Scala analysis: CD13_03_Iraq
Suite - Ensemble de Muhammad Al-Qubbbânjî (dukah, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 151.867 cents 151.867081 2: 350.732 cents 350.732366 3: 556.821 cents 556.820607 4: 844.813 cents 844.813466 5: 1049.684 cents 1049.683921 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 150.3161 cents 150.3161 1: 151.8671 cents 151.8671 2: 198.8653 cents 198.8653 3: 206.0882 cents 206.0882 4: 287.9929 cents 287.9929 5: 204.8705 cents 204.8705 6: 150.3161 cents 150.3161
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 150.31608 cents 1: 1 151.86708 cents 1: 1 198.86528 cents 1: 1 204.87046 cents 1: 1 206.08824 cents 1: 1 287.99286 cents 2: 1 302.18316 cents 2: 1 350.73237 cents 2: 1 355.18653 cents 2: 1 404.95353 cents 2: 1 492.86331 cents 2: 1 494.08110 cents 3: 1 501.04845 cents 3: 1 507.05362 cents 3: 1 556.82061 cents 3: 1 643.17939 cents 3: 1 692.94638 cents 3: 1 698.95155 cents 4: 1 705.91890 cents 4: 1 707.13669 cents 4: 1 795.04647 cents 4: 1 844.81347 cents 4: 1 849.26763 cents 4: 1 897.81684 cents 5: 1 912.00714 cents 5: 1 993.91176 cents 5: 1 995.12954 cents 5: 1 1001.13472 cents 5: 1 1048.13292 cents 5: 1 1049.68392 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 151.9 350.7 556.8 844.8 1049.7 1200.0 151.9 : 198.9 405.0 692.9 897.8 1048.1 1200.0 350.7 : 206.1 494.1 699.0 849.3 1001.1 1200.0 556.8 : 288.0 492.9 643.2 795.0 993.9 1200.0 844.8 : 204.9 355.2 507.1 705.9 912.0 1200.0 1049.7: 150.3 302.2 501.0 707.1 995.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.3161 .. 287.9929 cents 137.67678 cents 150.31608 cents 2: 302.1832 .. 494.0811 cents 191.89794 cents 14.19030 cents 3: 501.0484 .. 698.9516 cents 197.90311 cents 6.96735 cents 4: 705.9189 .. 897.8168 cents 191.89794 cents 6.96735 cents 5: 912.0071 .. 1049.6839 cents 137.67678 cents 14.19030 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 150.31608 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 287.99286 cents Average / Smallest step : 1.330530 Largest / Average step : 1.439964 Largest / Smallest step : 1.915915 Median interval of one step : 201.86787 cents, amount: 0 Least squares average step : 201.66447 cents, oct.: 1209.98684 cents Scale is strictly proper Step pattern alph. order: ABCDEF Step pattern size order : BCEFDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 6.96735 cents Scale diversity : 1.481654 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.285790 Rothenberg efficiency : 0.333333 redundancy: 0.666667 Efficiency x scale size : 2.000000 Number of different interval sizes : 30 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 1.21779 cents Number of recognisable fifths : 4, average 701.2384 cents Formal octave complements present : 1 = 16.6667% -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 42.9831 c. M: 49.6839 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 1 2 1 1 P M ME SD: 21.8008 c. M: 42.5349 c. 13: 2 2 2 3 2 2 SP M ME SD: 21.5916 c. M: 34.2993 c. Glacial-6 15: 2 2 3 4 2 2 N SD: 19.8015 c. M:-35.1865 c. 16: 2 3 2 4 3 2 P SD: 18.2466 c. M: 31.8206 c. 17: 2 3 3 4 3 2 P SD: 6.7072 c. M: 10.6906 c. 24: 3 4 4 6 4 3 P SD: 3.5950 c. M: 6.8206 c. 41: 5 7 7 10 7 5 P SD: 3.2359 c. M: 5.5256 c. 54: 7 9 9 13 9 7 SP SD: 3.3180 c. M: 5.2395 c. 64: 8 11 11 15 11 8 SP SD: 3.3520 c. M:-5.6794 c. 65: 8 11 11 16 11 8 P SD: 2.9629 c. M:-4.4173 c. 71: 9 12 12 17 12 9 SP SD: 1.9074 c. M:-4.1972 c. 78: 10 13 13 19 13 10 SP SD: 2.4738 c. M: 3.5301 c. 88: 11 15 15 21 15 11 SP SD: 1.9871 c. M:-3.8131 c. 95: 12 16 16 23 16 12 SP SD: 1.5117 c. M:-2.9518 c. 112: 14 19 19 27 19 14 SP SD: 1.5470 c. M:-2.8391 c. 119: 15 20 20 29 20 15 SP SD: 1.6338 c. M:-2.2454 c. 127: 16 21 22 30 22 16 SP SD: 1.7267 c. M: 3.8686 c. 134: 17 22 23 32 23 17 SP SD: 1.7178 c. M: 3.0224 c. 136: 17 23 23 33 23 17 SP SD: 1.5485 c. M:-2.2454 c. 151: 19 25 26 36 26 19 SP SD: 1.1927 c. M: 2.4294 c. 168: 21 28 29 40 29 21 SP SD: 1.1585 c. M: 1.9563 c. 175: 22 29 30 42 30 22 SP SD: 1.0169 c. M: 1.3920 c. 192: 24 32 33 46 33 24 SP SD: 0.9643 c. M: 1.8671 c. 222: 28 37 38 53 38 28 SP SD: 0.8357 c. M: 1.5702 c. 239: 30 40 41 57 41 30 SP SD: 0.8274 c. M: 1.2988 c. 246: 31 41 42 59 42 31 SP SD: 0.6862 c. M: 0.9110 c. 263: 33 44 45 63 45 33 SP SD: 0.6623 c. M: 1.2967 c. 325: 41 54 56 78 55 41 SP SD: 0.6347 c. M: 1.0685 c. 338: 43 56 58 81 58 42 SP SD: 0.7066 c. M:-1.2037 c. 345: 44 57 59 83 59 43 SP SD: 0.6490 c. M:-1.1764 c. 349: 44 58 60 84 59 44 SP SD: 0.6306 c. M:-1.0318 c. 362: 46 60 62 87 62 45 SP SD: 0.6275 c. M:-1.1448 c. 401: 51 66 69 96 69 50 SP SD: 0.6201 c. M: 0.9232 c. 418: 53 69 72 100 72 52 SP SD: 0.5829 c. M:-1.0338 c. 425: 54 70 73 102 73 53 SP SD: 0.5578 c. M:-0.6690 c. 442: 56 73 76 106 76 55 SP SD: 0.5103 c. M:-0.9948 c. 472: 60 78 81 113 81 59 SP SD: 0.4334 c. M: 0.7457 c. 489: 62 81 84 117 84 61 SP SD: 0.4018 c. M: 0.6417 c. 496: 63 82 85 119 85 62 SP SD: 0.3552 c. M:-0.5523 c. 513: 65 85 88 123 88 64 SP SD: 0.3079 c. M:-0.6085 c. 537: 68 89 92 129 92 67 SP SD: 0.3013 c. M:-0.5954 c. 575: 73 95 99 138 98 72 SP SD: 0.3082 c. M:-0.4807 c. 599: 76 99 103 144 102 75 SP SD: 0.3006 c. M:-0.5955 c. 608: 77 101 104 146 104 76 SP SD: 0.2932 c. M:-0.5834 c. 646: 82 107 111 155 110 81 SP SD: 0.3439 c. M:-0.4549 c. 663: 84 110 114 159 113 83 SP SD: 0.3656 c. M:-0.6455 c. 670: 85 111 115 161 114 84 SP SD: 0.3173 c. M:-0.5597 c. 687: 87 114 118 165 117 86 SP SD: 0.3311 c. M:-0.6014 c. 702: 89 116 121 168 120 88 SP SD: 0.2921 c. M:-0.4444 c. 726: 92 120 125 174 124 91 SP SD: 0.1945 c. M: 0.3191 c. 750: 95 124 129 180 128 94 SP SD: 0.1504 c. M: 0.3324 c. 767: 97 127 132 184 131 96 SP SD: 0.1457 c. M: 0.2760 c. 797: 101 132 137 191 136 100 SP SD: 0.1841 c. M:-0.2685 c. 821: 104 136 141 197 140 103 SP SD: 0.1166 c. M: 0.2320 c. 838: 106 139 144 201 143 105 SP SD: 0.1078 c. M:-0.2200 c. 845: 107 140 145 203 144 106 SP SD: 0.1279 c. M: 0.2165 c. 862: 109 143 148 207 147 108 SP SD: 0.1027 c. M:-0.1981 c. 1263: 160 209 217 303 216 158 SP SD: 0.1346 c. M:-0.1973 c. 1334: 169 221 229 320 228 167 SP SD: 0.0999 c. M:-0.1569 c. 1358: 172 225 233 326 232 170 SP SD: 0.0874 c. M:-0.1211 c. 1588: 201 263 273 381 271 199 SP SD: 0.0667 c. M:-0.1063 c. 1612: 204 267 277 387 275 202 SP SD: 0.0654 c. M: 0.1120 c. 2101: 266 348 361 504 359 263 SP SD: 0.0638 c. M:-0.1019 c. 2125: 269 352 365 510 363 266 SP SD: 0.0508 c. M:-0.1043 c. 2172: 275 360 373 521 371 272 SP SD: 0.0664 c. M:-0.0964 c. 2179: 276 361 374 523 372 273 SP SD: 0.0654 c. M:-0.1292 c. 2196: 278 364 377 527 375 275 SP SD: 0.0441 c. M:-0.0873 c. 2220: 281 368 381 533 379 278 SP SD: 0.0510 c. M:-0.0784 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 71.4292 cents 3 x x 4:5 x 6 S SD: 23.6136 cents 4 x 5 x x 7:8 SD: 29.4468 cents 5 x 6:7:8:9:10 S SD: 12.4739 cents 6 x 7:8:10:11:12 S SD: 21.9556 cents 8:9:10:11:13:15:16 SD: 12.3737 cents 10:11:12:14:16:18:20 S SD: 10.6230 cents 13:14:16:18:21:24:26 S SD: 5.3355 cents 21:23:26:29:34:39:42 SD: 5.2575 cents 22:24:27:30:36:40:44 S SD: 4.3688 cents 30:33:37:41:49:55:60 SD: 4.0919 cents 31:34:38:43:51:57:62 SD: 3.6319 cents 32:35:39:44:52:59:64 SD: 2.4576 cents 44:48:54:61:72:81:88 SD: 2.3544 cents 45:49:55:62:73:83:90 SD: 2.2982 cents 53:58:65:73:86:97:106 SD: 1.5634 cents 66:72:81:91:108:121:132 SD: 1.4646 cents 76:83:93:105:124:139:152 SD: 1.0130 cents 89:97:109:123:145:163:178 SD: 0.8094 cents 97:106:119:134:158:178:194 SD: 0.7713 cents 108:118:132:149:176:198:216 SD: 0.6177 cents 121:132:148:167:197:222:242 SD: 0.4865 cents 174:190:213:240:283:319:348 SD: 0.4791 cents 187:204:229:258:305:343:374 SD: 0.4212 cents 205:224:251:283:334:376:410 SD: 0.3642 cents 218:238:267:301:355:400:436 SD: 0.3588 cents 227:248:278:313:370:416:454 SD: 0.3403 cents 240:262:294:331:391:440:480 SD: 0.1250 cents 361:394:442:498:588:662:722 SD: 0.0990 cents 588:642:720:811:958:1078:1176 SD: 0.0844 cents