Scala analysis: CD16_07_Morocco
Une lune parfaite - 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: 200.120 cents 200.119611 2: 486.751 cents 486.750577 3: 699.599 cents 699.598904 4: 889.005 cents 889.005186 5: 991.967 cents 991.967023 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 208.0330 cents 208.0330 1: 200.1196 cents 200.1196 2: 286.6310 cents 286.6310 3: 212.8483 cents 212.8483 4: 189.4063 cents 189.4063 5: 102.9618 cents 102.9618 6: 208.0330 cents 208.0330
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 102.96184 cents 1: 1 189.40628 cents 1: 1 200.11961 cents 1: 1 208.03298 cents 1: 1 212.84833 cents 1: 1 286.63097 cents 2: 1 292.36812 cents 2: 1 310.99481 cents 2: 1 402.25461 cents 2: 1 408.15259 cents 2: 1 486.75058 cents 2: 1 499.47929 cents 3: 1 500.40110 cents 3: 1 505.21645 cents 3: 1 511.11443 cents 3: 1 688.88558 cents 3: 1 694.78355 cents 3: 1 699.59890 cents 4: 1 700.52071 cents 4: 1 713.24942 cents 4: 1 791.84741 cents 4: 1 797.74539 cents 4: 1 889.00519 cents 4: 1 907.63188 cents 5: 1 913.36903 cents 5: 1 987.15167 cents 5: 1 991.96702 cents 5: 1 999.88039 cents 5: 1 1010.59372 cents 5: 1 1097.03816 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 : 200.1 486.8 699.6 889.0 992.0 1200.0 200.1 : 286.6 499.5 688.9 791.8 999.9 1200.0 486.8 : 212.8 402.3 505.2 713.2 913.4 1200.0 699.6 : 189.4 292.4 500.4 700.5 987.2 1200.0 889.0 : 103.0 311.0 511.1 797.7 1010.6 1200.0 992.0 : 208.0 408.2 694.8 907.6 1097.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 102.9618 .. 286.6310 cents 183.66913 cents 102.96184 cents 2: 292.3681 .. 499.4793 cents 207.11117 cents 5.73715 cents 3: 500.4011 .. 699.5989 cents 199.19781 cents 0.92180 cents 4: 700.5207 .. 907.6319 cents 207.11117 cents 0.92180 cents 5: 913.3690 .. 1097.0382 cents 183.66913 cents 5.73715 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 102.96184 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 286.63097 cents Average / Smallest step : 1.942467 Largest / Average step : 1.433155 Largest / Smallest step : 2.783856 Median interval of one step : 204.07629 cents, amount: 0 Least squares average step : 208.66234 cents, oct.: 1251.97407 cents Scale is strictly proper Step pattern alph. order: ABCDEF Step pattern size order : CFEBAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.92180 cents Scale diversity : 1.438865 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.182701 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 : 0.92180 cents Number of recognisable fifths : 5, average 699.4076 cents Number of appreciable fifths : 4, average 702.0381 cents Formal octave complements present : 1 = 16.6667% Limited inverse transpositions with margin 194.3825 cents: 3 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 65.1051 c. M: 99.5989 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 2 1 1 1 1 P M ME SD: 26.2337 c. M:-36.6044 c. 11: 2 2 2 2 1 2 SP M ME SD: 29.6166 c. M: 50.3869 c. Schulter Hexatonic 12: 2 3 2 2 1 2 P G D3 SD: 7.7582 c. M:-13.2494 c. Mixolydian Hexatonic, P'yongjo: Korea, Yosen: Japan, Raga Darbar, Narayani, Suposhini, Andolika, Gorakh Kalyan, Rakta Hauns 34: 6 8 6 5 3 6 P SD: 6.9227 c. M:-11.6451 c. 35: 6 8 6 6 3 6 SP D3 SD: 6.8423 c. M: 13.8846 c. 40: 7 9 7 7 3 7 SP D3 SD: 7.7469 c. M:-10.9948 c. 41: 7 10 7 6 4 7 P SD: 6.8016 c. M: 10.9564 c. 42: 7 10 7 7 4 7 SP D3 SD: 6.6986 c. M: 13.8846 c. 45: 7 11 8 7 4 8 P SD: 7.9057 c. M: 13.4529 c. 46: 8 11 8 7 4 8 P SD: 5.4769 c. M:-8.9016 c. 47: 8 11 8 8 4 8 SP D3 SD: 5.1664 c. M: 10.2372 c. 50: 8 12 9 8 4 9 P SD: 5.6115 c. M: 8.1196 c. 54: 9 13 9 9 5 9 SP D3 SD: 5.5352 c. M: 10.7100 c. 57: 9 14 10 9 5 10 P SD: 5.3640 c. M: 10.6459 c. 58: 10 14 10 9 5 10 P SD: 5.1401 c. M:-9.8011 c. 59: 10 14 10 10 5 10 SP D3 SD: 4.7308 c. M: 8.0735 c. 62: 10 15 11 10 5 11 P SD: 3.7618 c. M: 6.5712 c. 74: 12 18 13 12 6 13 P SD: 2.9423 c. M: 5.5250 c. 76: 13 18 13 12 7 13 SP SD: 3.8334 c. M:-5.1435 c. 77: 13 18 14 12 7 13 P SD: 2.9512 c. M:-5.4356 c. 82: 14 19 15 13 7 14 P SD: 3.3865 c. M:-4.7584 c. 84: 14 20 15 13 7 15 P SD: 2.9205 c. M: 6.2527 c. 86: 14 21 15 14 7 15 P SD: 2.7943 c. M: 4.7708 c. 88: 15 21 15 14 8 15 SP SD: 3.4928 c. M:-4.4258 c. 89: 15 21 16 14 8 15 P SD: 2.6754 c. M:-5.7858 c. 91: 15 22 16 14 8 16 P SD: 2.7710 c. M: 5.4887 c. 96: 16 23 17 15 8 17 P SD: 1.9560 c. M: 4.4670 c. 103: 17 25 18 16 9 18 P SD: 2.1102 c. M: 3.5683 c. 108: 18 26 19 17 9 19 P SD: 1.5403 c. M: 3.0781 c. 138: 23 33 24 22 12 24 SP SD: 1.8380 c. M: 3.9467 c. 139: 23 33 25 22 12 24 P SD: 1.5355 c. M: 3.2973 c. 146: 24 35 26 23 13 25 P SD: 1.8585 c. M: 2.8593 c. 150: 25 36 26 24 13 26 SP SD: 1.6093 c. M: 3.5989 c. 151: 25 36 27 24 13 26 P SD: 1.2382 c. M: 1.9824 c. 163: 27 39 29 26 14 28 P SD: 1.2526 c. M:-1.8980 c. 173: 29 41 31 27 15 30 P SD: 0.8934 c. M: 1.2014 c. 185: 31 44 33 29 16 32 P SD: 0.6089 c. M:-0.9615 c. 197: 33 47 35 31 17 34 P SD: 0.6965 c. M:-0.9264 c. 247: 41 59 44 39 21 43 P SD: 0.6428 c. M: 0.9293 c. 259: 43 62 46 41 22 45 P SD: 0.4836 c. M: 0.8918 c. 293: 49 70 52 46 25 51 P SD: 0.5821 c. M: 0.8407 c. 340: 57 81 60 54 29 59 SP SD: 0.5801 c. M:-1.0569 c. 420: 70 100 75 66 36 73 P SD: 0.5365 c. M: 1.0363 c. 427: 71 102 76 67 37 74 P SD: 0.5167 c. M: 0.9490 c. 431: 72 103 76 68 37 75 SP SD: 0.6124 c. M: 0.8381 c. 432: 72 103 77 68 37 75 P SD: 0.3386 c. M: 0.6395 c. 439: 73 105 78 69 38 76 P SD: 0.3803 c. M: 0.6225 c. 444: 74 106 79 70 38 77 P SD: 0.2177 c. M:-0.4011 c. 767: 128 183 136 121 66 133 SP SD: 0.1995 c. M: 0.3481 c. 779: 130 186 138 123 67 135 SP SD: 0.1373 c. M: 0.2408 c. 791: 132 189 140 125 68 137 SP SD: 0.1638 c. M: 0.2310 c. 964: 161 230 171 152 83 167 SP SD: 0.1602 c. M:-0.2953 c. 1026: 171 245 182 162 88 178 SP SD: 0.1447 c. M: 0.2009 c. 1038: 173 248 184 164 89 180 SP SD: 0.0925 c. M: 0.1769 c. 1050: 175 251 186 166 90 182 SP SD: 0.1116 c. M: 0.1703 c. 1211: 202 289 215 191 104 210 SP SD: 0.1107 c. M: 0.2105 c. 1223: 204 292 217 193 105 212 SP SD: 0.0417 c. M: 0.0785 c. 2261: 377 540 401 357 194 392 SP SD: 0.0463 c. M: 0.0854 c. 2273: 379 543 403 359 195 394 SP SD: 0.0412 c. M: 0.0828 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 1.1780 cents 3 x 4 x 5 x 6 S SD: 4.0709 cents 4 x 5:6 x 7:8 S SD: 25.7738 cents 5:6:7 x 8:9:10 S SD: 33.9678 cents 6:7:8:9:10:11:12 H SD: 14.8181 cents 7:8:9:10:12 x 14 S SD: 22.2018 cents 8:9:11:12:13:14:16 SD: 14.0183 cents 9:10:12:13:15:16:18 SD: 11.1139 cents 10:11:13:15:17:18:20 SD: 10.3178 cents 14:16:19:21:23:25:28 SD: 10.1957 cents 15:17:20:22:25:27:30 SD: 8.1927 cents 16:18:21:24:27:28:32 S SD: 5.5144 cents 18:20:24:27:30:32:36 S SD: 3.6726 cents 24:27:32:36:40:43:48 SD: 3.6465 cents 30:34:40:45:50:53:60 SD: 3.6304 cents 31:35:41:46:52:55:62 SD: 3.4044 cents 34:38:45:51:57:60:68 SD: 2.1740 cents 40:45:53:60:67:71:80 SD: 1.0277 cents 58:65:77:87:97:103:116 SD: 0.9872 cents 89:100:118:133:149:158:178 SD: 0.9823 cents 98:110:130:147:164:174:196 SD: 0.7631 cents 139:156:184:208:232:247:278 SD: 0.7577 cents 145:163:192:217:242:257:290 SD: 0.6568 cents 154:173:204:231:257:273:308 SD: 0.6150 cents 155:174:205:232:259:275:310 SD: 0.5199 cents 163:183:216:244:272:289:326 SD: 0.4868 cents 173:194:229:259:289:307:346 SD: 0.4448 cents 195:219:258:292:326:346:390 SD: 0.4227 cents 203:228:269:304:339:360:406 SD: 0.2910 cents 213:239:282:319:356:378:426 SD: 0.2761 cents 237:266:314:355:396:420:474 SD: 0.2419 cents 277:311:367:415:463:491:554 SD: 0.1917 cents 416:467:551:623:695:738:832 SD: 0.1382 cents 450:505:596:674:752:798:900 SD: 0.1069 cents 490:550:649:734:819:869:980 SD: 0.0672 cents