Scala analysis: CD18_13_Tunisia
'Arûbî - L'ensemble de Muhammad Ghânim (muhayyar iraq, Tunisia)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 197.480 cents 197.480205 2: 366.669 cents 366.668582 3: 538.158 cents 538.157940 4: 686.384 cents 686.384219 5: 938.872 cents 938.871731 6: 993.094 cents 993.093808 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 206.9062 cents 206.9062 1: 197.4802 cents 197.4802 2: 169.1884 cents 169.1884 3: 171.4894 cents 171.4894 4: 148.2263 cents 148.2263 5: 252.4875 cents 252.4875 6: 54.2221 cents 54.2221 7: 206.9062 cents 206.9062
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 54.22208 cents 1: 1 148.22628 cents 1: 1 169.18838 cents 1: 1 171.48936 cents 1: 1 197.48021 cents 1: 1 206.90619 cents 1: 1 252.48751 cents 2: 1 261.12827 cents 2: 1 306.70959 cents 2: 1 319.71564 cents 2: 1 340.67773 cents 2: 1 366.66858 cents 2: 1 400.71379 cents 2: 1 404.38640 cents 3: 1 454.93587 cents 3: 1 458.60847 cents 3: 1 488.90401 cents 3: 1 513.61578 cents 3: 1 538.15794 cents 3: 1 572.20315 cents 3: 1 573.57477 cents 4: 1 626.42523 cents 4: 1 627.79685 cents 4: 1 661.84206 cents 4: 1 686.38422 cents 4: 1 711.09599 cents 4: 1 741.39153 cents 4: 1 745.06413 cents 5: 1 795.61360 cents 5: 1 799.28621 cents 5: 1 833.33142 cents 5: 1 859.32227 cents 5: 1 880.28436 cents 5: 1 893.29041 cents 5: 1 938.87173 cents 6: 1 947.51249 cents 6: 1 993.09381 cents 6: 1 1002.51979 cents 6: 1 1028.51064 cents 6: 1 1030.81162 cents 6: 1 1051.77372 cents 6: 1 1145.77792 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 : 197.5 366.7 538.2 686.4 938.9 993.1 1200.0 197.5 : 169.2 340.7 488.9 741.4 795.6 1002.5 1200.0 366.7 : 171.5 319.7 572.2 626.4 833.3 1030.8 1200.0 538.2 : 148.2 400.7 454.9 661.8 859.3 1028.5 1200.0 686.4 : 252.5 306.7 513.6 711.1 880.3 1051.8 1200.0 938.9 : 54.2 261.1 458.6 627.8 799.3 947.5 1200.0 993.1 : 206.9 404.4 573.6 745.1 893.3 1145.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.2221 .. 252.4875 cents 198.26544 cents 54.22208 cents 2: 261.1283 .. 404.3864 cents 143.25813 cents 8.64076 cents 3: 454.9359 .. 573.5748 cents 118.63891 cents 50.54947 cents 4: 626.4252 .. 745.0641 cents 118.63891 cents 52.85045 cents 5: 795.6136 .. 938.8717 cents 143.25813 cents 50.54947 cents 6: 947.5125 .. 1145.7779 cents 198.26544 cents 8.64076 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 54.22208 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 252.48751 cents Average / Smallest step : 3.161601 Largest / Average step : 1.472844 Largest / Smallest step : 4.656544 Median interval of one step : 171.48936 cents, amount: 1 Least squares average step : 173.88393 cents, oct.: 1217.18748 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : ECDBGAF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 8.64076 cents Scale diversity : 1.688682 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.233063 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 : 1.37163 cents Number of recognisable fifths : 2, average 698.7401 cents Number of appreciable fifths : 1, average 711.0960 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: 37.3292 c. M: 81.7289 c. Lebeng 9: 1 2 1 1 2 0 2 N D3 SD: 36.3315 c. M: 64.1469 c. 10: 2 1 1 2 2 0 2 P D3 S SD: 33.6078 c. M: 58.1579 c. 11: 2 1 2 1 3 0 2 N SD: 26.7771 c. M:-42.9465 c. 12: 2 2 1 2 2 1 2 P M ME S SD: 24.8350 c. M: 38.8717 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 13: 2 2 2 1 3 1 2 P D3 S SD: 19.9393 c. M: 40.2304 c. 16: 3 2 2 2 4 0 3 N SD: 19.8643 c. M:-36.1283 c. 17: 3 2 3 2 3 1 3 P T3 SD: 16.6971 c. M:-26.5479 c. 18: 3 3 2 2 4 1 3 P SD: 15.1552 c. M:-33.3314 c. 19: 3 3 3 2 4 1 3 P SD: 15.0075 c. M:-30.2631 c. 21: 3 3 3 3 4 1 4 SP T3 S SD: 20.3184 c. M: 26.0516 c. 22: 4 3 3 3 4 1 4 P SD: 14.5827 c. M:-22.7067 c. 23: 4 3 3 3 5 1 4 P SD: 8.1655 c. M: 16.4188 c. 29: 5 4 4 4 6 1 5 P SD: 9.0876 c. M:-17.0641 c. 33: 5 5 5 4 7 1 6 P SD: 8.4404 c. M: 15.6620 c. 35: 6 5 5 4 7 2 6 SP SD: 8.1147 c. M: 13.1574 c. 36: 6 5 5 5 7 2 6 SP SD: 6.4740 c. M:-13.6158 c. 40: 7 5 6 5 8 2 7 SP SD: 6.6113 c. M:-12.5198 c. 42: 7 6 6 5 9 2 7 P SD: 4.0553 c. M:-6.9062 c. 56: 9 8 8 7 12 2 10 P SD: 3.8510 c. M: 7.3795 c. 63: 10 9 9 8 13 3 11 SP SD: 4.3589 c. M: 7.0040 c. 65: 11 9 9 8 14 3 11 P SD: 3.3443 c. M:-5.5967 c. 82: 13 12 12 10 17 4 14 SP SD: 3.2801 c. M: 7.2363 c. 87: 14 13 12 11 18 4 15 SP SD: 3.0190 c. M:-5.7452 c. 89: 15 12 13 11 19 4 15 P SD: 3.3540 c. M:-4.9485 c. 91: 15 13 13 11 19 4 16 SP SD: 2.2943 c. M: 4.0828 c. 98: 16 14 14 12 21 4 17 P SD: 1.7400 c. M:-3.9854 c. 105: 17 15 15 13 22 5 18 SP SD: 1.5586 c. M: 3.1945 c. 134: 22 19 19 17 28 6 23 SP SD: 1.4204 c. M:-3.1680 c. 138: 23 19 20 17 29 6 24 SP SD: 1.3626 c. M:-2.5198 c. 147: 24 21 21 18 31 7 25 SP SD: 1.2938 c. M:-2.8246 c. 170: 28 24 24 21 36 8 29 SP SD: 1.2356 c. M:-2.2003 c. 180: 30 25 26 22 38 8 31 SP SD: 1.2622 c. M:-2.5198 c. 187: 31 26 27 23 39 9 32 SP SD: 1.1987 c. M: 1.9733 c. 196: 32 28 28 24 41 9 34 SP SD: 1.1878 c. M: 2.1370 c. 199: 33 28 28 25 42 9 34 SP SD: 1.4062 c. M:-1.8811 c. 201: 33 28 29 25 42 9 35 SP SD: 1.4034 c. M: 2.4895 c. 203: 33 29 29 25 43 9 35 SP SD: 1.0267 c. M: 2.4063 c. 219: 36 31 31 27 46 10 38 SP SD: 1.1350 c. M: 1.8854 c. 220: 36 31 32 27 46 10 38 SP SD: 1.0360 c. M:-1.8421 c. 225: 37 32 32 28 47 10 39 SP SD: 0.9182 c. M:-1.6158 c. 238: 39 34 34 29 50 11 41 SP SD: 0.9299 c. M:-1.3986 c. 243: 40 34 35 30 51 11 42 SP SD: 0.5551 c. M: 1.2365 c. 248: 41 35 35 31 52 11 43 SP SD: 0.8432 c. M: 1.1583 c. 261: 43 37 37 32 55 12 45 SP SD: 0.7618 c. M: 1.3267 c. 285: 47 40 41 35 60 13 49 SP SD: 0.4274 c. M:-0.7894 c. 341: 56 48 49 42 72 15 59 SP SD: 0.5025 c. M: 0.7184 c. 390: 64 55 56 48 82 18 67 SP SD: 0.4559 c. M:-0.7523 c. 395: 65 56 56 49 83 18 68 SP SD: 0.4161 c. M:-0.9264 c. 413: 68 58 59 51 87 19 71 SP SD: 0.4908 c. M: 0.6699 c. 419: 69 59 60 52 88 19 72 SP SD: 0.5041 c. M:-0.9666 c. 442: 73 62 63 55 93 20 76 SP SD: 0.4934 c. M:-0.7098 c. 451: 74 64 64 56 95 20 78 SP SD: 0.4819 c. M: 0.6857 c. 468: 77 66 67 58 98 21 81 SP SD: 0.4649 c. M:-0.7953 c. 469: 77 66 67 58 99 21 81 SP SD: 0.5519 c. M: 0.8445 c. 474: 78 67 68 58 100 21 82 SP SD: 0.5417 c. M:-1.0826 c. 475: 78 67 68 59 100 21 82 SP SD: 0.5091 c. M:-0.9177 c. 481: 79 68 69 59 101 22 83 SP SD: 0.4601 c. M: 0.8260 c. 488: 80 69 70 60 103 22 84 SP SD: 0.4196 c. M: 0.7589 c. 504: 83 71 72 62 106 23 87 SP SD: 0.4020 c. M: 0.7765 c. 510: 84 72 73 63 107 23 88 SP SD: 0.3971 c. M:-0.6746 c. 511: 84 72 73 63 108 23 88 SP SD: 0.3844 c. M: 0.6699 c. 528: 87 74 76 65 111 24 91 SP SD: 0.3646 c. M: 0.7595 c. 533: 88 75 76 66 112 24 92 SP SD: 0.3057 c. M:-0.6436 c. 596: 98 84 85 74 125 27 103 SP SD: 0.3877 c. M: 0.6167 c. 602: 99 85 86 74 127 27 104 SP SD: 0.3034 c. M: 0.6699 c. 615: 101 87 88 76 129 28 106 SP SD: 0.3050 c. M:-0.4450 c. 638: 105 90 91 79 134 29 110 SP SD: 0.1600 c. M: 0.3137 c. 736: 121 104 105 91 155 33 127 SP SD: 0.1592 c. M:-0.2587 c. 923: 152 130 132 114 194 42 159 SP SD: 0.1231 c. M: 0.1935 c. 979: 161 138 140 121 206 44 169 SP SD: 0.1276 c. M: 0.2440 c. 1021: 168 144 146 126 215 46 176 SP SD: 0.0973 c. M:-0.2076 c. 1374: 226 194 196 170 289 62 237 SP SD: 0.1009 c. M: 0.1667 c. 1525: 251 215 218 188 321 69 263 SP SD: 0.1005 c. M: 0.2203 c. 1554: 256 219 222 192 327 70 268 SP SD: 0.1131 c. M:-0.2032 c. 1617: 266 228 231 200 340 73 279 SP SD: 0.0932 c. M: 0.1439 c. 1659: 273 234 237 205 349 75 286 SP SD: 0.0331 c. M:-0.0584 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: 7.7854 cents 3 x x 4 x 5 x 6 S SD: 22.5603 cents 4 x 5 x 6 x 7:8 S SD: 8.7225 cents 5 x 6:7 x x 9:10 SD: 17.9782 cents 6:7 x 8:9:10:11:12 S SD: 18.8595 cents 7:8:9 x 10:12 x 14 S SD: 20.5870 cents 8:9:10:11:12 x 14:16 S SD: 6.3066 cents 12:13:15:16:18 x 21:24 SD: 13.2250 cents 13:15:16:18:19:22:23:26 SD: 9.9956 cents 14:16:17:19:21:24:25:28 SD: 7.2107 cents 16:18:20:22:24 x 28:32 S SD: 6.3066 cents 17:19:21:23:25:29:30:34 SD: 4.2714 cents 25:28:31:34:37:43:44:50 SD: 2.6140 cents 33:37:41:45:49:57:59:66 SD: 2.5015 cents 39:44:48:53:58:67:69:78 SD: 2.3253 cents 43:48:53:59:64:74:76:86 SD: 2.1063 cents 50:56:62:68:74:86:89:100 SD: 1.7727 cents 58:65:72:79:86:100:103:116 SD: 1.4812 cents 68:76:84:93:101:117:121:136 SD: 1.1392 cents 76:85:94:104:113:131:135:152 SD: 1.0656 cents 90:101:111:123:134:155:160:180 SD: 0.9670 cents 93:104:115:127:138:160:165:186 SD: 0.7610 cents 107:120:132:146:159:184:190:214 SD: 0.5066 cents 115:129:142:157:171:198:204:230 SD: 0.4278 cents 165:185:204:225:245:284:293:330 SD: 0.4249 cents 200:224:247:273:297:344:355:400 SD: 0.3758 cents 208:233:257:284:309:358:369:416 SD: 0.3301 cents 263:295:325:359:391:452:467:526 SD: 0.3127 cents 271:304:335:370:403:466:481:542 SD: 0.2742 cents 288:323:356:393:428:495:511:576 SD: 0.2566 cents 356:399:440:486:529:612:632:712 SD: 0.2104 cents 364:408:450:497:541:626:646:728 SD: 0.1727 cents 471:528:582:643:700:810:836:942 SD: 0.1465 cents 497:557:614:678:739:855:882:994 SD: 0.1453 cents 538:603:665:734:800:925:955:1076 SD: 0.1419 cents 546:612:675:745:812:939:969:1092 SD: 0.1309 cents