1: 1 119.55800 cents 1: 1 119.56694 cents 1: 1 120.90412 cents 1: 1 152.84190 cents 1: 1 153.02420 cents 2: 1 155.19870 cents 2: 1 156.55230 cents 2: 1 188.47366 cents 2: 1 188.66722 cents 2: 1 190.00440 cents 2: 1 190.13370 cents 2: 1 196.08330 cents 2: 1 196.18000 cents 2: 1 196.19850 cents 2: 1 202.43072 cents 2: 1 267.67760 cents 2: 1 272.39990 cents 3: 1 224.29898 cents 3: 1 233.19280 cents 3: 1 271.53100 cents 3: 1 304.78710 cents 3: 1 308.03166 cents 3: 1 308.04060 cents 3: 1 309.57134 cents 3: 1 309.57650 cents 3: 1 315.64130 cents 3: 1 317.08412 cents 3: 1 349.04040 cents 3: 1 349.20420 cents 4: 1 345.20310 cents 4: 1 352.75080 cents 4: 1 377.14088 cents 4: 1 384.67216 cents 4: 1 386.18440 cents 4: 1 386.21700 cents 4: 1 386.31370 cents 4: 1 391.09794 cents 4: 1 424.22990 cents 4: 1 427.59860 cents 4: 1 468.48320 cents 4: 1 470.10832 cents 5: 1 426.72970 cents 5: 1 496.69888 cents 5: 1 498.04500 cents 5: 1 500.87040 cents 5: 1 504.11496 cents 5: 1 504.23910 cents 5: 1 505.59270 cents 5: 1 505.75134 cents 5: 1 505.75650 cents 5: 1 505.77500 cents 5: 1 507.21782 cents 5: 1 539.20860 cents 6: 1 541.22446 cents 6: 1 541.38310 cents 6: 1 573.33938 cents 6: 1 576.31810 cents 6: 1 579.57160 cents 6: 1 582.39700 cents 6: 1 617.60300 cents 6: 1 620.42840 cents 6: 1 623.68190 cents 6: 1 626.66062 cents 6: 1 658.61690 cents 6: 1 658.77554 cents 7: 1 660.79140 cents 7: 1 692.78218 cents 7: 1 694.22500 cents 7: 1 694.24350 cents 7: 1 694.24866 cents 7: 1 694.40730 cents 7: 1 695.76090 cents 7: 1 695.88504 cents 7: 1 699.12960 cents 7: 1 701.95500 cents 7: 1 703.30112 cents 7: 1 773.27030 cents 8: 1 729.89168 cents 8: 1 731.51680 cents 8: 1 772.40140 cents 8: 1 775.77010 cents 8: 1 808.90206 cents 8: 1 813.68630 cents 8: 1 813.78300 cents 8: 1 813.81560 cents 8: 1 815.32784 cents 8: 1 822.85912 cents 8: 1 847.24920 cents 8: 1 854.79690 cents 9: 1 850.79580 cents 9: 1 850.95960 cents 9: 1 882.91588 cents 9: 1 884.35870 cents 9: 1 890.42350 cents 9: 1 890.42866 cents 9: 1 891.95940 cents 9: 1 891.96834 cents 9: 1 895.21290 cents 9: 1 928.46900 cents 9: 1 966.80720 cents 9: 1 975.70102 cents 10: 1 927.60010 cents 10: 1 932.32240 cents 10: 1 997.56928 cents 10: 1 1003.80150 cents 10: 1 1003.82000 cents 10: 1 1003.91670 cents 10: 1 1009.86630 cents 10: 1 1009.99560 cents 10: 1 1011.33278 cents 10: 1 1011.52634 cents 10: 1 1043.44770 cents 10: 1 1044.80130 cents 11: 1 1046.97580 cents 11: 1 1047.15810 cents 11: 1 1079.09588 cents 11: 1 1080.43306 cents 11: 1 1080.44200 cents 11: 1 1080.55720 cents 11: 1 1085.34660 cents 11: 1 1118.47340 cents 11: 1 1123.35950 cents 11: 1 1130.89972 cents 11: 1 1162.89050 cents 11: 1 1164.36824 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 12.00000 = 12
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 119.6 196.2 315.6 352.8 505.8 620.4 702.0 822.9 892.0 1011.5 1047.2 1200.0 119.6 : 76.6 196.1 233.2 386.2 500.9 582.4 703.3 772.4 892.0 927.6 1080.4 1200.0 196.2 : 119.4 156.6 309.6 424.2 505.8 626.7 695.8 815.3 851.0 1003.8 1123.4 1200.0 315.6 : 37.1 190.1 304.8 386.3 507.2 576.3 695.9 731.5 884.4 1003.9 1080.6 1200.0 352.8 : 153.0 267.7 349.2 470.1 539.2 658.8 694.4 847.2 966.8 1043.4 1162.9 1200.0 505.8 : 114.7 196.2 317.1 386.2 505.8 541.4 694.2 813.8 890.4 1009.9 1047.0 1200.0 620.4 : 81.5 202.4 271.5 391.1 426.7 579.6 699.1 775.8 895.2 932.3 1085.3 1200.0 702.0 : 120.9 190.0 309.6 345.2 498.0 617.6 694.2 813.7 850.8 1003.8 1118.5 1200.0 822.9 : 69.1 188.7 224.3 377.1 496.7 573.3 692.8 729.9 882.9 997.6 1079.1 1200.0 892.0 : 119.6 155.2 308.0 427.6 504.2 623.7 660.8 813.8 928.5 1010.0 1130.9 1200.0 1011.5: 35.6 188.5 308.0 384.7 504.1 541.2 694.2 808.9 890.4 1011.3 1080.4 1200.0 1047.2: 152.8 272.4 349.0 468.5 505.6 658.6 773.3 854.8 975.7 1044.8 1164.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 35.6318 .. 153.0242 cents 117.39244 cents 35.63176 cents 2: 155.1987 .. 272.3999 cents 117.20120 cents 2.17450 cents 3: 224.2990 .. 349.2042 cents 124.90522 cents -48.10092 cents 4: 345.2031 .. 470.1083 cents 124.90522 cents -4.00110 cents 5: 426.7297 .. 539.2086 cents 112.47890 cents -43.37862 cents 6: 541.2245 .. 658.7755 cents 117.55108 cents 2.01586 cents 7: 660.7914 .. 773.2703 cents 112.47890 cents 2.01586 cents 8: 729.8917 .. 854.7969 cents 124.90522 cents -43.37862 cents 9: 850.7958 .. 975.7010 cents 124.90522 cents -4.00110 cents 10: 927.6001 .. 1044.8013 cents 117.20120 cents -48.10092 cents 11: 1046.9758 .. 1164.3682 cents 117.39244 cents 2.17450 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 35.63176 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 153.02420 cents Average / Smallest step : 2.806485 Largest / Average step : 1.530242 Largest / Smallest step : 4.294601 Median interval of one step : 117.04810 cents, amount: 0 Least squares average step : 99.50696 cents, oct.: 1194.08349 cents Scale is not proper Step pattern alph. order: ABCDEFGHIJKL Step pattern size order : HDGBLFEJCIAK Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.86890 cents Scale diversity : 1.527326 Lumma stability : 0.066370 Lumma impropriety factor : 0.159134 Rothenberg efficiency : 0.166667 redundancy: 0.833333 Efficiency x scale size : 2.000000 Number of different interval sizes : 132 = 12.00000 / class Number of one step interval sizes : 12 Highest interval variety : 12 Mean interval variety : 12.00000 = 12 Median interval variety : 12 Lowest interval variety : 12 Smallest interval difference : 0.00516 cents Number of recognisable fifths : 10, average 696.5938 cents Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
12: 1 1 1 0 2 1 1 1 1 1 0 2 N T3 SD: 23.8444 c. M: 52.7508 c. 13: 1 1 1 1 1 2 1 1 1 1 0 2 N D3 SD: 26.8548 c. M: 44.2365 c. 16: 2 1 1 1 2 1 1 2 1 2 0 2 N D3 SD: 21.5386 c. M:-38.4737 c. 17: 2 1 2 0 2 2 1 2 1 1 1 2 N D3 SD: 19.1427 c. M:-37.2999 c. 19: 2 1 2 1 2 2 1 2 1 2 1 2 P M ME SD: 11.9785 c. M:-26.5261 c. Yasser's Supradiatonic, Genus diatonico-chromaticum inverse 23: 2 2 2 1 3 2 1 3 1 2 1 3 N SD: 12.8700 c. M: 23.6941 c. 24: 2 2 2 1 3 2 2 2 2 2 1 3 P T3 SD: 12.3552 c. M: 22.8591 c. Ice Bookshop 26: 3 1 3 1 3 2 2 3 1 3 1 3 N D3 I SD: 12.3922 c. M: 20.4284 c. 30: 3 2 3 1 4 3 2 3 1 3 1 4 N SD: 11.6123 c. M:-19.5716 c. 31: 3 2 3 1 4 3 2 3 2 3 1 4 N SD: 4.4667 c. M: 9.9559 c. 50: 5 3 5 2 6 5 3 5 3 5 2 6 N SD: 4.9019 c. M:-8.8419 c. 60: 6 4 6 2 7 6 4 6 4 6 1 8 N SD: 5.1593 c. M:-8.4737 c. 61: 6 4 6 2 8 6 4 6 3 6 2 8 N SD: 5.0342 c. M:-9.0798 c. 64: 6 4 7 2 8 6 4 7 4 6 2 8 N SD: 4.9667 c. M: 8.6985 c. 68: 7 4 7 2 9 6 5 7 4 6 2 9 N SD: 4.6406 c. M:-8.0406 c. 71: 7 5 7 2 9 7 5 7 4 7 2 9 N SD: 4.2657 c. M:-7.9042 c. 73: 7 5 7 2 10 7 5 7 4 8 2 9 N SD: 4.5403 c. M:-7.6517 c. 75: 7 5 8 2 10 7 5 7 5 7 2 10 N SD: 4.8049 c. M: 7.5580 c. 77: 8 5 7 3 9 8 5 8 4 8 2 10 N SD: 4.1679 c. M: 7.0737 c. 79: 8 5 8 2 10 8 5 8 5 8 2 10 N SD: 3.2714 c. M:-6.1952 c. 87: 9 5 9 3 11 8 6 9 5 8 3 11 N SD: 3.6156 c. M:-5.8699 c. 89: 9 6 8 3 12 8 6 9 5 9 3 11 N SD: 3.4673 c. M:-6.5846 c. 91: 9 6 9 3 11 9 6 9 6 9 2 12 N SD: 3.4266 c. M: 5.3999 c. 92: 9 6 9 3 12 9 6 9 5 10 2 12 N SD: 3.3238 c. M:-5.8650 c. 93: 9 6 9 3 12 9 6 10 5 9 3 12 N SD: 3.5236 c. M: 5.9639 c. 95: 10 6 9 3 12 9 7 9 6 9 3 12 N SD: 3.4510 c. M:-6.7578 c. 98: 10 6 10 3 12 10 6 10 6 10 3 12 N SD: 3.3588 c. M:-5.9031 c. 99: 10 6 10 3 13 9 7 10 6 9 3 13 N SD: 2.9736 c. M: 5.4657 c. 102: 10 7 10 3 13 10 7 10 6 10 3 13 N SD: 2.0894 c. M:-3.9274 c. 109: 11 7 11 3 14 10 8 11 6 11 3 14 N SD: 2.1156 c. M: 3.9146 c. 128: 13 8 13 4 16 12 9 13 7 13 4 16 N SD: 1.9903 c. M:-3.4992 c. 133: 13 9 13 4 17 13 9 13 8 13 4 17 N SD: 1.4553 c. M:-2.2977 c. 140: 14 9 14 4 18 13 10 14 8 14 4 18 N SD: 1.2609 c. M: 3.2855 c. 159: 16 10 16 5 20 15 11 16 9 16 5 20 N SD: 1.1248 c. M:-1.9662 c. 171: 17 11 17 5 22 16 12 17 10 17 5 22 N SD: 1.2745 c. M: 2.8845 c. 190: 19 12 19 6 24 18 13 19 11 19 6 24 N SD: 1.0181 c. M: 1.8065 c. 244: 24 16 24 8 31 23 17 24 14 25 7 31 N SD: 1.1700 c. M: 1.7955 c. 251: 25 16 25 8 32 24 17 25 15 25 7 32 N SD: 1.0266 c. M:-2.0645 c. 261: 26 17 26 8 33 25 18 26 15 26 8 33 N SD: 0.9130 c. M:-1.6001 c. 273: 27 18 27 8 35 26 19 27 16 27 8 35 N SD: 0.9018 c. M:-1.6037 c. 280: 28 18 28 8 36 27 19 28 16 28 8 36 N SD: 0.8796 c. M:-1.5016 c. 282: 28 18 28 9 36 27 19 28 17 28 8 36 N SD: 0.8735 c. M:-1.6576 c. 292: 29 19 29 9 37 28 20 29 17 29 9 37 N SD: 0.6415 c. M:-1.0618 c. 354: 35 23 35 11 45 34 24 36 20 35 11 45 N SD: 0.6209 c. M: 1.3568 c. 385: 38 25 38 12 49 37 26 39 22 38 12 49 N SD: 0.7343 c. M: 1.6562 c. 391: 39 25 39 12 50 37 27 39 23 39 11 50 N SD: 0.6489 c. M:-1.2614 c. 408: 41 26 40 13 52 39 28 41 23 41 12 52 N SD: 0.6358 c. M:-1.0302 c. 410: 41 26 41 13 52 39 28 41 24 41 12 52 N SD: 0.6693 c. M:-1.3955 c. 422: 42 27 42 13 54 40 29 42 25 42 12 54 N SD: 0.5598 c. M: 1.0582 c. 432: 43 28 43 13 55 41 30 43 25 43 13 55 N SD: 0.6106 c. M:-1.0254 c. 433: 43 28 43 13 56 41 29 44 25 43 13 55 N SD: 0.5966 c. M:-1.3844 c. 439: 44 28 43 14 56 42 30 44 25 44 13 56 N SD: 0.5534 c. M: 1.2905 c. 441: 44 28 44 14 56 42 30 44 26 44 13 56 N SD: 0.5359 c. M: 1.0904 c. 448: 45 28 45 14 57 43 30 45 26 45 13 57 N SD: 0.6306 c. M:-1.0002 c. 453: 45 29 45 14 58 43 31 46 26 45 13 58 N SD: 0.5156 c. M:-0.9819 c. 470: 47 30 47 14 60 45 32 47 27 47 14 60 N SD: 0.5160 c. M:-0.9544 c. 472: 47 30 47 15 60 45 32 48 27 47 14 60 N SD: 0.4066 c. M:-0.8697 c. 503: 50 32 50 16 64 48 34 51 29 50 15 64 N SD: 0.3576 c. M: 0.7308 c. 605: 60 39 60 19 77 58 41 61 35 60 18 77 N SD: 0.3095 c. M:-0.6026 c. 643: 64 41 64 20 82 61 44 65 37 64 19 82 N SD: 0.2829 c. M: 0.8328 c. 650: 65 41 65 20 83 62 44 66 37 65 19 83 N SD: 0.3152 c. M:-0.5255 c. 674: 67 43 67 21 86 64 46 68 39 67 20 86 N SD: 0.3756 c. M: 0.8438 c. 681: 68 43 68 21 87 65 46 69 39 68 20 87 N SD: 0.3357 c. M: 0.6334 c. 745: 74 48 74 23 95 71 51 75 43 74 22 95 N SD: 0.2350 c. M:-0.3896 c. 752: 75 48 75 23 96 72 51 76 43 75 22 96 N SD: 0.2448 c. M:-0.5451 c. 776: 77 50 77 24 99 74 53 78 45 77 23 99 N SD: 0.2394 c. M: 0.4858 c. 783: 78 50 78 24 100 75 53 79 45 78 23 100 N SD: 0.1668 c. M: 0.4148 c. 942: 94 60 94 29 120 90 64 95 54 94 28 120 N SD: 0.1295 c. M:-0.2823 c. 973: 97 62 97 30 124 93 66 98 56 97 29 124 N SD: 0.1547 c. M: 0.2842 c. 1075: 107 69 107 33 137 103 73 108 62 107 32 137 N SD: 0.1626 c. M:-0.2666 c. 1224: 122 78 122 38 156 117 83 123 71 122 36 156 N SD: 0.1566 c. M: 0.3101 c. 1286: 128 82 128 40 164 123 87 130 74 128 38 164 N SD: 0.1519 c. M: 0.2447 c. 1414: 141 90 141 44 180 135 96 143 81 141 42 180 N SD: 0.1494 c. M:-0.3375 c. 1426: 142 91 142 44 182 136 97 144 82 142 42 182 N SD: 0.1422 c. M: 0.3138 c. 1445: 144 92 144 45 184 138 98 146 83 144 43 184 N SD: 0.1173 c. M: 0.2249 c. 1547: 154 99 154 48 197 148 105 156 89 154 46 197 N SD: 0.0938 c. M:-0.1904 c. 1578: 157 101 157 49 201 151 107 159 91 157 47 201 N SD: 0.0811 c. M: 0.1664 c. 1718: 171 110 171 53 219 164 117 173 99 171 51 219 N SD: 0.0877 c. M: 0.1723 c. 2166: 216 138 216 67 276 207 147 218 125 216 64 276 N SD: 0.0952 c. M:-0.1578 c. 2190: 218 140 218 68 279 209 149 221 126 218 65 279 N SD: 0.0862 c. M:-0.1546 c. 2221: 221 142 221 69 283 212 151 224 128 221 66 283 N SD: 0.0931 c. M: 0.1673 c. 2228: 222 142 222 69 284 213 151 225 128 222 66 284 N SD: 0.0834 c. M: 0.1597 c. 2330: 232 149 232 72 297 223 158 235 134 232 69 297 N SD: 0.0826 c. M:-0.1725 c. 2361: 235 151 235 73 301 226 160 238 136 235 70 301 N SD: 0.0789 c. M:-0.1561 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: 0.0000 cents 3 x x x x 4 x x x 5 x x 6 S SD: 3.6136 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 13.5780 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 7.8959 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 8.3349 cents 7 x 8 x x 9:10 x 11:12 x 13:14 S SD: 14.3967 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 10.5221 cents 9 x 10 x 11:12:13 x 14:15:16 x 18 S SD: 8.0953 cents 10 x 11:12 x 13:14:15:16:17:18 x 20 S SD: 8.5362 cents 11:12 x 13 x 15:16:17:18 x x 20:22 SD: 10.5607 cents 12:13 x 14:15:16:17:18:19:20 x 22:24 S SD: 7.0979 cents 13:14:15 x 16:17:19:20:21:22:23:24:26 SD: 8.5878 cents 14:15:16 x 17:19:20:21 x 23:25:26:28 SD: 6.1255 cents 15:16:17:18 x 20:21:23:24:25:27 x 30 SD: 6.0042 cents 16:17:18:19:20:21:23:24:26:27 x 29:32 SD: 5.6250 cents 18:19:20 x 22:24:26:27:29:30:32:33:36 SD: 3.5480 cents 19:20:21:23 x 25:27:29:31:32:34:35:38 SD: 6.1243 cents 20:21:22:24:25:27:29:30:32:33:36:37:40 SD: 5.9556 cents 21:23:24:25:26:28:30:32:34:35:38 x 42 SD: 6.0098 cents 22:24:25:26:27:29:31:33:35:37:39:40:44 SD: 5.7487 cents 23:25:26 x 28:31:33:35:37:39:41:42:46 SD: 4.4680 cents 24:26:27:29 x 32:34:36:39:40:43:44:48 SD: 3.2862 cents 26:28:29:31:32:35:37:39:42:44:47:48:52 SD: 2.9592 cents 28:30:31 x 34:38:40:42:45:47:50:51:56 SD: 3.3721 cents 30:32:34:36:37:40:43:45:48:50:54:55:60 SD: 2.4137 cents 33:35:37:40 x 44:47:50:53:55:59:60:66 SD: 3.2691 cents 34:36:38:41:42:46:49:51:55:57:61:62:68 SD: 2.9952 cents 35:38:39:42:43:47:50:53:56:59:63:64:70 SD: 2.8664 cents 36:39:40:43:44:48:52:54:58:60:65:66:72 SD: 2.8472 cents 39:42:44:47:48:52:56:59:63:65:70:71:78 SD: 2.4441 cents 40:43:45:48:49:54:57:60:64:67:72:73:80 SD: 1.8454 cents 44:47:49:53:54:59:63:66:71:74:79:81:88 SD: 1.5882 cents 56:60:63:67:69:75:80:84:90:94:100:103:112 SD: 1.4786 cents 58:62:65:70:71:78:83:87:93:97:104:106:116 SD: 1.2283 cents 70:75:78:84:86:94:100:105:113:117:126:128:140 SD: 1.2052 cents 74:79:83:89:91:99:106:111:119:124:133:135:148 SD: 1.0253 cents 84:90:94:101:103:113:120:126:135:141:151:154:168 SD: 0.9313 cents 98:105:110:118:120:131:140:147:158:164:176:179:196 SD: 0.8822 cents 100:107:112:120:123:134:143:150:161:167:179:183:200 SD: 0.7139 cents 110:118:123:132:135:147:157:165:177:184:197:201:220 SD: 0.7058 cents 124:133:139:149:152:166:177:186:199:208:222:227:248 SD: 0.6920 cents 125:134:140:150:153:167:179:188:201:209:224:229:250 SD: 0.6334 cents 141:151:158:169:173:189:202:212:227:236:253:258:282 SD: 0.4889 cents 150:161:168:180:184:201:215:225:241:251:269:275:300 SD: 0.4392 cents 194:208:217:233:238:260:278:291:312:325:348:355:388 SD: 0.3695 cents 200:214:224:240:245:268:286:300:322:335:359:366:400 SD: 0.3364 cents 248:266:278:298:304:332:355:372:399:415:445:454:496 SD: 0.2972 cents 266:285:298:319:326:356:381:399:428:445:477:487:532 SD: 0.2307 cents 306:328:343:367:375:410:438:459:492:512:549:560:612 SD: 0.2154 cents 350:375:392:420:429:469:501:525:563:586:628:641:700 SD: 0.1130 cents 460:493:515:552:564:616:658:690:740:770:825:842:920 SD: 0.1026 cents