Scala analysis: CD16_12_Morocco
Ton absence - 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: 211.263 cents 211.262762 2: 377.628 cents 377.627965 3: 510.189 cents 510.189002 4: 709.093 cents 709.092801 5: 925.745 cents 925.745222 6: 1011.225 cents 1011.225076 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 188.7749 cents 188.7749 1: 211.2628 cents 211.2628 2: 166.3652 cents 166.3652 3: 132.5610 cents 132.5610 4: 198.9038 cents 198.9038 5: 216.6524 cents 216.6524 6: 85.4799 cents 85.4799 7: 188.7749 cents 188.7749
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85.47985 cents 1: 1 132.56104 cents 1: 1 166.36520 cents 1: 1 188.77492 cents 1: 1 198.90380 cents 1: 1 211.26276 cents 1: 1 216.65242 cents 2: 1 274.25478 cents 2: 1 298.92624 cents 2: 1 302.13227 cents 2: 1 331.46484 cents 2: 1 377.62797 cents 2: 1 400.03769 cents 2: 1 415.55622 cents 3: 1 485.51754 cents 3: 1 490.90720 cents 3: 1 497.83004 cents 3: 1 501.03607 cents 3: 1 510.18900 cents 3: 1 548.11726 cents 3: 1 566.40289 cents 4: 1 633.59711 cents 4: 1 651.88274 cents 4: 1 689.81100 cents 4: 1 698.96393 cents 4: 1 702.16996 cents 4: 1 709.09280 cents 4: 1 714.48246 cents 5: 1 784.44378 cents 5: 1 799.96231 cents 5: 1 822.37204 cents 5: 1 868.53516 cents 5: 1 897.86773 cents 5: 1 901.07376 cents 5: 1 925.74522 cents 6: 1 983.34758 cents 6: 1 988.73724 cents 6: 1 1001.09620 cents 6: 1 1011.22508 cents 6: 1 1033.63480 cents 6: 1 1067.43896 cents 6: 1 1114.52015 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 : 211.3 377.6 510.2 709.1 925.7 1011.2 1200.0 211.3 : 166.4 298.9 497.8 714.5 800.0 988.7 1200.0 377.6 : 132.6 331.5 548.1 633.6 822.4 1033.6 1200.0 510.2 : 198.9 415.6 501.0 689.8 901.1 1067.4 1200.0 709.1 : 216.7 302.1 490.9 702.2 868.5 1001.1 1200.0 925.7 : 85.5 274.3 485.5 651.9 784.4 983.3 1200.0 1011.2: 188.8 400.0 566.4 699.0 897.9 1114.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.4799 .. 216.6524 cents 131.17257 cents 85.47985 cents 2: 274.2548 .. 415.5562 cents 141.30144 cents 57.60236 cents 3: 485.5175 .. 566.4029 cents 80.88535 cents 69.96132 cents 4: 633.5971 .. 714.4825 cents 80.88535 cents 67.19422 cents 5: 784.4438 .. 925.7452 cents 141.30144 cents 69.96132 cents 6: 983.3476 .. 1114.5201 cents 131.17257 cents 57.60236 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 85.47985 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 216.65242 cents Average / Smallest step : 2.005485 Largest / Average step : 1.263806 Largest / Smallest step : 2.534544 Median interval of one step : 188.77492 cents, amount: 1 Least squares average step : 174.49667 cents, oct.: 1221.47667 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : FCBEGAD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 57.60236 cents Scale diversity : 1.664625 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.411068 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 : 3.20603 cents Number of recognisable fifths : 5, average 702.9040 cents Number of appreciable fifths : 4, average 700.0094 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 141.3014 cents: 1 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.5714 c. M: 68.6024 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 35.9307 c. M:-55.4416 c. 10: 2 1 1 2 2 0 2 P D3 S SD: 29.1898 c. M: 51.2251 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 15.1312 c. M: 25.7452 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: 14.5032 c. M: 24.6868 c. 18: 3 3 2 3 3 1 3 P T3 SD: 16.6227 c. M:-24.2405 c. 19: 3 3 2 3 4 1 3 P SD: 12.9555 c. M: 21.7891 c. 22: 4 3 2 4 4 2 3 SP S SD: 12.3718 c. M:-25.1386 c. 23: 4 3 3 4 4 1 4 SP S SD: 13.7607 c. M:-21.3420 c. 24: 4 3 3 4 4 2 4 SP D3 S SD: 16.3247 c. M: 27.6280 c. Dance scale of Yi people: China 25: 4 4 3 4 4 2 4 SP T3 SD: 12.2310 c. M: 19.2628 c. 26: 5 3 3 4 5 2 4 SP SD: 10.4431 c. M:-19.5065 c. 28: 5 4 3 5 5 2 4 SP SD: 12.3314 c. M:-19.4786 c. 29: 5 4 3 5 5 2 5 SP SD: 10.8868 c. M: 18.1216 c. 30: 5 4 4 5 5 2 5 SP S SD: 10.7692 c. M: 17.6280 c. 31: 5 5 3 5 6 2 5 SP SD: 9.5415 c. M: 17.7144 c. 32: 6 4 4 5 6 2 5 SP SD: 8.9952 c. M:-14.8110 c. 35: 6 5 4 6 6 2 6 SP SD: 8.0509 c. M: 16.9394 c. 38: 7 5 4 6 7 3 6 SP SD: 7.8152 c. M: 14.3560 c. 39: 7 5 5 6 7 3 6 SP SD: 6.3244 c. M:-12.8879 c. 40: 7 6 4 7 7 3 6 SP SD: 7.2582 c. M:-12.3720 c. 42: 7 6 5 7 7 3 7 SP SD: 8.1622 c. M: 11.4595 c. 44: 8 6 5 7 8 3 7 SP SD: 4.4111 c. M:-7.9928 c. 51: 9 7 6 8 9 4 8 SP SD: 4.3653 c. M: 8.0982 c. 56: 10 8 6 9 10 4 9 SP SD: 4.3163 c. M:-8.0863 c. 57: 10 8 6 10 10 4 9 SP SD: 3.2117 c. M:-6.6967 c. 69: 12 10 7 12 12 5 11 SP SD: 3.8466 c. M: 5.8412 c. 70: 12 10 8 11 13 5 11 SP SD: 3.5199 c. M: 6.2357 c. 79: 14 11 9 13 14 6 12 SP SD: 3.9992 c. M:-6.4964 c. 80: 14 11 9 13 15 5 13 SP SD: 3.4256 c. M: 6.2251 c. 83: 15 11 9 14 15 6 13 SP SD: 2.7527 c. M:-5.6047 c. 89: 16 12 10 15 16 6 14 SP SD: 3.2987 c. M:-5.5139 c. 91: 16 13 10 15 16 7 14 SP SD: 3.2335 c. M:-4.7896 c. 95: 17 13 10 16 17 7 15 SP SD: 2.7976 c. M: 4.9258 c. 96: 17 13 11 16 17 7 15 SP SD: 1.9845 c. M:-3.4072 c. 101: 18 14 11 17 18 7 16 SP SD: 2.0995 c. M:-3.7785 c. 108: 19 15 12 18 19 8 17 SP SD: 1.5763 c. M: 3.5230 c. 115: 20 16 13 19 21 8 18 SP SD: 1.7552 c. M:-2.9504 c. 127: 22 18 14 21 23 9 20 SP SD: 1.3025 c. M: 3.3887 c. 144: 25 20 16 24 26 10 23 SP SD: 2.0151 c. M: 2.9294 c. 146: 26 20 16 24 27 10 23 SP SD: 1.7211 c. M:-3.0219 c. 153: 27 21 17 25 28 11 24 SP SD: 1.3311 c. M: 3.2104 c. 158: 28 22 17 26 29 11 25 SP SD: 1.5922 c. M: 2.7637 c. 159: 28 22 18 26 29 11 25 SP SD: 1.5047 c. M:-3.0185 c. 171: 30 24 19 28 31 12 27 SP SD: 1.0403 c. M:-2.0917 c. 188: 33 26 21 31 34 13 30 SP SD: 1.1594 c. M: 2.7144 c. 193: 34 27 21 32 35 14 30 SP SD: 1.0979 c. M:-2.2464 c. 198: 35 27 22 33 36 14 31 SP SD: 1.1070 c. M: 1.8704 c. 210: 37 29 23 35 38 15 33 SP SD: 0.6754 c. M: 1.6176 c. 223: 39 31 25 37 40 16 35 SP SD: 0.8949 c. M: 1.3973 c. 228: 40 32 25 38 41 16 36 SP SD: 0.8673 c. M:-1.4335 c. 254: 45 35 28 42 46 18 40 SP SD: 0.5575 c. M:-1.3357 c. 266: 47 37 29 44 48 19 42 SP SD: 0.8050 c. M:-1.3194 c. 301: 53 42 33 50 54 22 47 SP SD: 0.7730 c. M:-1.3995 c. 305: 54 42 34 50 55 22 48 SP SD: 0.8648 c. M:-1.2864 c. 306: 54 42 34 51 55 22 48 SP SD: 0.6096 c. M: 1.1574 c. 311: 55 43 34 52 56 22 49 SP SD: 0.6391 c. M:-0.9559 c. 318: 56 44 35 53 57 23 50 SP SD: 0.5673 c. M: 1.2169 c. 337: 59 47 37 56 61 24 53 SP SD: 0.6136 c. M: 1.1737 c. 362: 64 50 40 60 65 26 57 SP SD: 0.5162 c. M:-0.8919 c. 369: 65 51 41 61 67 26 58 SP SD: 0.4682 c. M:-1.0840 c. 381: 67 53 42 63 69 27 60 SP SD: 0.2532 c. M: 0.4314 c. 477: 84 66 53 79 86 34 75 SP SD: 0.2552 c. M:-0.5028 c. 687: 121 95 76 114 124 49 108 SP SD: 0.1534 c. M: 0.3354 c. 743: 131 103 82 123 134 53 117 SP SD: 0.2247 c. M:-0.3119 c. 814: 143 113 90 135 147 58 128 SP SD: 0.2001 c. M: 0.4520 c. 858: 151 119 95 142 155 61 135 SP SD: 0.1275 c. M:-0.3005 c. 953: 168 132 105 158 172 68 150 SP SD: 0.1868 c. M:-0.2797 c. 1068: 188 148 118 177 193 76 168 SP SD: 0.0727 c. M: 0.1040 c. 1557: 274 216 172 258 281 111 245 SP SD: 0.0617 c. M: 0.1190 c. 2244: 395 311 248 372 405 160 353 SP SD: 0.0471 c. M: 0.0879 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: 3.5689 cents 3 x x 4 x 5 x 6 S SD: 14.3771 cents 4 x 5 x 6 x 7:8 S SD: 10.9661 cents 5 x 6:7:8 x 9:10 S SD: 28.3220 cents 6:7 x 8:9:10:11:12 S SD: 13.3936 cents 7:8:9 x 11:12:13:14 SD: 18.8540 cents 8:9:10:11:12 x 14:16 S SD: 10.0964 cents 14:16:17:19:21:24:25:28 SD: 7.3141 cents 16:18:20:21:24:27:29:32 SD: 7.0934 cents 17:19:21:23:26:29:30:34 SD: 6.6133 cents 20:23:25:27:30:34:36:40 SD: 5.0456 cents 23:26:29:31:35:39:41:46 SD: 4.8709 cents 24:27:30:32:36:41:43:48 SD: 2.6051 cents 38:43:47:51:57:65:68:76 SD: 1.9116 cents 53:60:66:71:80:90:95:106 SD: 1.6220 cents 61:69:76:82:92:104:109:122 SD: 1.1652 cents 79:89:98:106:119:135:142:158 SD: 1.1532 cents 85:96:106:114:128:145:152:170 SD: 1.0275 cents 91:103:113:122:137:155:163:182 SD: 0.9476 cents 93:105:116:125:140:159:167:186 SD: 0.9293 cents 99:112:123:133:149:169:178:198 SD: 0.7958 cents 116:131:144:156:175:198:208:232 SD: 0.7369 cents 123:139:153:165:185:210:221:246 SD: 0.6308 cents 131:148:163:176:197:224:235:262 SD: 0.6088 cents 140:158:174:188:211:239:251:280 SD: 0.3644 cents 184:208:229:247:277:314:330:368 SD: 0.2660 cents 263:297:327:353:396:449:472:526 SD: 0.2589 cents 300:339:373:403:452:512:538:600 SD: 0.1727 cents 324:366:403:435:488:553:581:648 SD: 0.0589 cents