Scala analysis: dimensionsquared
dimension squared
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/25 196.198479 middle second 2: 117/100 271.810236 3: 6/5 315.641287 minor third 4: 613/500 352.750775 5: 505.775 cents 505.774990 6: 3/2 701.955001 perfect fifth 7: 1573/1000 784.222405 8: 817.469 cents 817.469220 9: 892.063 cents 892.062850 10: 1011.526 cents 1011.526340 11: 1831/1000 1047.158149 12: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 2000/1831 152.8419 1: 28/25 196.1985 middle second 2: 117/112 75.6118 3: 40/39 43.8311 tridecimal minor diesis 4: 613/600 37.1095 5: 153.0242 cents 153.0242 6: 196.1800 cents 196.1800 7: 1573/1500 82.2674 8: 33.2468 cents 33.2468 9: 74.5936 cents 74.5936 10: 119.4635 cents 119.4635 11: 35.6318 cents 35.6318 12: 2000/1831 152.8419
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 33.24682 cents 1: 1 35.63181 cents 1: 1 613/600 37.109 cents 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 74.59363 cents 1: 1 117/112 75.612 cents 1: 1 1573/1500 82.267 cents 1: 1 119.46349 cents 1: 1 2000/1831 152.842 cents 1: 1 153.02422 cents 1: 1 196.18001 cents 1: 1 28/25 196.198 cents middle second 2: 1 613/585 80.941 cents 2: 1 107.84045 cents 2: 1 115.51422 cents 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 155.09530 cents 2: 1 188.47366 cents 2: 1 190.13370 cents 2: 1 194.05712 cents 2: 1 117/100 271.810 cents 2: 1 278.44741 cents 2: 1 2240/1831 349.040 cents 2: 1 750/613 349.204 cents 3: 1 613/560 156.552 cents 3: 1 190.10785 cents 3: 1 227.30394 cents 3: 1 229.68893 cents 3: 1 233.96475 cents 3: 1 307.93715 cents 3: 1 311.69423 cents 3: 1 6/5 315.641 cents minor third 3: 1 384.67214 cents 3: 1 5/4 386.314 cents major third 3: 1 2340/1831 424.652 cents 3: 1 1573/1226 431.472 cents 4: 1 1831/1573 262.936 cents 4: 1 309.57134 cents 4: 1 309.57651 cents 4: 1 613/500 352.751 cents 4: 1 382.53078 cents 4: 1 386.28786 cents 4: 1 50/39 430.145 cents 4: 1 460.28390 cents 4: 1 464.71845 cents 4: 1 2400/1831 468.483 cents 4: 1 1573/1200 468.581 cents 4: 1 504.13563 cents 5: 1 1831/1500 345.203 cents 5: 1 2000/1573 415.778 cents 5: 1 501.82793 cents 5: 1 504.11495 cents 5: 1 2452/1831 505.593 cents 5: 1 505.75135 cents 5: 1 75/56 505.757 cents marvelous fourth 5: 1 505.77499 cents 5: 1 121/90 512.412 cents 5: 1 539.31208 cents 5: 1 578.72926 cents 5: 1 579.74739 cents 6: 1 4/3 498.045 cents perfect fourth 6: 1 541.22443 cents 6: 1 541.38316 cents 6: 1 545.65898 cents 6: 1 576.42156 cents 6: 1 1573/1120 588.024 cents 6: 1 2240/1573 611.976 cents 6: 1 623.57844 cents 6: 1 654.34102 cents 6: 1 658.61684 cents 6: 1 658.77557 cents 6: 1 3/2 701.955 cents perfect fifth 7: 1 620.25261 cents 7: 1 621.27074 cents 7: 1 660.68792 cents 7: 1 180/121 687.588 cents 7: 1 694.22501 cents 7: 1 112/75 694.243 cents marvelous fifth 7: 1 694.24865 cents 7: 1 1831/1226 694.407 cents 7: 1 695.88505 cents 7: 1 698.17207 cents 7: 1 1573/1000 784.222 cents 7: 1 3000/1831 854.797 cents 8: 1 695.86437 cents 8: 1 2400/1573 731.419 cents 8: 1 1831/1200 731.517 cents 8: 1 735.28155 cents 8: 1 739.71610 cents 8: 1 39/25 769.855 cents 8: 1 813.71214 cents 8: 1 817.46922 cents 8: 1 1000/613 847.249 cents 8: 1 890.42349 cents 8: 1 890.42866 cents 8: 1 3146/1831 937.064 cents 9: 1 2452/1573 768.528 cents 9: 1 1831/1170 775.348 cents 9: 1 8/5 813.686 cents minor sixth 9: 1 815.32786 cents 9: 1 5/3 884.359 cents major sixth, BP sixth 9: 1 888.30577 cents 9: 1 892.06285 cents 9: 1 966.03525 cents 9: 1 970.31107 cents 9: 1 972.69606 cents 9: 1 1009.89215 cents 9: 1 1120/613 1043.448 cents 10: 1 613/375 850.796 cents 10: 1 1831/1120 850.960 cents 10: 1 921.55259 cents 10: 1 200/117 928.190 cents 10: 1 1005.94288 cents 10: 1 1009.86630 cents 10: 1 1011.52634 cents 10: 1 1044.90470 cents 10: 1 28/15 1080.557 cents grave major seventh 10: 1 1084.48578 cents 10: 1 1092.15955 cents 10: 1 1170/613 1119.059 cents 11: 1 25/14 1003.802 cents middle minor seventh 11: 1 1003.81999 cents 11: 1 1046.97578 cents 11: 1 1831/1000 1047.158 cents 11: 1 1080.53651 cents 11: 1 3000/1573 1117.733 cents 11: 1 224/117 1124.388 cents 11: 1 1125.40637 cents 11: 1 39/20 1156.169 cents 11: 1 1200/613 1162.891 cents 11: 1 1164.36819 cents 11: 1 1166.75318 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 : 196.2 271.8 315.6 352.8 505.8 702.0 784.2 817.5 892.1 1011.5 1047.2 1200.0 196.2 : 75.6 119.4 156.6 309.6 505.8 588.0 621.3 695.9 815.3 851.0 1003.8 1200.0 271.8 : 43.8 80.9 234.0 430.1 512.4 545.7 620.3 739.7 775.3 928.2 1124.4 1200.0 315.6 : 37.1 190.1 386.3 468.6 501.8 576.4 695.9 731.5 884.4 1080.6 1156.2 1200.0 352.8 : 153.0 349.2 431.5 464.7 539.3 658.8 694.4 847.2 1043.4 1119.1 1162.9 1200.0 505.8 : 196.2 278.4 311.7 386.3 505.8 541.4 694.2 890.4 966.0 1009.9 1047.0 1200.0 702.0 : 82.3 115.5 190.1 309.6 345.2 498.0 694.2 769.9 813.7 850.8 1003.8 1200.0 784.2 : 33.2 107.8 227.3 262.9 415.8 612.0 687.6 731.4 768.5 921.6 1117.7 1200.0 817.5 : 74.6 194.1 229.7 382.5 578.7 654.3 698.2 735.3 888.3 1084.5 1166.8 1200.0 892.1 : 119.5 155.1 307.9 504.1 579.7 623.6 660.7 813.7 1009.9 1092.2 1125.4 1200.0 1011.5: 35.6 188.5 384.7 460.3 504.1 541.2 694.2 890.4 972.7 1005.9 1080.5 1200.0 1047.2: 152.8 349.0 424.7 468.5 505.6 658.6 854.8 937.1 970.3 1044.9 1164.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.2468 .. 196.1985 cents 162.95166 cents 33.24682 cents 2: 80.9405 .. 349.2042 cents 438750/375769, 268.2637 cents 3065/3276,-115.2579 cents 3: 156.5523 .. 431.4716 cents 440440/375769, 274.9193 cents 375769/420000,-192.6519 cents 4: 262.9357 .. 504.1356 cents 241.19988 cents 2244806/2474329,-168.5359 cents 5: 345.2031 .. 579.7474 cents 234.54424 cents -158.93248 cents 6: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents -81.70239 cents 7: 620.2526 .. 854.7969 cents 234.54424 cents -81.70239 cents 8: 695.8644 .. 937.0643 cents 241.19988 cents -158.93248 cents 9: 768.5284 .. 1043.4477 cents 440440/375769, 274.9193 cents 2244806/2474329,-168.5359 cents 10: 850.7958 .. 1119.0595 cents 438750/375769, 268.2637 cents 375769/420000,-192.6519 cents 11: 1003.8015 .. 1166.7532 cents 162.95166 cents 3065/3276,-115.2579 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 33.24682 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 28/25, 196.1985 cents Average / Smallest step : 3.007807 Largest / Average step : 1.961985 Largest / Smallest step : 5.901271 Median interval of one step : 78.93958 cents, amount: 0 Least squares average step : 101.43112 cents, oct.: 1217.17348 cents Scale is not proper Step pattern alph. order: ABCDEFGHIJKL Step pattern size order : LFDCJKGAEHBI Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.02068 cents Scale diversity : 1.571586 Lumma stability : 0.055411 Lumma impropriety factor : 0.831345 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 : 0.00517 cents Number of recognisable fifths : 9, average 695.1765 cents Number of appreciable fifths : 8, average 696.1251 cents Formal octave complements present : 1 = 8.3333% -- Rational properties -- Prime limit : 1831 (not all pitches rational)
FIT/MODE
12: 2 1 0 1 1 2 1 0 1 1 0 2 N SD: 22.9079 c. M:-47.2492 c. 14: 2 1 1 0 2 2 1 0 1 2 0 2 N SD: 22.6243 c. M: 46.0406 c. 17: 3 1 0 1 2 3 1 1 1 1 1 2 N SD: 17.9853 c. M: 33.2883 c. 18: 3 1 1 0 3 3 1 0 1 2 1 2 N SD: 18.6805 c. M:-31.3783 c. 19: 3 1 1 1 2 3 1 1 1 2 1 2 N SD: 14.7873 c. M:-26.5261 c. 23: 4 1 1 1 3 3 2 1 1 2 1 3 N SD: 12.9268 c. M: 23.6941 c. 24: 4 1 1 1 3 4 2 0 2 2 1 3 N SD: 11.3195 c. M: 21.8102 c. 26: 4 2 1 1 3 4 2 1 1 3 1 3 N SD: 10.0493 c. M:-16.4800 c. 31: 5 2 1 1 4 5 2 1 2 3 1 4 N SD: 4.5632 c. M: 10.0289 c. 50: 8 3 2 2 6 8 4 1 3 5 2 6 N SD: 5.4223 c. M:-8.8419 c. 57: 9 4 2 2 7 9 4 2 3 6 2 7 N SD: 4.6625 c. M: 7.8523 c. 66: 11 4 2 2 9 11 4 2 4 7 2 8 N SD: 4.8291 c. M:-7.3873 c. 69: 11 4 3 2 9 11 5 2 4 7 2 9 N SD: 4.7139 c. M: 10.9407 c. 71: 12 4 3 2 9 12 4 2 5 7 2 9 N SD: 4.5610 c. M:-7.9042 c. 72: 12 4 3 2 9 12 5 2 5 7 2 9 N SD: 3.9331 c. M:-7.9371 c. 75: 12 5 3 2 10 12 5 2 5 7 2 10 N SD: 3.6690 c. M: 7.1581 c. 78: 13 5 3 2 10 13 5 2 5 8 2 10 N SD: 3.5839 c. M:-7.4356 c. 79: 13 5 3 2 10 13 6 2 5 8 2 10 N SD: 3.5782 c. M:-6.1952 c. 81: 13 5 3 3 10 13 6 2 5 8 3 10 N SD: 3.6652 c. M: 5.6587 c. 84: 14 5 3 3 10 14 6 2 5 9 2 11 N SD: 3.5552 c. M: 6.3486 c. 85: 14 5 3 3 11 14 6 2 5 9 2 11 N SD: 3.4372 c. M:-6.3658 c. 92: 15 6 3 3 12 15 6 3 5 10 2 12 N SD: 3.1742 c. M:-5.8650 c. 93: 15 6 3 3 12 15 7 2 6 9 3 12 N SD: 3.6235 c. M: 5.9639 c. 94: 15 6 4 3 12 15 6 3 6 9 3 12 N SD: 3.3685 c. M: 5.4990 c. 98: 16 6 4 3 12 16 7 3 6 10 3 12 N SD: 3.1482 c. M:-5.9031 c. 99: 16 6 4 3 13 16 7 2 7 9 3 13 N SD: 3.6947 c. M: 5.4657 c. 100: 16 6 4 3 13 16 7 3 6 10 3 13 N SD: 4.2029 c. M: 7.8102 c. 101: 17 6 4 3 13 16 7 3 6 10 3 13 N SD: 3.0877 c. M:-5.7817 c. 102: 17 6 4 3 13 17 7 3 6 10 3 13 N SD: 2.7773 c. M:-6.0602 c. 104: 17 7 3 4 13 17 7 3 6 11 3 13 N SD: 3.0800 c. M:-5.1128 c. 106: 17 7 4 3 14 17 7 3 7 10 3 14 N SD: 2.8956 c. M: 5.6487 c. 109: 18 7 4 3 14 18 7 3 7 11 3 14 N SD: 2.1241 c. M:-3.6248 c. 128: 21 8 5 4 16 21 9 3 8 13 4 16 N SD: 2.0249 c. M:-3.4992 c. 133: 22 8 5 4 17 22 9 4 8 13 4 17 N SD: 1.4976 c. M:-3.5834 c. 147: 24 9 6 4 19 24 10 4 9 15 4 19 N SD: 1.5511 c. M:-2.7261 c. 159: 26 10 6 5 20 26 11 4 10 16 5 20 N SD: 1.2140 c. M: 2.3749 c. 164: 27 10 6 5 21 27 11 5 10 16 5 21 N SD: 1.2061 c. M:-2.0430 c. 190: 31 12 7 6 24 31 13 5 12 19 6 24 N SD: 1.1455 c. M: 2.7324 c. 242: 40 15 9 7 31 40 16 7 15 24 7 31 N SD: 1.1437 c. M:-2.1772 c. 251: 41 16 9 8 32 41 17 7 16 25 7 32 N SD: 0.9690 c. M:-2.0195 c. 256: 42 16 9 8 33 42 17 7 16 26 7 33 N SD: 1.2170 c. M: 1.8456 c. 261: 43 16 10 8 33 43 18 7 16 26 8 33 N SD: 1.1186 c. M:-1.9845 c. 269: 44 17 10 8 34 44 19 7 17 27 8 34 N SD: 0.9759 c. M: 1.6858 c. 282: 46 18 10 9 36 46 19 8 18 28 8 36 N SD: 0.7885 c. M:-1.5542 c. 292: 48 18 11 9 37 48 20 8 18 29 9 37 N SD: 0.6385 c. M:-1.0618 c. 323: 53 20 12 10 41 53 22 9 20 32 10 41 N SD: 0.4827 c. M: 1.0000 c. 465: 76 29 17 15 59 76 32 13 29 46 14 59 N SD: 0.5394 c. M: 0.8425 c. 496: 81 31 18 16 63 81 34 14 31 49 15 63 N SD: 0.5230 c. M: 1.1252 c. 503: 82 32 18 16 64 82 35 14 31 50 15 64 N SD: 0.4558 c. M:-0.8210 c. 533: 87 34 19 17 68 87 36 15 33 53 16 68 N SD: 0.5300 c. M:-0.7916 c. 534: 87 34 19 17 68 87 37 15 33 53 16 68 N SD: 0.4682 c. M: 1.0345 c. 543: 89 34 20 17 69 89 37 15 34 54 16 69 N SD: 0.5051 c. M:-0.8404 c. 552: 90 35 20 17 71 90 38 15 34 55 17 70 N SD: 0.5159 c. M: 0.7585 c. 562: 92 35 21 17 72 92 38 16 35 56 16 72 N SD: 0.4965 c. M: 0.8948 c. 574: 94 36 21 18 73 94 39 16 36 57 17 73 N SD: 0.3262 c. M:-0.6201 c. 605: 99 38 22 19 77 99 41 17 38 60 18 77 N SD: 0.3088 c. M: 0.7513 c. 612: 100 39 22 19 78 100 42 17 38 61 18 78 N SD: 0.2459 c. M:-0.7388 c. 650: 106 41 24 20 83 106 45 18 40 65 19 83 N SD: 0.3227 c. M: 0.5062 c. 745: 122 47 27 23 95 122 51 21 46 74 22 95 N SD: 0.3090 c. M:-0.7858 c. 759: 124 48 28 23 97 124 52 21 47 76 22 97 N SD: 0.2786 c. M:-0.5642 c. 776: 127 49 28 24 99 127 53 22 48 77 23 99 N SD: 0.2508 c. M:-0.5720 c. 826: 135 52 30 26 105 135 57 23 51 82 25 105 N SD: 0.2715 c. M:-0.4485 c. 904: 148 57 33 28 115 148 62 25 56 90 27 115 N SD: 0.2255 c. M:-0.3466 c. 935: 153 59 34 29 119 153 64 26 58 93 28 119 N SD: 0.1375 c. M:-0.2753 c. 1224: 200 77 45 38 156 200 84 34 76 122 36 156 N SD: 0.1409 c. M: 0.2416 c. 1255: 205 79 46 39 160 205 86 35 78 125 37 160 N SD: 0.1280 c. M: 0.2565 c. 1547: 253 97 57 48 197 253 106 43 96 154 46 197 N SD: 0.1159 c. M: 0.3170 c. 1578: 258 99 58 49 201 258 108 44 98 157 47 201 N SD: 0.1232 c. M: 0.3273 c. 1585: 259 100 58 49 202 259 109 44 98 158 47 202 N SD: 0.1095 c. M: 0.2017 c. 1616: 264 102 59 50 206 264 111 45 100 161 48 206 N SD: 0.1258 c. M: 0.2312 c. 1718: 281 108 63 53 219 281 118 47 107 171 51 219 N SD: 0.1137 c. M: 0.2399 c. 1867: 305 118 68 58 238 305 128 52 116 186 55 238 N SD: 0.0988 c. M: 0.1621 c. 2159: 353 136 79 67 275 353 148 60 134 215 64 275 N SD: 0.0725 c. M:-0.1904 c. 2190: 358 138 80 68 279 358 150 61 136 218 65 279 N SD: 0.0570 c. M:-0.1259 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 3 x 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: 3.6379 cents 4 x x x 5 x 6 x x x 7 x 8 S SD: 13.5780 cents 5 x x 6 x 7 x x 8 x 9 x 10 S SD: 15.4140 cents 6 x 7 x x 8:9 x x 10 x 11:12 S SD: 2.0301 cents 7:8 x x x 9 x 11 x 12 x 13:14 SD: 15.3770 cents 8:9 x x 10:11:12 x 13 x 14:15:16 S SD: 10.6838 cents 9:10 x x 11:12 x 14 x 15:16 x 18 S SD: 4.4008 cents 10:11 x 12 x 13:15 x 16:17:18 x 20 SD: 8.2814 cents 11:12:13 x x 15 x 17:18 x x 20:22 SD: 10.7547 cents 12:13:14 x 15:16:18:19 x 20 x 22:24 S SD: 7.6369 cents 13 x 15 x 16:17 x 20:21:22:23:24:26 SD: 7.9308 cents 14:16 x x 17:19:21:22 x 23:25:26:28 SD: 6.8071 cents 15:17 x 18 x 20:23 x 24:25:27 x 30 SD: 5.6429 cents 16:18 x 19:20:21:24:25:26:27 x 29:32 SD: 6.2489 cents 17:19:20 x 21:23:26 x 27:28:30:31:34 SD: 6.0236 cents 18:20:21 x 22:24:27:28:29:30:32:33:36 S SD: 2.9394 cents 19:21:22:23 x 25:29:30 x 32:34:35:38 SD: 5.6594 cents 21:24 x 25:26:28:32:33:34:35:38 x 42 SD: 5.5481 cents 22:25:26 x 27:29:33 x 35:37:39:40:44 SD: 5.0058 cents 23:26:27 x 28:31:35:36:37:39:41:42:46 SD: 3.9769 cents 24:27:28:29 x 32:36:38 x 40:43:44:48 SD: 2.1994 cents 27:30 x 32:33:36:41:42:43:45:48:49:54 SD: 4.3013 cents 28:31:33 x 34:38:42:44:45:47:50:51:56 SD: 3.5701 cents 30:34:35:36:37:40:45:47:48:50:54:55:60 SD: 2.3194 cents 33:37:39:40 x 44:50:52:53:55:59:60:66 SD: 3.1848 cents 34:38:40:41:42:46:51:53:55:57:61:62:68 SD: 2.8723 cents 35:39:41:42:43:47:53:55:56:59:63:64:70 SD: 2.0226 cents 40:45:47:48:49:54:60:63:64:67:72:73:80 SD: 1.6560 cents 58:65:68:70:71:78:87:91:93:97:104:106:116 SD: 1.1892 cents 70:78:82:84:86:94:105:110:112:117:126:128:140 SD: 1.1310 cents 76:85:89:91:93:102:114:120:122:127:136:139:152 SD: 0.9256 cents 94:105:110:113:115:126:141:148:151:157:169:172:188 SD: 0.8007 cents 100:112:117:120:123:134:150:157:160:167:179:183:200 SD: 0.7886 cents 101:113:118:121:124:135:152:159:162:169:181:185:202 SD: 0.7163 cents 106:119:124:127:130:142:159:167:170:177:190:194:212 SD: 0.6117 cents 124:139:145:149:152:166:186:195:199:208:222:227:248 SD: 0.4861 cents 141:158:165:169:173:189:212:222:226:236:253:258:282 SD: 0.4611 cents 159:178:186:191:195:213:239:250:255:266:285:291:318 SD: 0.3883 cents 194:217:227:233:238:260:291:305:311:325:348:355:388 SD: 0.3056 cents 224:251:262:269:275:300:336:352:359:375:402:410:448 SD: 0.3029 cents 242:271:283:290:297:324:363:381:388:405:434:443:484 SD: 0.3003 cents 248:278:290:298:304:332:372:390:398:415:445:454:496 SD: 0.2954 cents 260:291:304:312:319:348:390:409:417:435:466:476:520 SD: 0.2459 cents 300:336:351:360:368:402:450:472:481:502:538:549:600 SD: 0.1563 cents 424:475:496:509:520:568:636:667:680:710:761:776:848 SD: 0.1511 cents 460:515:538:552:564:616:690:724:738:770:825:842:920 SD: 0.1478 cents 466:522:545:559:571:624:699:733:747:780:836:853:932 SD: 0.1359 cents 510:571:597:612:625:683:765:802:818:854:915:934:1020 SD: 0.1337 cents 534:598:625:641:655:715:801:840:856:894:958:978:1068 SD: 0.1235 cents