Scala analysis: CD16_17_Morocco
Mon amour, lorsque je le contemple - L'ensemble de 'Umar Fâ'id Al-Ju'aydî (ushshaq, Morocco)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 217.191 cents 217.191277 2: 504.397 cents 504.396978 3: 715.156 cents 715.155680 4: 917.422 cents 917.422204 5: 1004.334 cents 1004.333655 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 195.6663 cents 195.6663 1: 217.1913 cents 217.1913 2: 287.2057 cents 287.2057 3: 210.7587 cents 210.7587 4: 202.2665 cents 202.2665 5: 86.9115 cents 86.9115 6: 195.6663 cents 195.6663
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 86.91145 cents 1: 1 195.66634 cents 1: 1 202.26652 cents 1: 1 210.75870 cents 1: 1 217.19128 cents 1: 1 287.20570 cents 2: 1 282.57780 cents 2: 1 289.17798 cents 2: 1 412.85762 cents 2: 1 413.02523 cents 2: 1 497.96440 cents 2: 1 504.39698 cents 3: 1 484.84432 cents 3: 1 499.76907 cents 3: 1 499.93668 cents 3: 1 700.06332 cents 3: 1 700.23093 cents 3: 1 715.15568 cents 4: 1 695.60302 cents 4: 1 702.03560 cents 4: 1 786.97477 cents 4: 1 787.14238 cents 4: 1 910.82202 cents 4: 1 917.42220 cents 5: 1 912.79430 cents 5: 1 982.80872 cents 5: 1 989.24130 cents 5: 1 997.73348 cents 5: 1 1004.33366 cents 5: 1 1113.08855 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 : 217.2 504.4 715.2 917.4 1004.3 1200.0 217.2 : 287.2 498.0 700.2 787.1 982.8 1200.0 504.4 : 210.8 413.0 499.9 695.6 912.8 1200.0 715.2 : 202.3 289.2 484.8 702.0 989.2 1200.0 917.4 : 86.9 282.6 499.8 787.0 997.7 1200.0 1004.3: 195.7 412.9 700.1 910.8 1113.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 86.9115 .. 287.2057 cents 200.29425 cents 86.91145 cents 2: 282.5778 .. 504.3970 cents 221.81918 cents -4.62790 cents 3: 484.8443 .. 715.1557 cents 230.31136 cents -19.55266 cents 4: 695.6030 .. 917.4222 cents 221.81918 cents -19.55266 cents 5: 912.7943 .. 1113.0885 cents 200.29425 cents -4.62791 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 86.91145 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 287.20570 cents Average / Smallest step : 2.301193 Largest / Average step : 1.436029 Largest / Smallest step : 3.304578 Median interval of one step : 206.51261 cents, amount: 0 Least squares average step : 211.67922 cents, oct.: 1270.07534 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : EFDCAB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.80467 cents Scale diversity : 1.361674 Lumma stability : 0.144852 Lumma impropriety factor : 0.040301 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 : 0.16760 cents Number of recognisable fifths : 5, average 702.6177 cents Number of appreciable fifths : 4, average 699.4832 cents Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 215.3866 cents: 3 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 79.8560 c. M: 117.4222 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 2 1 1 1 1 P M ME SD: 34.8326 c. M: 60.2793 c. 10: 2 2 2 2 0 2 P M DE SD: 28.6277 c. M: 44.3337 c. 12: 2 3 2 2 1 2 P G D3 SD: 12.0200 c. M: 17.4222 c. Mixolydian Hexatonic, P'yongjo: Korea, Yosen: Japan, Raga Darbar, Narayani, Suposhini, Andolika, Gorakh Kalyan, Rakta Hauns 17: 3 4 3 3 1 3 P G D3 SD: 8.9472 c. M: 16.0984 c. 29: 5 7 5 5 2 5 P G D3 SD: 8.9517 c. M: 11.7074 c. 33: 6 8 6 5 3 5 N SD: 8.4756 c. M:-13.8482 c. 35: 6 9 6 6 2 6 N D3 SD: 8.3934 c. M: 11.4770 c. 37: 7 9 6 6 3 6 N SD: 8.1468 c. M:-14.5219 c. 38: 7 9 7 6 3 6 N SD: 5.4958 c. M:-11.1601 c. 43: 8 10 8 7 3 7 N SD: 5.1989 c. M:-10.4257 c. 48: 9 11 9 8 3 8 N SD: 6.4990 c. M:-9.8443 c. 50: 9 12 9 8 4 8 N SD: 3.3637 c. M: 5.4222 c. 55: 10 13 10 9 4 9 N SD: 2.3347 c. M:-4.8443 c. 67: 12 16 12 11 5 11 N SD: 2.3415 c. M: 3.9894 c. 109: 20 26 19 18 8 18 N SD: 2.3414 c. M: 3.6607 c. 111: 20 27 19 19 8 18 N SD: 1.8623 c. M:-3.7111 c. 116: 21 28 20 20 8 19 N SD: 1.8059 c. M:-3.2675 c. 122: 22 29 22 20 9 20 N SD: 2.0310 c. M:-2.8771 c. 123: 22 30 21 21 9 20 N SD: 2.0103 c. M: 2.9606 c. 128: 23 31 22 22 9 21 N SD: 1.6413 c. M: 2.6557 c. 136: 25 32 24 23 10 22 N SD: 1.6487 c. M:-3.3970 c. 148: 27 35 26 25 11 24 N SD: 1.3635 c. M:-1.7276 c. 154: 28 37 27 26 11 25 N SD: 1.4910 c. M:-2.0965 c. 161: 29 39 28 27 12 26 N SD: 1.3605 c. M:-2.4353 c. 166: 30 40 29 28 12 27 N SD: 0.7819 c. M:-1.6271 c. 178: 32 43 31 30 13 29 N SD: 0.8441 c. M: 1.4609 c. 183: 33 44 32 31 13 30 N SD: 0.6526 c. M: 1.0550 c. 221: 40 53 39 37 16 36 N SD: 0.7001 c. M:-1.5864 c. 233: 42 56 41 39 17 38 N SD: 0.5594 c. M: 0.8823 c. 238: 43 57 42 40 17 39 N SD: 0.5537 c. M: 0.9723 c. 314: 57 75 55 53 23 51 N SD: 0.4663 c. M:-0.7619 c. 331: 60 79 58 56 24 54 N SD: 0.4648 c. M: 0.9563 c. 369: 67 88 65 62 27 60 N SD: 0.4274 c. M:-0.6949 c. 386: 70 92 68 65 28 63 N SD: 0.3939 c. M: 0.7700 c. 404: 73 97 71 68 29 66 N SD: 0.4482 c. M:-0.6859 c. 416: 75 100 73 70 30 68 N SD: 0.4446 c. M: 0.8451 c. 480: 87 115 84 81 35 78 N SD: 0.3944 c. M:-0.6663 c. 485: 88 116 85 82 35 79 N SD: 0.3487 c. M:-0.5407 c. 497: 90 119 87 84 36 81 N SD: 0.2236 c. M: 0.4676 c. 547: 99 131 96 92 40 89 N SD: 0.2527 c. M: 0.4204 c. 552: 100 132 97 93 40 90 N SD: 0.0889 c. M:-0.2000 c. 1049: 190 251 184 177 76 171 N SD: 0.1088 c. M: 0.1890 c. 1116: 202 267 196 188 81 182 N SD: 0.1067 c. M: 0.2179 c. 1270: 230 304 223 214 92 207 N SD: 0.1078 c. M:-0.1700 c. 1282: 232 307 225 216 93 209 N SD: 0.0707 c. M:-0.1272 c. 1287: 233 308 226 217 93 210 N SD: 0.0672 c. M: 0.1379 c. 1520: 275 364 267 256 110 248 N SD: 0.0845 c. M: 0.1231 c. 1668: 302 399 293 281 121 272 N SD: 0.0806 c. M: 0.1560 c. 1822: 330 436 320 307 132 297 N SD: 0.0900 c. M:-0.1523 c. 1834: 332 439 322 309 133 299 N SD: 0.0495 c. M: 0.0831 c. 2386: 432 571 419 402 173 389 N SD: 0.0480 c. M:-0.0761 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 6.6003 cents 3 x 4 x 5 x 6 S SD: 11.2227 cents 4 x 5:6 x 7:8 S SD: 31.0027 cents 5:6:7:8 x 9:10 S SD: 32.0491 cents 6:7:8:9:10:11:12 H SD: 12.6968 cents 8:9:11:12 x 14:16 SD: 12.3499 cents 9:10:12:14:15:16:18 S SD: 11.6521 cents 13:15:17:20:22:23:26 SD: 10.2580 cents 14:16:19:21:24:25:28 SD: 5.7898 cents 20:23:27:30:34:36:40 SD: 5.7610 cents 21:24:28:32:36:38:42 SD: 5.7301 cents 23:26:31:35:39:41:46 SD: 3.0608 cents 29:33:39:44:49:52:58 SD: 2.8344 cents 39:44:52:59:66:70:78 SD: 2.5043 cents 45:51:60:68:76:80:90 SD: 2.4234 cents 47:53:63:71:80:84:94 SD: 1.7144 cents 53:60:71:80:90:95:106 SD: 1.1900 cents 74:84:99:112:126:132:148 SD: 0.9466 cents 103:117:138:156:175:184:206 SD: 0.8899 cents 104:118:139:157:177:186:208 SD: 0.8519 cents 106:120:142:160:180:189:212 SD: 0.8336 cents 112:127:150:169:190:200:224 SD: 0.6815 cents 113:128:151:171:192:202:226 SD: 0.6319 cents 127:144:170:192:216:227:254 SD: 0.3991 cents 172:195:230:260:292:307:344 SD: 0.3692 cents 186:211:249:281:316:332:372 SD: 0.3339 cents 225:255:301:340:382:402:450 SD: 0.2374 cents 299:339:400:452:508:534:598 SD: 0.1240 cents 352:399:471:532:598:629:704 SD: 0.1218 cents 524:594:701:792:890:936:1048 SD: 0.1135 cents 538:610:720:813:914:961:1076 SD: 0.0778 cents