Scala analysis: CD11_03_rast_Iraq
Suite - Ensemble de Muhammad Al-Qubbbânjî (rast, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 215.860 cents 215.860309 2: 375.946 cents 375.945890 3: 498.025 cents 498.025096 4: 695.841 cents 695.840873 5: 909.967 cents 909.967087 6: 993.169 cents 993.169405 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 206.8306 cents 206.8306 1: 215.8603 cents 215.8603 2: 160.0856 cents 160.0856 3: 122.0792 cents 122.0792 4: 197.8158 cents 197.8158 5: 214.1262 cents 214.1262 6: 83.2023 cents 83.2023 7: 206.8306 cents 206.8306
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 83.20232 cents 1: 1 122.07921 cents 1: 1 160.08558 cents 1: 1 197.81578 cents 1: 1 206.83059 cents 1: 1 214.12621 cents 1: 1 215.86031 cents 2: 1 282.16479 cents 2: 1 290.03291 cents 2: 1 297.32853 cents 2: 1 319.89498 cents 2: 1 375.94589 cents 2: 1 411.94199 cents 2: 1 422.69090 cents 3: 1 479.98056 cents 3: 1 495.14431 cents 3: 1 498.02510 cents 3: 1 504.15913 cents 3: 1 505.89322 cents 3: 1 534.02120 cents 3: 1 582.77648 cents 4: 1 617.22352 cents 4: 1 665.97880 cents 4: 1 694.10678 cents 4: 1 695.84087 cents 4: 1 701.97490 cents 4: 1 704.85569 cents 4: 1 720.01944 cents 5: 1 777.30910 cents 5: 1 788.05801 cents 5: 1 824.05411 cents 5: 1 880.10502 cents 5: 1 902.67147 cents 5: 1 909.96709 cents 5: 1 917.83521 cents 6: 1 984.13969 cents 6: 1 985.87379 cents 6: 1 993.16940 cents 6: 1 1002.18422 cents 6: 1 1039.91442 cents 6: 1 1077.92079 cents 6: 1 1116.79768 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 : 215.9 375.9 498.0 695.8 910.0 993.2 1200.0 215.9 : 160.1 282.2 480.0 694.1 777.3 984.1 1200.0 375.9 : 122.1 319.9 534.0 617.2 824.1 1039.9 1200.0 498.0 : 197.8 411.9 495.1 702.0 917.8 1077.9 1200.0 695.8 : 214.1 297.3 504.2 720.0 880.1 1002.2 1200.0 910.0 : 83.2 290.0 505.9 666.0 788.1 985.9 1200.0 993.2 : 206.8 422.7 582.8 704.9 902.7 1116.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.2023 .. 215.8603 cents 132.65799 cents 83.20232 cents 2: 282.1648 .. 422.6909 cents 140.52612 cents 66.30448 cents 3: 479.9806 .. 582.7765 cents 102.79592 cents 57.28966 cents 4: 617.2235 .. 720.0194 cents 102.79592 cents 34.44703 cents 5: 777.3091 .. 917.8352 cents 140.52612 cents 57.28966 cents 6: 984.1397 .. 1116.7977 cents 132.65799 cents 66.30448 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 83.20232 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 215.86031 cents Average / Smallest step : 2.060382 Largest / Average step : 1.259185 Largest / Smallest step : 2.594403 Median interval of one step : 197.81578 cents, amount: 1 Least squares average step : 172.52888 cents, oct.: 1207.70214 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : GCBDFAE Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.44703 cents Scale diversity : 1.662526 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.373367 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 : 1.73409 cents Number of recognisable fifths : 4, average 699.1946 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 32.6884 c. M: 52.8242 c. Lebeng 10: 2 1 1 2 2 0 2 P D3 S SD: 27.6433 c. M:-50.0329 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 11.9364 c. M:-24.0541 c. G.Hypophrygian, G.Ionian (Iastian), M.Mixolydian, G.M.Hypoionian, Hypermixolydian, Mischung 3, Khamaj That, Mela Harikambhoji, Raga Balahamsa, Bhim, Devamanohari, Harini, Janjhuti, Kaamaai, Khambhavati, Surati, Gregorian nr.7, Enharmonic Byzantine Liturgical, Rast descending: Greece, Ching, Shang: China 17: 3 2 2 3 3 1 3 SP D3 S SD: 10.3193 c. M: 23.0047 c. 22: 4 3 2 4 4 1 4 P SD: 9.9600 c. M:-17.3056 c. Khamaj That 28: 5 4 3 4 5 2 5 P SD: 9.4096 c. M:-16.2606 c. 29: 5 4 3 5 5 2 5 SP SD: 4.6754 c. M: 8.9638 c. 45: 8 6 5 7 8 3 8 SP SD: 4.5881 c. M:-8.6416 c. 57: 10 8 6 9 10 4 10 SP SD: 4.2570 c. M:-7.2381 c. 65: 12 8 7 11 11 5 11 SP SD: 4.6709 c. M: 6.7151 c. 67: 12 9 7 11 12 4 12 SP SD: 3.7335 c. M: 8.0948 c. 74: 13 10 8 12 13 5 13 SP SD: 3.3303 c. M: 5.0495 c. 83: 15 11 8 14 15 6 14 SP SD: 3.0828 c. M: 6.4588 c. 90: 16 12 9 15 16 6 16 SP SD: 3.6779 c. M: 6.5027 c. 92: 17 12 9 15 17 6 16 SP SD: 3.3610 c. M:-5.8788 c. 95: 17 13 9 16 17 7 16 SP SD: 3.0036 c. M: 5.3935 c. 98: 18 13 10 16 17 7 17 SP SD: 3.1881 c. M:-4.5479 c. 99: 18 13 10 16 18 7 17 SP SD: 2.1455 c. M: 4.9318 c. 109: 20 14 11 18 20 7 19 SP SD: 2.7567 c. M:-4.3232 c. 111: 20 15 11 18 20 8 19 SP SD: 1.9876 c. M: 3.9490 c. 115: 21 15 12 19 20 8 20 SP SD: 2.3224 c. M:-3.2896 c. 116: 21 15 12 19 21 8 20 SP SD: 1.8591 c. M: 3.5321 c. 121: 22 16 12 20 22 8 21 SP SD: 1.7518 c. M:-2.4296 c. 128: 23 17 13 21 23 9 22 SP SD: 1.0235 c. M: 2.0909 c. 140: 25 19 14 23 25 10 24 SP SD: 1.2132 c. M: 1.5746 c. 150: 27 20 15 25 27 10 26 SP SD: 1.1741 c. M:-2.0329 c. 157: 28 21 16 26 28 11 27 SP SD: 1.0266 c. M: 1.8476 c. 195: 35 26 20 32 35 13 34 SP SD: 1.0243 c. M: 2.4002 c. 207: 37 28 21 34 37 14 36 SP SD: 0.9593 c. M: 1.8651 c. 210: 38 28 21 35 37 15 36 SP SD: 1.1177 c. M: 1.3957 c. 224: 40 30 23 37 40 15 39 SP SD: 1.1158 c. M: 2.0980 c. 227: 41 30 23 38 40 16 39 SP SD: 1.0115 c. M:-1.9565 c. 233: 42 31 24 38 42 16 40 SP SD: 0.9419 c. M:-1.6209 c. 243: 44 32 25 40 43 17 42 SP SD: 0.8682 c. M:-1.4236 c. 245: 44 33 25 40 44 17 42 SP SD: 0.9618 c. M:-1.5667 c. 255: 46 34 26 42 45 18 44 SP SD: 0.8223 c. M: 1.7318 c. 262: 47 35 27 43 47 18 45 SP SD: 0.8281 c. M:-1.4833 c. 272: 49 36 28 45 48 19 47 SP SD: 0.7849 c. M:-1.2180 c. 278: 50 37 28 46 50 19 48 SP SD: 0.7909 c. M: 1.6222 c. 285: 51 38 29 47 51 20 49 SP SD: 0.9142 c. M: 1.2090 c. 290: 52 39 29 48 52 20 50 SP SD: 0.7176 c. M: 1.4734 c. 323: 58 43 33 53 58 22 56 SP SD: 0.7029 c. M: 1.2189 c. 335: 60 45 34 55 60 23 58 SP SD: 0.6135 c. M: 0.9349 c. 373: 67 50 38 61 67 26 64 SP SD: 0.6204 c. M: 0.9347 c. 376: 68 50 38 62 67 26 65 SP SD: 0.5778 c. M:-1.1610 c. 383: 69 51 39 63 68 27 66 SP SD: 0.5392 c. M: 1.3509 c. 390: 70 52 40 64 70 27 67 SP SD: 0.5400 c. M:-0.8021 c. 393: 71 52 40 65 70 27 68 SP SD: 0.5174 c. M:-0.9336 c. 400: 72 53 41 66 71 28 69 SP SD: 0.5216 c. M: 0.9671 c. 405: 73 54 41 67 72 28 70 SP SD: 0.3832 c. M: 0.5768 c. 533: 96 71 54 88 95 37 92 SP SD: 0.2841 c. M: 0.4641 c. 562: 101 75 57 93 100 39 97 SP SD: 0.2925 c. M: 0.5162 c. 638: 115 85 65 105 114 44 110 SP SD: 0.2846 c. M:-0.4406 c. 645: 116 86 66 106 115 45 111 SP SD: 0.2667 c. M:-0.5796 c. 667: 120 89 68 110 119 46 115 SP SD: 0.2471 c. M:-0.4110 c. 766: 138 102 78 126 137 53 132 SP SD: 0.1915 c. M:-0.3277 c. 778: 140 104 79 128 139 54 134 SP SD: 0.1962 c. M:-0.4037 c. 795: 143 106 81 131 142 55 137 SP SD: 0.0985 c. M:-0.2216 c. 1200: 216 160 122 198 214 83 207 SP SD: 0.1057 c. M: 0.1694 c. 1328: 239 177 135 219 237 92 229 SP SD: 0.0791 c. M: 0.1335 c. 1973: 355 263 201 325 352 137 340 SP SD: 0.0641 c. M:-0.0996 c. 2007: 361 268 204 331 358 139 346 SP SD: 0.0754 c. M:-0.1378 c. 2106: 379 281 214 347 376 146 363 SP SD: 0.0731 c. M:-0.1225 c. 2123: 382 283 216 350 379 147 366 SP SD: 0.0503 c. M:-0.0659 c. 2135: 384 285 217 352 381 148 368 SP SD: 0.0336 c. M:-0.0728 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: 3.0571 cents 3 x x 4 x 5 x 6 S SD: 8.5361 cents 4 x 5 x 6 x 7:8 S SD: 6.7891 cents 5 x 6:7 x 8:9:10 S SD: 28.7342 cents 6:7 x 8:9:10:11:12 S SD: 13.3884 cents 7:8:9 x 10:12 x 14 S SD: 20.4035 cents 8:9:10:11:12 x 14:16 S SD: 10.1659 cents 12:14:15:16:18:20:21:24 S SD: 9.0298 cents 13:15:16:17:19:22:23:26 SD: 8.9857 cents 14:16:17:19:21:24:25:28 SD: 8.3872 cents 15:17:19:20:22:25:27:30 SD: 8.3754 cents 16:18:20:21:24:27:28:32 S SD: 5.7841 cents 21:24:26:28:31:36:37:42 SD: 5.4103 cents 22:25:27:29:33:37:39:44 SD: 4.5592 cents 24:27:30:32:36:41:43:48 SD: 4.1655 cents 29:33:36:39:43:49:51:58 SD: 3.8677 cents 30:34:37:40:45:51:53:60 SD: 2.6415 cents 36:41:45:48:54:61:64:72 SD: 2.2533 cents 45:51:56:60:67:76:80:90 SD: 1.1876 cents 75:85:93:100:112:127:133:150 SD: 0.6586 cents 111:126:138:148:166:188:197:222 SD: 0.6325 cents 120:136:149:160:179:203:213:240 SD: 0.5476 cents 156:177:194:208:233:264:277:312 SD: 0.5145 cents 165:187:205:220:247:279:293:330 SD: 0.4241 cents 174:197:216:232:260:294:309:348 SD: 0.4151 cents 210:238:261:280:314:355:373:420 SD: 0.2944 cents 240:272:298:320:359:406:426:480 SD: 0.2826 cents 279:316:347:372:417:472:495:558 SD: 0.2568 cents 285:323:354:380:426:482:506:570 SD: 0.1770 cents 354:401:440:472:529:599:628:708 SD: 0.1699 cents 408:462:507:544:610:690:724:816 SD: 0.1323 cents 453:513:563:604:677:766:804:906 SD: 0.1303 cents 483:547:600:644:722:817:857:966 SD: 0.1090 cents 519:588:645:692:776:878:921:1038 SD: 0.1065 cents 528:598:656:704:789:893:937:1056 SD: 0.0921 cents 564:639:701:752:843:954:1001:1128 SD: 0.0848 cents