Scala analysis: levy-09-tori
Ex. 9: Bismillah Khan, Toṛi
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99.000 cents 99.000000 2: 303.000 cents 303.000000 3: 617.000 cents 617.000000 4: 705.000 cents 705.000000 5: 805.000 cents 805.000000 6: 1116.000 cents 1116.000000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 84.0000 cents 84.0000 1: 99.0000 cents 99.0000 2: 204.0000 cents 204.0000 3: 314.0000 cents 314.0000 4: 88.0000 cents 88.0000 5: 100.0000 cents 100.0000 6: 311.0000 cents 311.0000 7: 84.0000 cents 84.0000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 84.00000 cents 1: 1 88.00000 cents 1: 1 99.00000 cents 1: 1 100.00000 cents 1: 1 204.00000 cents 1: 1 311.00000 cents 1: 1 314.00000 cents 2: 1 183.00000 cents 2: 1 188.00000 cents 2: 1 303.00000 cents 2: 1 395.00000 cents 2: 1 402.00000 cents 2: 1 411.00000 cents 2: 1 518.00000 cents 3: 1 387.00000 cents 3: 1 494.00000 cents 3: 1 495.00000 cents 3: 1 499.00000 cents 3: 1 502.00000 cents 3: 1 606.00000 cents 3: 1 617.00000 cents 4: 1 583.00000 cents 4: 1 594.00000 cents 4: 1 698.00000 cents 4: 1 701.00000 cents 4: 1 705.00000 cents 4: 1 706.00000 cents 4: 1 813.00000 cents 5: 1 682.00000 cents 5: 1 789.00000 cents 5: 1 798.00000 cents 5: 1 805.00000 cents 5: 1 897.00000 cents 5: 1 1012.00000 cents 5: 1 1017.00000 cents 6: 1 886.00000 cents 6: 1 889.00000 cents 6: 1 996.00000 cents 6: 1 1100.00000 cents 6: 1 1101.00000 cents 6: 1 1112.00000 cents 6: 1 1116.00000 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 : 99.0 303.0 617.0 705.0 805.0 1116.0 1200.0 99.0 : 204.0 518.0 606.0 706.0 1017.0 1101.0 1200.0 303.0 : 314.0 402.0 502.0 813.0 897.0 996.0 1200.0 617.0 : 88.0 188.0 499.0 583.0 682.0 886.0 1200.0 705.0 : 100.0 411.0 495.0 594.0 798.0 1112.0 1200.0 805.0 : 311.0 395.0 494.0 698.0 1012.0 1100.0 1200.0 1116.0: 84.0 183.0 387.0 701.0 789.0 889.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.0000 .. 314.0000 cents 230.00000 cents 84.00000 cents 2: 183.0000 .. 518.0000 cents 335.00000 cents -131.00000 cents 3: 387.0000 .. 617.0000 cents 230.00000 cents -131.00000 cents 4: 583.0000 .. 813.0000 cents 230.00000 cents -34.00000 cents 5: 682.0000 .. 1017.0000 cents 335.00000 cents -131.00000 cents 6: 886.0000 .. 1116.0000 cents 230.00000 cents -131.00000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 84.00000 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 314.00000 cents Average / Smallest step : 2.040816 Largest / Average step : 1.831667 Largest / Smallest step : 3.738095 Median interval of one step : 100.00000 cents, amount: 1 Least squares average step : 174.97857 cents, oct.: 1224.85000 cents Scale is not proper Scale is a mode of a 1200-tone equal temperament with octave 1200.000 cents degrees: 99 303 617 705 805 1116 1200 Least number of segments generator : 601 of 601.000 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 901 of 901.000 cents and inv. generated superset size: 287 = 280 more = 4100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEFG Step pattern size order : CEGBDFA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 8.00000 cents Scale diversity : 1.468299 Lumma stability : 0.140000 Lumma impropriety factor : 0.465000 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 : 1.00000 cents Number of recognisable fifths : 4, average 702.5000 cents Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 92.5103 c. M: 131.5714 c. 8: 0 2 2 0 1 2 1 N S SD: 63.8133 c. M: 105.0000 c. 9: 0 2 2 1 1 2 1 N SD: 56.1242 c. M: 99.0000 c. 10: 1 2 2 1 1 2 1 P D3 S SD: 30.9954 c. M:-57.0000 c. 11: 1 2 3 0 1 3 1 N SD: 31.5930 c. M: 50.4545 c. 12: 1 2 3 1 1 3 1 N SD: 9.2967 c. M: 17.0000 c. Todi That, Mela Shubhapantuvarali, Raga Gamakasamantam, Hemavanti, Kaam Ranjani, Multani, Harsh Minor, Chromatic Lydian inverse, Maqam Athar Kurd 25: 2 4 7 2 2 6 2 N SD: 10.5085 c. M: 15.0000 c. 27: 2 5 7 2 2 7 2 N SD: 6.3420 c. M: 10.1111 c. 39: 3 7 10 3 3 10 3 N SD: 4.9379 c. M: 8.3077 c. 58: 5 10 15 4 5 15 4 N SD: 3.6819 c. M:-7.3448 c. 60: 5 10 16 4 5 16 4 N SD: 3.4847 c. M: 5.0000 c. 70: 6 12 18 5 6 18 5 N SD: 2.7769 c. M:-5.5714 c. 72: 6 12 19 5 6 19 5 N SD: 2.9412 c. M: 5.0000 c. 82: 7 14 21 6 7 21 6 N SD: 2.8564 c. M:-4.3171 c. 84: 7 14 22 6 7 22 6 N SD: 3.1692 c. M: 5.0000 c. 85: 7 14 23 6 7 22 6 N SD: 2.9634 c. M: 6.5294 c. 87: 7 15 23 6 7 23 6 N SD: 2.6392 c. M: 5.0000 c. 88: 7 15 23 7 7 23 6 N SD: 2.7925 c. M:-4.0909 c. 95: 8 16 25 7 8 24 7 N SD: 2.5323 c. M: 4.4211 c. 99: 8 17 26 7 8 26 7 N SD: 2.2399 c. M: 5.0000 c. 111: 9 19 29 8 9 29 8 N SD: 2.3923 c. M: 5.0000 c. 118: 10 20 31 8 10 31 8 N SD: 2.4861 c. M:-3.3390 c. 119: 10 20 31 9 10 31 8 N SD: 1.7707 c. M:-3.3277 c. 124: 10 21 33 9 10 32 9 N SD: 2.2150 c. M: 3.0968 c. 128: 11 21 34 9 11 33 9 N SD: 2.2135 c. M:-4.1250 c. 130: 11 22 34 9 11 34 9 N SD: 1.9900 c. M: 3.4615 c. 131: 11 22 34 10 11 34 9 N SD: 1.6038 c. M: 3.2595 c. 134: 11 23 35 10 11 35 9 N SD: 1.7664 c. M:-3.4030 c. 143: 12 24 38 10 12 37 10 N SD: 1.6863 c. M:-3.9790 c. 146: 12 25 38 11 12 38 10 N SD: 1.1086 c. M:-1.8493 c. 158: 13 27 41 12 13 41 11 N SD: 0.9228 c. M: 1.8101 c. 197: 16 34 51 15 16 51 14 N SD: 1.3648 c. M: 1.7716 c. 198: 16 34 52 14 17 51 14 N SD: 1.2674 c. M: 2.0303 c. 204: 17 35 53 15 17 53 14 N SD: 1.4140 c. M:-2.8824 c. 206: 17 35 54 15 17 54 14 N SD: 1.0343 c. M:-2.4466 c. 218: 18 37 57 16 18 57 15 N SD: 0.7831 c. M:-1.4312 c. 230: 19 39 60 17 19 60 16 N SD: 0.8452 c. M: 1.5217 c. 243: 20 41 64 18 20 63 17 N SD: 0.8137 c. M: 1.7654 c. 276: 23 47 72 20 23 72 19 N SD: 0.9068 c. M:-1.3913 c. 282: 23 48 74 21 23 73 20 N SD: 0.9043 c. M:-1.3830 c. 286: 24 48 75 21 24 74 20 N SD: 0.7672 c. M:-1.6993 c. 288: 24 49 75 21 24 75 20 N SD: 0.7843 c. M:-1.1667 c. 289: 24 49 76 21 24 75 20 N SD: 0.8667 c. M:-1.6851 c. 298: 25 50 78 22 25 77 21 N SD: 0.8542 c. M:-1.6711 c. 300: 25 51 78 22 25 78 21 N SD: 0.8452 c. M:-1.0000 c. 301: 25 51 79 22 25 78 21 N SD: 0.5247 c. M:-0.9402 c. 313: 26 53 82 23 26 81 22 N SD: 0.3505 c. M:-0.6805 c. 459: 38 78 120 34 38 119 32 N SD: 0.4032 c. M:-0.8824 c. 471: 39 80 123 35 39 122 33 N SD: 0.3607 c. M:-0.7325 c. 511: 42 87 134 37 43 132 36 N SD: 0.4287 c. M:-0.6125 c. 519: 43 88 136 38 43 135 36 N SD: 0.3911 c. M:-0.7630 c. 531: 44 90 139 39 44 138 37 N SD: 0.2947 c. M: 0.4802 c. 642: 53 109 168 47 54 166 45 N SD: 0.2836 c. M:-0.6075 c. 657: 54 112 172 48 55 170 46 N SD: 0.2751 c. M:-0.4795 c. 669: 55 114 175 49 56 173 47 N SD: 0.2339 c. M:-0.3812 c. 729: 60 124 191 53 61 189 51 N SD: 0.2330 c. M: 0.4733 c. 741: 61 126 194 54 62 192 52 N SD: 0.2498 c. M: 0.5466 c. 827: 68 141 216 61 69 214 58 N SD: 0.2522 c. M: 0.3301 c. 844: 70 143 221 62 70 219 59 N SD: 0.2482 c. M:-0.5261 c. 848: 70 144 222 62 71 220 59 N SD: 0.2413 c. M:-0.5094 c. 860: 71 146 225 63 72 223 60 N SD: 0.2162 c. M: 0.3488 c. 875: 72 149 229 64 73 227 61 N SD: 0.1771 c. M:-0.3429 c. 887: 73 151 232 65 74 230 62 N SD: 0.1237 c. M: 0.2401 c. 1173: 97 199 307 86 98 304 82 N SD: 0.1460 c. M:-0.2327 c. 1188: 98 202 311 87 99 308 83 N SD: 0.0939 c. M:-0.1717 c. 1200: 99 204 314 88 100 311 84 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 1.5225 cents 3 x x 4 x 5 x 6 S SD: 47.6656 cents 4 x 5 x 6 x x 8 S SD: 27.7898 cents 5 x 6:7 x 8 x 10 S SD: 9.4362 cents 6 x 7 x 9:10:11:12 SD: 21.9571 cents 7 x 8:10 x 11:13:14 SD: 17.4678 cents 8 x 10:11:12:13:15:16 SD: 19.2179 cents 9:10:11:13 x 14:17:18 SD: 17.5938 cents 10:11:12:14:15:16:19:20 SD: 10.8924 cents 12:13:14:17:18:19:23:24 SD: 8.1719 cents 14:15:17:20:21:22:27:28 SD: 7.1060 cents 16:17:19:23:24:25:30:32 SD: 6.4190 cents 19:20:23:27:29:30:36:38 SD: 6.3521 cents 20:21:24:29:30:32:38:40 SD: 4.8834 cents 30:32:36:43:45:48:57:60 SD: 3.0928 cents 32:34:38:46:48:51:61:64 SD: 2.0523 cents 51:54:61:73:77:81:97:102 SD: 1.7917 cents 52:55:62:74:78:83:99:104 SD: 1.2413 cents 68:72:81:97:102:108:130:136 SD: 1.1510 cents 84:89:100:120:126:134:160:168 SD: 0.7100 cents 105:111:125:150:158:167:200:210 SD: 0.6109 cents 135:143:161:193:203:215:257:270 SD: 0.4789 cents 157:166:187:224:236:250:299:314 SD: 0.4600 cents 187:198:223:267:281:298:356:374 SD: 0.4138 cents 189:200:225:270:284:301:360:378 SD: 0.2612 cents 287:304:342:410:431:457:547:574 SD: 0.2245 cents 304:322:362:434:457:484:579:608 SD: 0.2120 cents 360:381:429:514:541:573:686:720 SD: 0.1744 cents 392:415:467:560:589:624:747:784 SD: 0.0971 cents 591:626:704:844:888:941:1126:1182 SD: 0.0969 cents