Scala analysis: CD17_01_Tunisia
La nûba Rasd al-dhil : introduction Istiftâh - L'ensemble de Muhammad Ghânim (rasd al-dhil, Tunisia)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 167.433 cents 167.432769 2: 275.711 cents 275.710911 3: 470.447 cents 470.447225 4: 657.899 cents 657.899293 5: 780.785 cents 780.785378 6: 976.985 cents 976.984678 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 223.0153 cents 223.0153 1: 167.4328 cents 167.4328 2: 108.2781 cents 108.2781 3: 194.7363 cents 194.7363 4: 187.4521 cents 187.4521 5: 122.8861 cents 122.8861 6: 196.1993 cents 196.1993 7: 223.0153 cents 223.0153
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 108.27814 cents 1: 1 122.88609 cents 1: 1 167.43277 cents 1: 1 187.45207 cents 1: 1 194.73631 cents 1: 1 196.19930 cents 1: 1 223.01532 cents 2: 1 275.71091 cents 2: 1 303.01446 cents 2: 1 310.33815 cents 2: 1 319.08539 cents 2: 1 382.18838 cents 2: 1 390.44809 cents 2: 1 419.21462 cents 3: 1 470.44723 cents 3: 1 490.46652 cents 3: 1 498.72623 cents 3: 1 505.07447 cents 3: 1 506.53745 cents 3: 1 542.10071 cents 3: 1 586.64739 cents 4: 1 613.35261 cents 4: 1 657.89929 cents 4: 1 693.46255 cents 4: 1 694.92553 cents 4: 1 701.27377 cents 4: 1 709.53348 cents 4: 1 729.55277 cents 5: 1 780.78538 cents 5: 1 809.55191 cents 5: 1 817.81162 cents 5: 1 880.91461 cents 5: 1 889.66185 cents 5: 1 896.98554 cents 5: 1 924.28909 cents 6: 1 976.98468 cents 6: 1 1003.80070 cents 6: 1 1005.26369 cents 6: 1 1012.54793 cents 6: 1 1032.56723 cents 6: 1 1077.11391 cents 6: 1 1091.72186 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 : 167.4 275.7 470.4 657.9 780.8 977.0 1200.0 167.4 : 108.3 303.0 490.5 613.4 809.6 1032.6 1200.0 275.7 : 194.7 382.2 505.1 701.3 924.3 1091.7 1200.0 470.4 : 187.5 310.3 506.5 729.6 897.0 1005.3 1200.0 657.9 : 122.9 319.1 542.1 709.5 817.8 1012.5 1200.0 780.8 : 196.2 419.2 586.6 694.9 889.7 1077.1 1200.0 977.0 : 223.0 390.4 498.7 693.5 880.9 1003.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 108.2781 .. 223.0153 cents 114.73718 cents 108.27814 cents 2: 275.7109 .. 419.2146 cents 143.50371 cents 52.69559 cents 3: 470.4472 .. 586.6474 cents 116.20017 cents 51.23260 cents 4: 613.3526 .. 729.5528 cents 116.20017 cents 26.70522 cents 5: 780.7854 .. 924.2891 cents 143.50371 cents 51.23260 cents 6: 976.9847 .. 1091.7219 cents 114.73718 cents 52.69559 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 108.27814 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 223.01532 cents Average / Smallest step : 1.583224 Largest / Average step : 1.300923 Largest / Smallest step : 2.059652 Median interval of one step : 187.45207 cents, amount: 1 Least squares average step : 163.76877 cents, oct.: 1146.38142 cents Scale is strictly proper Step pattern alph. order: ABCDEFG Step pattern size order : CAEDBFG Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 26.70522 cents Scale diversity : 1.626911 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.375932 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 : 1.46299 cents Number of recognisable fifths : 4, average 699.7988 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: 47.3765 c. M:-76.3575 c. Lebeng 8: 1 1 1 1 1 1 2 P M ME S SD: 40.6002 c. M: 76.9847 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 32.8432 c. M:-62.8861 c. Pseudo Pelog, Pelogic-7, Antiionian 10: 1 1 2 1 1 2 2 P D3 S SD: 39.5548 c. M: 60.7854 c. 11: 1 1 2 2 1 2 2 P D3 S SD: 34.2340 c. M: 58.3419 c. 13: 2 1 2 2 1 3 2 N T3 SD: 23.2376 c. M: 42.3238 c. 15: 2 1 3 2 2 2 3 P D3 SD: 18.5158 c. M: 35.7109 c. 16: 2 2 2 3 1 3 3 P T3 SD: 19.1089 c. M: 30.7854 c. 17: 2 2 3 2 2 3 3 SP D3 S SD: 16.6904 c. M: 26.2563 c. Safi al-Din's maqam Husaini 18: 3 1 3 3 2 3 3 P T3 SD: 17.4540 c. M:-32.5672 c. 20: 3 2 3 3 2 3 4 P T3 S SD: 12.7204 c. M:-24.2891 c. 22: 3 2 4 3 2 4 4 P SD: 10.4929 c. M:-20.4619 c. Gandhaara Grama (Sarngadeva der. ma-grama) 23: 3 2 4 4 2 4 4 SP SD: 11.7295 c. M:-20.3616 c. 26: 4 2 4 4 3 4 5 P SD: 9.1716 c. M:-17.1826 c. 29: 4 3 4 5 3 5 5 SP SD: 10.2680 c. M:-16.1188 c. 31: 4 3 5 5 3 5 6 SP SD: 7.0223 c. M: 12.5941 c. 38: 5 4 6 6 4 6 7 SP SD: 6.3323 c. M: 9.5380 c. 43: 6 4 7 7 4 7 8 SP SD: 4.9039 c. M:-11.8681 c. 48: 7 4 8 7 5 8 9 P SD: 5.0470 c. M: 7.8993 c. 49: 7 4 8 8 5 8 9 SP SD: 3.9384 c. M: 6.3232 c. 64: 9 6 10 10 7 10 12 SP SD: 3.5263 c. M:-6.7146 c. 66: 9 6 11 10 7 11 12 SP SD: 3.0282 c. M:-4.8335 c. 69: 10 6 11 11 7 11 13 SP SD: 3.1816 c. M:-6.4803 c. 71: 10 6 12 11 7 12 13 SP SD: 2.9698 c. M: 5.2884 c. 79: 11 7 13 12 8 13 15 SP SD: 3.5572 c. M: 6.1018 c. 80: 11 7 13 13 8 13 15 SP SD: 3.3204 c. M: 5.7109 c. 86: 12 8 14 13 9 14 16 SP SD: 2.1325 c. M:-3.9714 c. 108: 15 10 17 17 11 18 20 SP SD: 2.2142 c. M: 3.7806 c. 109: 15 10 18 17 11 18 20 SP SD: 2.0696 c. M:-2.9473 c. 117: 16 11 19 18 12 19 22 SP SD: 1.8963 c. M: 3.3302 c. 123: 17 11 20 19 13 20 23 SP SD: 2.1893 c. M: 4.2408 c. 128: 18 11 21 20 13 21 24 SP SD: 2.1734 c. M: 3.8359 c. 130: 18 12 21 20 14 21 24 SP SD: 1.9414 c. M:-3.8300 c. 135: 19 12 22 21 14 22 25 SP SD: 0.8696 c. M:-1.4561 c. 166: 23 15 27 26 17 27 31 SP SD: 0.7452 c. M: 1.1677 c. 252: 35 23 41 39 26 41 47 SP SD: 0.6558 c. M:-0.9813 c. 301: 42 27 49 47 31 49 56 SP SD: 0.3449 c. M: 0.6279 c. 452: 63 41 73 71 46 74 84 SP SD: 0.3374 c. M: 0.5357 c. 538: 75 49 87 84 55 88 100 SP SD: 0.3452 c. M:-0.8690 c. 544: 76 49 88 85 56 89 101 SP SD: 0.3287 c. M: 0.5943 c. 553: 77 50 90 86 57 90 103 SP SD: 0.3569 c. M: 0.4928 c. 587: 82 53 95 92 60 96 109 SP SD: 0.2282 c. M:-0.3631 c. 753: 105 68 122 118 77 123 140 SP SD: 0.1718 c. M: 0.3277 c. 839: 117 76 136 131 86 137 156 SP SD: 0.1532 c. M:-0.3320 c. 888: 124 80 144 139 91 145 165 SP SD: 0.1619 c. M:-0.2957 c. 910: 127 82 148 142 93 149 169 SP SD: 0.1570 c. M:-0.3220 c. 974: 136 88 158 152 100 159 181 SP SD: 0.1797 c. M:-0.3235 c. 1005: 140 91 163 157 103 164 187 SP SD: 0.1551 c. M: 0.2686 c. 1054: 147 95 171 165 108 172 196 SP SD: 0.1691 c. M:-0.2393 c. 1076: 150 97 175 168 110 176 200 SP SD: 0.1412 c. M: 0.2462 c. 1140: 159 103 185 178 117 186 212 SP SD: 0.1244 c. M:-0.2673 c. 1211: 169 109 197 189 124 198 225 SP SD: 0.1336 c. M:-0.2382 c. 1319: 184 119 214 206 135 216 245 SP SD: 0.1069 c. M: 0.1940 c. 1454: 203 131 236 227 149 238 270 SP SD: 0.0970 c. M:-0.1818 c. 1485: 207 134 241 232 152 243 276 SP SD: 0.1297 c. M: 0.1793 c. 1497: 209 135 243 234 153 245 278 SP SD: 0.1179 c. M:-0.2169 c. 1554: 217 140 252 243 159 254 289 SP SD: 0.1081 c. M: 0.1770 c. 1592: 222 144 258 249 163 260 296 SP SD: 0.1139 c. M:-0.1685 c. 1620: 226 146 263 253 166 265 301 SP SD: 0.0847 c. M: 0.1554 c. 1663: 232 150 270 260 170 272 309 SP SD: 0.0791 c. M:-0.1885 c. 1906: 266 172 309 298 195 312 354 SP SD: 0.0872 c. M: 0.1429 c. 1915: 267 173 311 299 196 313 356 SP SD: 0.0818 c. M:-0.1533 c. 2050: 286 185 333 320 210 335 381 SP SD: 0.0816 c. M:-0.1869 c. 2072: 289 187 336 324 212 339 385 SP SD: 0.0812 c. M: 0.1770 c. 2158: 301 195 350 337 221 353 401 SP SD: 0.0570 c. M:-0.1000 c. 2293: 320 207 372 358 235 375 426 SP SD: 0.0543 c. M:-0.0850 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: 22.0279 cents 3 x x 4 x x 5:6 S SD: 32.2166 cents 4 x x 5:6 x 7:8 S SD: 23.8300 cents 5 x 6 x 7:8:9:10 S SD: 20.0094 cents 6 x 7:8:9 x 11:12 SD: 17.9101 cents 7 x 8:9:10:11:12:14 S SD: 13.7370 cents 8:9 x 11:12:13:14:16 SD: 19.3271 cents 9:10:11:12:13:14:16:18 S SD: 12.1185 cents 10:11:12:13:15:16:18:20 SD: 11.5498 cents 11:12:13:14:16:17:19:22 SD: 10.1387 cents 12:13:14:16:18:19:21:24 SD: 8.9196 cents 13:14:15:17:19:20:23:26 SD: 8.6799 cents 16:18:19:21:23:25:28:32 SD: 7.5819 cents 17:19:20:22:25:27:30:34 SD: 6.0335 cents 19:21:22:25:28:30:33:38 SD: 5.0820 cents 28:31:33:37:41:44:49:56 SD: 2.7627 cents 39:43:46:51:57:61:69:78 SD: 2.4654 cents 41:45:48:54:60:64:72:82 SD: 1.9739 cents 58:64:68:76:85:91:102:116 SD: 0.7939 cents 121:133:142:159:177:190:213:242 SD: 0.7287 cents 128:141:150:168:187:201:225:256 SD: 0.3016 cents 186:205:218:244:272:292:327:372 SD: 0.2037 cents 307:338:360:403:449:482:540:614 SD: 0.1875 cents 365:402:428:479:534:573:642:730 SD: 0.1550 cents 435:479:510:571:636:683:765:870 SD: 0.1456 cents 493:543:578:647:721:774:867:986 SD: 0.0843 cents