Scala analysis: mysterious
Spectras Mysterious Ratios
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 567/500 217.704768 2: 1333/1000 497.612137 3: 717/500 624.054029 4: 827.159 cents 827.158990 5: 447/250 1006.016084 6: 933/500 1079.938783 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 1000/933 120.0612 1: 567/500 217.7048 2: 1333/1134 279.9074 3: 1434/1333 126.4419 4: 203.1050 cents 203.1050 5: 178.8571 cents 178.8571 6: 311/298 73.9227 7: 1000/933 120.0612
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 311/298 73.923 cents 1: 1 1000/933 120.061 cents 1: 1 1434/1333 126.442 cents 1: 1 178.85709 cents 1: 1 203.10496 cents 1: 1 567/500 217.705 cents 1: 1 1333/1134 279.907 cents 2: 1 500/447 193.984 cents 2: 1 252.77979 cents 2: 1 329.54685 cents 2: 1 378/311 337.766 cents 2: 1 298/239 381.962 cents 2: 1 239/189 406.349 cents 2: 1 1333/1000 497.612 cents 3: 1 372.84101 cents 3: 1 189/149 411.689 cents 3: 1 311/239 455.885 cents 3: 1 1788/1333 508.404 cents 3: 1 609.45422 cents 3: 1 1333/933 617.673 cents 3: 1 717/500 624.054 cents 4: 1 1000/717 575.946 cents 4: 1 1866/1333 582.327 cents 4: 1 590.54578 cents 4: 1 1333/894 691.596 cents 4: 1 478/311 744.115 cents 4: 1 298/189 788.311 cents 4: 1 827.15899 cents 5: 1 2000/1333 702.388 cents 5: 1 378/239 793.651 cents 5: 1 239/149 818.038 cents 5: 1 311/189 862.234 cents 5: 1 870.45315 cents 5: 1 947.22021 cents 5: 1 447/250 1006.016 cents 6: 1 2268/1333 920.093 cents 6: 1 1000/567 982.295 cents 6: 1 996.89504 cents 6: 1 1021.14291 cents 6: 1 1333/717 1073.558 cents 6: 1 933/500 1079.939 cents 6: 1 596/311 1126.077 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 7.00000 = 7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 217.7 497.6 624.1 827.2 1006.0 1079.9 1200.0 217.7 : 279.9 406.3 609.5 788.3 862.2 982.3 1200.0 497.6 : 126.4 329.5 508.4 582.3 702.4 920.1 1200.0 624.1 : 203.1 382.0 455.9 575.9 793.7 1073.6 1200.0 827.2 : 178.9 252.8 372.8 590.5 870.5 996.9 1200.0 1006.0: 73.9 194.0 411.7 691.6 818.0 1021.1 1200.0 1079.9: 120.1 337.8 617.7 744.1 947.2 1126.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.9227 .. 279.9074 cents 198617/176337, 205.9847 cents 311/298, 73.9227 cents 2: 193.9839 .. 497.6121 cents 595851/500000, 303.6282 cents 189000/198617,-85.9235 cents 3: 372.8410 .. 624.0540 cents 251.21302 cents -124.77113 cents 4: 575.9460 .. 827.1590 cents 251.21302 cents 500000/514089,-48.1081 cents 5: 702.3879 .. 1006.0161 cents 595851/500000, 303.6282 cents -124.77113 cents 6: 920.0926 .. 1126.0773 cents 198617/176337, 205.9847 cents 189000/198617,-85.9235 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 311/298, 73.9227 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 1333/1134, 279.9074 cents Average / Smallest step : 2.319025 Largest / Average step : 1.632793 Largest / Smallest step : 3.786487 Median interval of one step : 178.85709 cents, amount: 1 Least squares average step : 187.88172 cents, oct.: 1315.17201 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : FGCEDAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 5.33942 cents Scale diversity : 1.706717 Lumma stability : 0.123204 Lumma impropriety factor : 0.391248 Rothenberg efficiency : 0.285714 redundancy: 0.714286 Efficiency x scale size : 2.000000 Number of different interval sizes : 42 = 7.00000 / class Number of one step interval sizes : 7 Highest interval variety : 7 Mean interval variety : 7.00000 = 7 Median interval variety : 7 Lowest interval variety : 7 Smallest interval difference : 35721/35611, 5.3394 cents Number of recognisable fifths : 2, average 696.9920 cents Formal octave complements present : 1 = 14.2857% -- Rational properties -- Prime limit : 311 (not all pitches rational)
FIT/MODE
7: 1 2 1 1 1 0 1 N T3 SD: 38.2993 c. M:-61.6603 c. 9: 2 2 1 1 2 0 1 N SD: 37.9499 c. M:-60.6506 c. 10: 2 2 1 2 1 1 1 N D3 SD: 22.8918 c. M: 46.0161 c. 12: 2 3 1 2 2 1 1 N SD: 17.2130 c. M: 27.1590 c. 17: 3 4 2 3 2 1 2 N SD: 13.7936 c. M: 21.1153 c. 19: 3 5 2 3 3 1 2 N SD: 12.0054 c. M: 28.2311 c. 27: 5 6 3 5 4 1 3 N SD: 10.9377 c. M:-17.2855 c. 29: 5 7 3 5 4 2 3 N SD: 6.6847 c. M: 12.9126 c. 33: 6 8 3 6 5 2 3 N SD: 8.6152 c. M:-12.1657 c. 38: 7 9 4 6 6 2 4 N SD: 5.6457 c. M:-7.6510 c. 39: 7 9 4 7 6 2 4 N SD: 5.5880 c. M:-9.3685 c. 48: 9 11 5 8 7 3 5 N SD: 4.2268 c. M:-7.2952 c. 60: 11 14 6 10 9 4 6 N SD: 4.0506 c. M: 7.1590 c. 61: 11 14 7 10 9 4 6 N SD: 3.3313 c. M: 5.8089 c. 62: 11 15 6 11 9 4 6 N SD: 4.1110 c. M:-5.6137 c. 67: 12 16 7 11 10 4 7 N SD: 3.3560 c. M: 5.3119 c. 68: 12 16 7 12 10 4 7 N SD: 3.8853 c. M: 6.4070 c. 73: 13 17 8 12 11 5 7 N SD: 3.7692 c. M: 5.2412 c. 77: 14 18 8 13 12 4 8 N SD: 3.2329 c. M:-6.9709 c. 81: 15 19 8 14 12 5 8 N SD: 3.1913 c. M:-6.0916 c. 82: 15 19 9 14 12 5 8 N SD: 3.8209 c. M:-6.9874 c. 87: 16 20 9 15 13 5 9 N SD: 2.3583 c. M: 4.0767 c. 94: 17 22 10 16 14 6 9 N SD: 2.4656 c. M:-5.1676 c. 100: 18 23 11 17 15 6 10 N SD: 2.3620 c. M: 5.6121 c. 106: 19 25 11 18 16 6 11 N SD: 2.1352 c. M: 4.4671 c. 123: 22 29 13 21 18 8 12 N SD: 1.8600 c. M: 3.0706 c. 131: 24 30 14 22 20 8 13 N SD: 1.9157 c. M: 2.9556 c. 132: 24 31 14 22 20 8 13 N SD: 2.0455 c. M:-3.2187 c. 138: 25 32 15 23 21 8 14 N SD: 1.6569 c. M:-2.6796 c. 142: 26 33 15 24 21 9 14 N SD: 1.2497 c. M:-2.0135 c. 161: 29 38 17 27 24 10 16 N SD: 1.2184 c. M:-2.0329 c. 171: 31 40 18 29 25 11 17 N SD: 1.0944 c. M: 2.5073 c. 181: 33 42 19 31 27 11 18 N SD: 1.0672 c. M:-1.7187 c. 200: 36 47 21 34 30 12 20 N SD: 1.0493 c. M:-1.9839 c. 210: 38 49 22 36 31 13 21 N SD: 0.7614 c. M:-1.4124 c. 248: 45 58 26 42 37 15 25 N SD: 0.4929 c. M: 0.9065 c. 379: 69 88 40 64 57 23 38 N SD: 0.5758 c. M:-0.8441 c. 390: 71 91 41 66 58 24 39 N SD: 0.5232 c. M:-0.8494 c. 402: 73 94 42 68 60 25 40 N SD: 0.4465 c. M:-0.8953 c. 408: 74 95 43 69 61 25 41 N SD: 0.4398 c. M: 0.6884 c. 458: 83 107 48 78 68 28 46 N SD: 0.4084 c. M:-0.7886 c. 490: 89 114 52 83 73 30 49 N SD: 0.3962 c. M:-0.5961 c. 502: 91 117 53 85 75 31 50 N SD: 0.3018 c. M:-0.5393 c. 550: 100 128 58 93 82 34 55 N SD: 0.2270 c. M:-0.4770 c. 711: 129 166 75 120 106 44 71 N SD: 0.2209 c. M:-0.4185 c. 750: 136 175 79 127 112 46 75 N SD: 0.1544 c. M:-0.3839 c. 760: 138 177 80 129 113 47 76 N SD: 0.2175 c. M: 0.3698 c. 779: 141 182 82 132 116 48 78 N SD: 0.2109 c. M: 0.5032 c. 798: 145 186 84 135 119 49 80 N SD: 0.1686 c. M:-0.3403 c. 892: 162 208 94 151 133 55 89 N SD: 0.2128 c. M:-0.3303 c. 921: 167 215 97 156 137 57 92 N SD: 0.1355 c. M:-0.2026 c. 1169: 212 273 123 198 174 72 117 N SD: 0.1323 c. M:-0.2493 c. 1300: 236 303 137 220 194 80 130 N SD: 0.0909 c. M:-0.1414 c. 1329: 241 310 140 225 198 82 133 N SD: 0.0941 c. M: 0.1470 c. 1471: 267 343 155 249 219 91 147 N SD: 0.0940 c. M: 0.1697 c. 1577: 286 368 166 267 235 97 158 N SD: 0.0811 c. M: 0.1671 c. 1671: 303 390 176 283 249 103 167 N SD: 0.0906 c. M:-0.1330 c. 1719: 312 401 181 291 256 106 172 N SD: 0.0713 c. M:-0.1191 c. 2079: 377 485 219 352 310 128 208 N SD: 0.0624 c. M: 0.1002 c. 2221: 403 518 234 376 331 137 222 N SD: 0.0481 c. M:-0.1152 c. 2327: 422 543 245 394 347 143 233 N SD: 0.0651 c. M: 0.0935 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 38.9505 cents 3 x 4 x 5 x x 6 S SD: 19.0671 cents 4 x 5:6 x 7 x 8 S SD: 35.2128 cents 5:6 x 7:8:9 x 10 S SD: 21.5712 cents 6:7:8:9:10 x 11:12 S SD: 18.7770 cents 7:8:9:10:11 x 13:14 SD: 13.1205 cents 8:9:11 x 13:14:15:16 SD: 11.4332 cents 9:10:12:13:15:16:17:18 SD: 10.3214 cents 13:15:17:19:21:23:24:26 SD: 8.7760 cents 14:16:19:20:23:25:26:28 SD: 6.8595 cents 15:17:20:22:24:27:28:30 SD: 6.1243 cents 16:18:21:23:26:29:30:32 SD: 5.9441 cents 21:24:28:30:34:38:39:42 SD: 3.9666 cents 23:26:31:33:37:41:43:46 SD: 3.0381 cents 30:34:40:43:48:54:56:60 SD: 2.5470 cents 37:42:49:53:60:66:69:74 SD: 2.2477 cents 39:44:52:56:63:70:73:78 SD: 1.8438 cents 51:58:68:73:82:91:95:102 SD: 1.2925 cents 60:68:80:86:97:107:112:120 SD: 0.9333 cents 90:102:120:129:145:161:168:180 SD: 0.3264 cents 150:170:200:215:242:268:280:300 SD: 0.3104 cents 217:246:289:311:350:388:405:434 SD: 0.2866 cents 240:272:320:344:387:429:448:480 SD: 0.2254 cents 297:337:396:426:479:531:554:594 SD: 0.1994 cents 336:381:448:482:542:601:627:672 SD: 0.1725 cents 387:439:516:555:624:692:722:774 SD: 0.1158 cents 477:541:636:684:769:853:890:954 SD: 0.0991 cents 537:609:716:770:866:960:1002:1074 SD: 0.0825 cents