Scala analysis: CD16_03_Morocco
Soyez les bienvenus - 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: 186.071 cents 186.070957 2: 291.718 cents 291.718110 3: 495.868 cents 495.867985 4: 687.233 cents 687.232764 5: 790.432 cents 790.432483 6: 981.117 cents 981.117023 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 218.8830 cents 218.8830 1: 186.0710 cents 186.0710 2: 105.6472 cents 105.6472 3: 204.1499 cents 204.1499 4: 191.3648 cents 191.3648 5: 103.1997 cents 103.1997 6: 190.6845 cents 190.6845 7: 218.8830 cents 218.8830
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 103.19972 cents 1: 1 105.64715 cents 1: 1 186.07096 cents 1: 1 190.68454 cents 1: 1 191.36478 cents 1: 1 204.14987 cents 1: 1 218.88298 cents 2: 1 291.71811 cents 2: 1 293.88426 cents 2: 1 294.56450 cents 2: 1 309.79703 cents 2: 1 395.51465 cents 2: 1 404.95393 cents 2: 1 409.56752 cents 3: 1 485.24904 cents 3: 1 495.86798 cents 3: 1 498.71437 cents 3: 1 501.16181 cents 3: 1 510.60109 cents 3: 1 512.76724 cents 3: 1 595.63847 cents 4: 1 604.36153 cents 4: 1 687.23276 cents 4: 1 689.39891 cents 4: 1 698.83819 cents 4: 1 701.28563 cents 4: 1 704.13202 cents 4: 1 714.75096 cents 5: 1 790.43248 cents 5: 1 795.04607 cents 5: 1 804.48535 cents 5: 1 890.20297 cents 5: 1 905.43550 cents 5: 1 906.11574 cents 5: 1 908.28189 cents 6: 1 981.11702 cents 6: 1 995.85013 cents 6: 1 1008.63522 cents 6: 1 1009.31546 cents 6: 1 1013.92904 cents 6: 1 1094.35285 cents 6: 1 1096.80028 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 : 186.1 291.7 495.9 687.2 790.4 981.1 1200.0 186.1 : 105.6 309.8 501.2 604.4 795.0 1013.9 1200.0 291.7 : 204.1 395.5 498.7 689.4 908.3 1094.4 1200.0 495.9 : 191.4 294.6 485.2 704.1 890.2 995.9 1200.0 687.2 : 103.2 293.9 512.8 698.8 804.5 1008.6 1200.0 790.4 : 190.7 409.6 595.6 701.3 905.4 1096.8 1200.0 981.1 : 218.9 405.0 510.6 714.8 906.1 1009.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 103.1997 .. 218.8830 cents 115.68326 cents 103.19972 cents 2: 291.7181 .. 409.5675 cents 117.84941 cents 72.83513 cents 3: 485.2490 .. 595.6385 cents 110.38944 cents 75.68152 cents 4: 604.3615 .. 714.7510 cents 110.38944 cents 8.72305 cents 5: 790.4325 .. 908.2819 cents 117.84941 cents 75.68152 cents 6: 981.1170 .. 1096.8003 cents 115.68326 cents 72.83513 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 103.19972 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 218.88298 cents Average / Smallest step : 1.661134 Largest / Average step : 1.276817 Largest / Smallest step : 2.120965 Median interval of one step : 190.68454 cents, amount: 1 Least squares average step : 166.03505 cents, oct.: 1162.24534 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : CBFEADG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 8.72305 cents Scale diversity : 1.443664 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.426796 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 : 0.68024 cents Number of recognisable fifths : 6, average 699.2731 cents Number of appreciable fifths : 4, average 698.4137 cents Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 115.6833 cents: 6 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 37.5563 c. M:-66.7104 c. Lebeng 9: 1 1 2 1 1 1 2 P M ME S SD: 32.9724 c. M: 52.7376 c. Pseudo Pelog, Pelogic-7, Antiionian 11: 2 1 2 1 1 2 2 N D3 SD: 30.5685 c. M:-49.5866 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 11.2808 c. M:-18.8830 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 21: 3 2 4 3 2 3 4 SP T3 SD: 10.5381 c. M:-18.4177 c. 26: 4 2 5 4 2 4 5 P T3 SD: 8.9579 c. M: 14.7950 c. 32: 5 3 5 5 3 5 6 P T3 S SD: 6.9314 c. M: 12.2328 c. 33: 5 3 6 5 3 5 6 SP T3 SD: 6.5370 c. M:-13.2229 c. 37: 6 3 6 6 3 6 7 N T3 S SD: 7.6547 c. M: 12.0541 c. 38: 6 3 7 6 3 6 7 P T3 SD: 5.5825 c. M:-9.3952 c. 44: 7 4 7 7 4 7 8 P T3 S SD: 4.5767 c. M:-8.2819 c. 53: 8 5 9 8 5 8 10 SP SD: 4.7946 c. M: 7.9875 c. 56: 9 5 9 9 5 9 10 P T3 S SD: 4.6756 c. M:-8.2819 c. 58: 9 5 10 9 5 9 11 P SD: 4.1120 c. M: 8.7032 c. 59: 9 5 10 10 5 9 11 SP S SD: 4.8874 c. M: 7.7324 c. 61: 9 6 10 10 5 10 11 SP SD: 4.3041 c. M: 9.0218 c. 65: 10 6 11 10 6 10 12 SP SD: 2.8850 c. M: 4.1558 c. 70: 11 6 12 11 6 11 13 P SD: 2.0537 c. M: 3.9742 c. 82: 13 7 14 13 7 13 15 P SD: 1.7716 c. M:-4.1729 c. 114: 18 10 19 18 10 18 21 P SD: 2.2907 c. M:-3.4027 c. 124: 19 11 21 20 11 19 23 SP SD: 2.2541 c. M: 3.6977 c. 126: 20 11 21 20 11 20 23 P SD: 2.2209 c. M:-4.4052 c. 128: 20 11 22 20 11 21 23 P SD: 2.1258 c. M:-3.2580 c. 131: 20 12 22 21 11 21 24 SP SD: 1.6752 c. M: 2.8649 c. 141: 22 12 24 23 12 22 26 SP SD: 1.8264 c. M: 2.3936 c. 143: 22 13 24 23 12 23 26 SP SD: 1.2275 c. M:-1.9882 c. 176: 27 16 30 28 15 28 32 SP SD: 1.3207 c. M: 1.9800 c. 181: 28 16 31 29 15 29 33 SP SD: 1.1604 c. M:-2.2700 c. 182: 28 16 31 29 16 29 33 SP SD: 1.2627 c. M: 1.6082 c. 194: 30 17 33 31 17 31 35 SP SD: 1.2037 c. M:-2.3881 c. 201: 31 18 34 32 17 32 37 SP SD: 1.3042 c. M: 2.3728 c. 206: 32 18 35 33 18 32 38 SP SD: 1.2094 c. M: 2.4762 c. 208: 32 19 35 33 18 33 38 SP SD: 1.1414 c. M:-2.5127 c. 213: 33 19 36 34 18 34 39 SP SD: 0.8591 c. M: 1.7001 c. 225: 35 20 38 36 19 36 41 SP SD: 0.8302 c. M:-1.6152 c. 251: 39 22 43 40 21 40 46 SP SD: 1.0020 c. M: 1.5879 c. 252: 39 22 43 40 22 40 46 SP SD: 0.7929 c. M: 1.5185 c. 264: 41 23 45 42 23 42 48 SP SD: 0.5837 c. M: 0.8691 c. 334: 52 29 57 53 29 53 61 SP SD: 0.5546 c. M: 1.0052 c. 361: 56 32 61 58 31 57 66 SP SD: 0.5938 c. M:-0.8559 c. 363: 56 32 62 58 31 58 66 SP SD: 0.5735 c. M: 0.9470 c. 395: 61 35 67 63 34 63 72 SP SD: 0.5060 c. M: 0.7545 c. 407: 63 36 69 65 35 65 74 SP SD: 0.3865 c. M:-0.7012 c. 433: 67 38 74 69 37 69 79 SP SD: 0.3928 c. M: 0.7250 c. 445: 69 39 76 71 38 71 81 SP SD: 0.3394 c. M: 0.4822 c. 477: 74 42 81 76 41 76 87 SP SD: 0.2758 c. M: 0.4954 c. 489: 76 43 83 78 42 78 89 SP SD: 0.2954 c. M:-0.4781 c. 510: 79 45 87 81 44 81 93 SP SD: 0.2560 c. M:-0.6026 c. 651: 101 57 111 104 56 103 119 SP SD: 0.3133 c. M: 0.4739 c. 653: 101 58 111 104 56 104 119 SP SD: 0.2999 c. M:-0.4718 c. 695: 108 61 118 111 60 110 127 SP SD: 0.2843 c. M:-0.4039 c. 723: 112 64 123 115 62 115 132 SP SD: 0.2809 c. M:-0.3981 c. 774: 120 68 132 123 67 123 141 SP SD: 0.2516 c. M: 0.4111 c. 794: 123 70 135 127 68 126 145 SP SD: 0.2080 c. M:-0.4247 c. 856: 133 75 146 136 74 136 156 SP SD: 0.2674 c. M:-0.3937 c. 859: 133 76 146 137 74 136 157 SP SD: 0.2409 c. M: 0.4418 c. 871: 135 77 148 139 75 138 159 SP SD: 0.2360 c. M:-0.3827 c. 876: 136 77 149 140 75 139 160 SP SD: 0.2195 c. M:-0.4385 c. 910: 141 80 155 145 78 145 166 SP SD: 0.2504 c. M: 0.5424 c. 917: 142 81 156 146 79 146 167 SP SD: 0.1870 c. M:-0.3443 c. 987: 153 87 168 157 85 157 180 SP SD: 0.1509 c. M: 0.3027 c. 999: 155 88 170 159 86 159 182 SP SD: 0.1641 c. M:-0.2644 c. 1058: 164 93 180 169 91 168 193 SP SD: 0.1335 c. M: 0.2247 c. 1128: 175 99 192 180 97 179 206 SP SD: 0.1455 c. M: 0.2660 c. 1140: 177 100 194 182 98 181 208 SP SD: 0.1292 c. M:-0.2448 c. 1271: 197 112 216 203 109 202 232 SP SD: 0.1279 c. M: 0.1953 c. 1283: 199 113 218 205 110 204 234 SP SD: 0.1161 c. M:-0.2185 c. 1304: 202 115 222 208 112 207 238 SP SD: 0.1264 c. M:-0.1905 c. 1348: 209 119 229 215 116 214 246 SP SD: 0.1138 c. M:-0.2700 c. 1353: 210 119 230 216 116 215 247 SP SD: 0.1375 c. M: 0.1886 c. 1360: 211 120 231 217 117 216 248 SP SD: 0.1557 c. M:-0.3407 c. 1374: 213 121 234 219 118 218 251 SP SD: 0.1534 c. M: 0.3310 c. 1386: 215 122 236 221 119 220 253 SP SD: 0.1410 c. M:-0.2359 c. 1432: 222 126 244 228 123 228 261 SP SD: 0.1407 c. M:-0.2214 c. 1523: 236 134 259 243 131 242 278 SP SD: 0.1680 c. M: 0.2672 c. 1529: 237 135 260 244 131 243 279 SP SD: 0.1588 c. M:-0.2754 c. 1530: 237 135 260 244 132 243 279 SP SD: 0.1357 c. M: 0.1886 c. 1535: 238 135 261 245 132 244 280 SP SD: 0.1064 c. M: 0.2328 c. 1547: 240 136 263 247 133 246 282 SP SD: 0.1013 c. M: 0.1989 c. 1568: 243 138 267 250 135 249 286 SP SD: 0.0830 c. M: 0.1365 c. 1650: 256 145 281 263 142 262 301 SP SD: 0.0857 c. M:-0.1320 c. 1781: 276 157 303 284 153 283 325 SP SD: 0.0667 c. M: 0.1080 c. 1793: 278 158 305 286 154 285 327 SP SD: 0.0584 c. M:-0.1069 c. 2045: 317 180 348 326 176 325 373 SP SD: 0.0524 c. M: 0.0934 c. 2057: 319 181 350 328 177 327 375 SP SD: 0.0498 c. M:-0.1178 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: 7.3611 cents 3 x x 4 x 5 x 6 S SD: 31.3172 cents 4 x 5 x 6 x 7:8 S SD: 24.1300 cents 5 x 6:7 x 8:9:10 S SD: 19.9510 cents 6 x 7:8:9 x 11:12 SD: 14.8275 cents 7:8 x 9:10:11:12:14 S SD: 18.9731 cents 8:9 x 11:12:13:14:16 SD: 13.1975 cents 9:10:11:12:13:14:16:18 S SD: 11.5677 cents 10:11:12:13:15:16:18:20 SD: 9.9380 cents 12:13:14:16:18:19:21:24 SD: 8.1720 cents 16:18:19:21:24:25:28:32 SD: 5.8310 cents 17:19:20:23:25:27:30:34 SD: 5.3456 cents 21:23:25:28:31:33:37:42 SD: 4.8567 cents 26:29:31:35:39:41:46:52 SD: 4.0104 cents 27:30:32:36:40:43:48:54 SD: 3.2761 cents 33:37:39:44:49:52:58:66 SD: 2.0022 cents 43:48:51:57:64:68:76:86 SD: 1.6266 cents 54:60:64:72:80:85:95:108 SD: 1.4659 cents 60:67:71:80:89:95:106:120 SD: 1.3857 cents 72:80:85:96:107:114:127:144 SD: 1.1721 cents 88:98:104:117:131:139:155:176 SD: 0.6140 cents 142:158:168:189:211:224:250:284 SD: 0.4624 cents 168:187:199:224:250:265:296:336 SD: 0.4583 cents 185:206:219:246:275:292:326:370 SD: 0.3914 cents 202:225:239:269:300:319:356:404 SD: 0.3862 cents 211:235:250:281:314:333:372:422 SD: 0.3310 cents 256:285:303:341:381:404:451:512 SD: 0.2265 cents 283:315:335:377:421:447:499:566 SD: 0.2261 cents 299:333:354:398:445:472:527:598 SD: 0.2206 cents 316:352:374:421:470:499:557:632 SD: 0.1719 cents 404:450:478:538:601:638:712:808 SD: 0.1553 cents 425:473:503:566:632:671:749:850 SD: 0.1289 cents 458:510:542:610:681:723:807:916 SD: 0.1059 cents