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