Scala analysis: CD14_02_Algeria
Tûshiya - L'ensemble d'Al-'Arabî Ben Sârî (raml al-ashiyya, Algeria)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 109.330 cents 109.330371 2: 203.738 cents 203.737962 3: 304.572 cents 304.571842 4: 490.860 cents 490.859907 5: 589.512 cents 589.511530 6: 695.719 cents 695.719260 7: 790.081 cents 790.080778 8: 984.799 cents 984.798741 9: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 215.2013 cents 215.2013 1: 109.3304 cents 109.3304 2: 94.4076 cents 94.4076 3: 100.8339 cents 100.8339 4: 186.2881 cents 186.2881 5: 98.6516 cents 98.6516 6: 106.2077 cents 106.2077 7: 94.3615 cents 94.3615 8: 194.7180 cents 194.7180 9: 215.2013 cents 215.2013
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 94.36152 cents 1: 1 94.40759 cents 1: 1 98.65162 cents 1: 1 100.83388 cents 1: 1 106.20773 cents 1: 1 109.33037 cents 1: 1 186.28807 cents 1: 1 194.71796 cents 1: 1 215.20126 cents 2: 1 195.24147 cents 2: 1 200.56925 cents 2: 1 203.73796 cents 2: 1 204.85935 cents 2: 1 284.93969 cents 2: 1 287.12194 cents 2: 1 289.07948 cents 2: 1 324.53163 cents 2: 1 409.91922 cents 3: 1 299.22087 cents 3: 1 304.57184 cents 3: 1 381.52954 cents 3: 1 385.77357 cents 3: 1 391.14742 cents 3: 1 395.28721 cents 3: 1 418.93922 cents 3: 1 504.28074 cents 3: 1 519.24959 cents 4: 1 480.18116 cents 4: 1 485.50894 cents 4: 1 490.85991 cents 4: 1 491.98130 cents 4: 1 493.93883 cents 4: 1 519.77310 cents 4: 1 610.48847 cents 4: 1 613.61111 cents 4: 1 613.65718 cents 5: 1 586.34282 cents 5: 1 586.38889 cents 5: 1 589.51153 cents 5: 1 680.22690 cents 5: 1 706.06117 cents 5: 1 708.01870 cents 5: 1 709.14009 cents 5: 1 714.49106 cents 5: 1 719.81884 cents 6: 1 680.75041 cents 6: 1 695.71926 cents 6: 1 781.06078 cents 6: 1 804.71279 cents 6: 1 808.85258 cents 6: 1 814.22643 cents 6: 1 818.47046 cents 6: 1 895.42816 cents 6: 1 900.77913 cents 7: 1 790.08078 cents 7: 1 875.46837 cents 7: 1 910.92052 cents 7: 1 912.87806 cents 7: 1 915.06031 cents 7: 1 995.14065 cents 7: 1 996.26204 cents 7: 1 999.43075 cents 7: 1 1004.75853 cents 8: 1 984.79874 cents 8: 1 1005.28204 cents 8: 1 1013.71193 cents 8: 1 1090.66963 cents 8: 1 1093.79227 cents 8: 1 1099.16612 cents 8: 1 1101.34838 cents 8: 1 1105.59241 cents 8: 1 1105.63848 cents Highest number of different intervals for one interval class: 9 Average number of different intervals per interval class: 9.00000 = 9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 109.3 203.7 304.6 490.9 589.5 695.7 790.1 984.8 1200.0 109.3 : 94.4 195.2 381.5 480.2 586.4 680.8 875.5 1090.7 1200.0 203.7 : 100.8 287.1 385.8 492.0 586.3 781.1 996.3 1105.6 1200.0 304.6 : 186.3 284.9 391.1 485.5 680.2 895.4 1004.8 1099.2 1200.0 490.9 : 98.7 204.9 299.2 493.9 709.1 818.5 912.9 1013.7 1200.0 589.5 : 106.2 200.6 395.3 610.5 719.8 814.2 915.1 1101.3 1200.0 695.7 : 94.4 289.1 504.3 613.6 708.0 808.9 995.1 1093.8 1200.0 790.1 : 194.7 409.9 519.2 613.7 714.5 900.8 999.4 1105.6 1200.0 984.8 : 215.2 324.5 418.9 519.8 706.1 804.7 910.9 1005.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 94.3615 .. 215.2013 cents 120.83974 cents 94.36152 cents 2: 195.2415 .. 409.9192 cents 214.67775 cents -19.95979 cents 3: 299.2209 .. 519.2496 cents 220.02872 cents -110.69835 cents 4: 480.1812 .. 613.6572 cents 133.47603 cents -39.06843 cents 5: 586.3428 .. 719.8188 cents 133.47603 cents -27.31437 cents 6: 680.7504 .. 900.7791 cents 220.02872 cents -39.06843 cents 7: 790.0808 .. 1004.7585 cents 214.67775 cents -110.69835 cents 8: 984.7987 .. 1105.6385 cents 120.83974 cents -19.95979 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 94.36152 cents, class 1 Average step (divided formal octave): 133.3333 cents Largest one step interval : 215.20126 cents Average / Smallest step : 1.413005 Largest / Average step : 1.614009 Largest / Smallest step : 2.280604 Median interval of one step : 106.20773 cents, amount: 1 Least squares average step : 121.84137 cents, oct.: 1096.57232 cents Scale is not proper Step pattern alph. order: ABCDEFGHI Step pattern size order : FBDGCEAHI Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 0.52351 cents Scale diversity : 1.404102 Lumma stability : 0.157269 Lumma impropriety factor : 0.305640 Rothenberg efficiency : 0.222222 redundancy: 0.777778 Efficiency x scale size : 2.000000 Number of different interval sizes : 72 = 9.00000 / class Number of one step interval sizes : 9 Highest interval variety : 9 Mean interval variety : 9.00000 = 9 Median interval variety : 9 Lowest interval variety : 9 Smallest interval difference : 0.04607 cents Number of recognisable fifths : 6, average 708.8749 cents Number of appreciable fifths : 4, average 704.7348 cents Formal octave complements present : 1 = 11.1111% Limited inverse transpositions with margin 214.6778 cents: 7 -- Rational properties --
FIT/MODE
9: 1 0 1 1 1 1 1 1 2 N T3 SD: 49.4103 c. M: 90.8599 c. 10: 1 1 1 1 1 1 1 1 2 P M ME S SD: 30.5968 c. M:-55.4282 c. 11: 1 1 1 1 1 1 1 2 2 N D3 S SD: 29.8856 c. M: 54.4963 c. 12: 1 1 1 2 1 1 1 2 2 N D3 S SD: 8.5847 c. M:-15.2013 c. Locrian/Aeolian mixed 29: 3 2 2 5 2 3 2 5 5 N SD: 9.0180 c. M: 14.9167 c. 34: 3 3 3 5 3 3 2 6 6 N SD: 8.6167 c. M: 13.6102 c. 35: 3 3 3 5 3 3 3 6 6 N S SD: 6.8020 c. M: 10.8599 c. 40: 4 3 3 6 4 3 3 7 7 N SD: 7.9112 c. M: 10.8599 c. 41: 4 3 3 7 3 4 3 7 7 N SD: 6.8023 c. M: 11.8889 c. 43: 4 3 4 7 3 4 3 7 8 N SD: 6.4035 c. M:-11.4657 c. 46: 4 4 4 7 4 4 3 8 8 N SD: 6.8860 c. M:-10.4885 c. 47: 4 4 4 7 4 4 4 7 9 N SD: 6.2260 c. M: 14.5860 c. 49: 4 4 4 8 4 4 4 8 9 N SD: 7.2824 c. M: 11.3712 c. 51: 5 4 4 8 4 5 4 8 9 N SD: 6.3337 c. M:-10.1631 c. 52: 5 4 4 8 5 4 4 9 9 N SD: 5.9637 c. M:-10.4885 c. 55: 5 4 5 8 5 5 4 9 10 N SD: 4.8268 c. M: 10.8599 c. 57: 5 5 4 9 5 5 5 9 10 N SD: 6.0072 c. M:-9.9192 c. 59: 5 5 5 9 5 5 5 9 11 N SD: 4.2995 c. M: 8.5276 c. 66: 6 5 6 10 5 6 5 11 12 N SD: 4.6420 c. M: 8.2626 c. 67: 6 5 6 10 6 6 5 11 12 N SD: 3.5893 c. M: 7.2778 c. 71: 6 6 6 11 6 6 6 11 13 N SD: 3.5713 c. M: 7.9219 c. 74: 7 6 6 11 6 7 6 12 13 N SD: 4.3983 c. M:-7.0728 c. 76: 7 6 6 12 6 7 6 12 14 N SD: 3.1667 c. M: 5.8514 c. 78: 7 6 7 12 6 7 6 13 14 N SD: 3.2319 c. M: 5.4654 c. 83: 8 6 7 13 7 7 7 13 15 N SD: 3.0863 c. M:-6.3323 c. 88: 8 7 7 14 7 8 7 14 16 N SD: 2.1386 c. M: 4.5718 c. 90: 8 7 8 14 7 8 7 15 16 N SD: 2.5928 c. M: 3.7380 c. 100: 9 8 8 16 8 9 8 16 18 N SD: 1.8477 c. M: 4.5718 c. 122: 11 10 10 19 10 11 9 20 22 N SD: 1.8037 c. M: 3.1955 c. 129: 12 10 11 20 10 12 10 21 23 N SD: 1.9534 c. M: 3.4650 c. 134: 12 11 11 21 11 12 10 22 24 N SD: 1.6859 c. M:-2.7882 c. 141: 13 11 12 22 11 13 11 23 25 N SD: 1.8438 c. M:-2.7571 c. 152: 14 12 13 23 13 13 12 25 27 N SD: 1.7937 c. M:-3.3229 c. 155: 14 12 13 24 13 14 12 25 28 N SD: 1.7816 c. M: 3.1180 c. 157: 14 13 13 24 13 14 12 26 28 N SD: 1.7279 c. M: 2.8196 c. 161: 15 12 14 25 13 14 13 26 29 N SD: 1.5774 c. M: 2.5516 c. 166: 15 13 14 26 13 15 13 27 30 N SD: 1.8284 c. M: 3.9694 c. 167: 15 13 14 26 14 15 13 27 30 N SD: 1.6173 c. M: 2.7754 c. 169: 15 14 14 26 14 15 13 28 30 N SD: 1.5848 c. M: 2.8215 c. 173: 16 13 15 27 14 15 14 28 31 N SD: 1.3840 c. M: 2.5819 c. 178: 16 14 15 28 14 16 14 29 32 N SD: 1.4984 c. M: 2.9947 c. 185: 17 14 16 29 15 16 15 30 33 N SD: 1.4442 c. M: 2.6569 c. 188: 17 15 16 29 15 17 15 30 34 N SD: 1.2953 c. M: 2.2775 c. 190: 17 15 16 30 15 17 15 31 34 N SD: 1.4062 c. M: 2.1431 c. 193: 18 15 16 30 16 17 15 31 35 N SD: 1.3622 c. M:-2.5867 c. 196: 18 15 17 30 16 18 15 32 35 N SD: 1.3417 c. M:-2.2399 c. 200: 18 16 17 31 16 18 16 32 36 N SD: 1.1481 c. M:-1.9192 c. 205: 19 16 17 32 17 18 16 33 37 N SD: 1.1170 c. M:-1.8891 c. 217: 20 17 18 34 18 19 17 35 39 N SD: 1.1000 c. M:-2.1935 c. 222: 20 18 18 35 18 20 17 36 40 N SD: 1.2134 c. M: 1.8691 c. 228: 21 18 19 35 19 20 18 37 41 N SD: 0.9332 c. M:-1.5252 c. 240: 22 19 20 37 20 21 19 39 43 N SD: 0.6469 c. M:-1.2620 c. 252: 23 20 21 39 21 22 20 41 45 N SD: 0.6170 c. M:-1.0239 c. 340: 31 27 28 53 28 30 27 55 61 N SD: 0.5334 c. M: 1.0424 c. 418: 38 33 35 65 34 37 33 68 75 N SD: 0.5243 c. M: 0.9948 c. 430: 39 34 36 67 35 38 34 70 77 N SD: 0.4517 c. M: 0.8355 c. 442: 40 35 37 69 36 39 35 72 79 N SD: 0.4990 c. M: 0.7331 c. 485: 44 38 41 75 40 43 38 79 87 N SD: 0.5966 c. M: 0.9630 c. 492: 45 39 41 76 41 43 39 80 88 N SD: 0.5959 c. M:-1.1401 c. 495: 45 39 42 76 41 44 39 80 89 N SD: 0.5514 c. M: 1.1629 c. 497: 45 39 42 77 41 44 39 81 89 N SD: 0.5376 c. M: 0.9211 c. 501: 46 39 42 78 41 44 40 81 90 N SD: 0.5243 c. M: 1.1085 c. 507: 46 40 43 78 42 45 40 82 91 N SD: 0.4640 c. M: 0.9191 c. 519: 47 41 44 80 43 46 41 84 93 N SD: 0.4617 c. M: 0.6865 c. 535: 49 42 45 83 44 47 42 87 96 N SD: 0.4013 c. M:-0.5762 c. 536: 49 42 45 83 44 48 42 87 96 N SD: 0.3923 c. M: 0.7056 c. 547: 50 43 46 85 45 48 43 89 98 N SD: 0.3729 c. M:-0.6164 c. 623: 57 49 52 97 51 55 49 101 112 N SD: 0.3515 c. M: 0.5291 c. 635: 58 50 53 99 52 56 50 103 114 N SD: 0.2798 c. M:-0.4787 c. 690: 63 54 58 107 57 61 54 112 124 N SD: 0.3037 c. M: 0.5156 c. 702: 64 55 59 109 58 62 55 114 126 N SD: 0.2275 c. M: 0.3372 c. 843: 77 66 71 131 69 75 66 137 151 N SD: 0.2129 c. M:-0.3661 c. 890: 81 70 75 138 73 79 70 144 160 N SD: 0.2188 c. M: 0.5291 c. 902: 82 71 76 140 74 80 71 146 162 N SD: 0.1701 c. M: 0.3198 c. 1083: 99 85 91 168 89 96 85 176 194 N SD: 0.1669 c. M:-0.3649 c. 1095: 100 86 92 170 90 97 86 178 196 N SD: 0.1818 c. M:-0.4067 c. 1142: 104 90 96 177 94 101 90 185 205 N SD: 0.1187 c. M: 0.2103 c. 1154: 105 91 97 179 95 102 91 187 207 N SD: 0.1050 c. M:-0.2138 c. 1789: 163 141 150 278 147 158 141 290 321 N SD: 0.1047 c. M:-0.1748 c. 1844: 168 145 155 286 152 163 145 299 331 N SD: 0.1003 c. M: 0.2000 c. 1856: 169 146 156 288 153 164 146 301 333 N SD: 0.0812 c. M:-0.1436 c. 1985: 181 156 167 308 163 176 156 322 356 N SD: 0.0682 c. M:-0.1133 c. 1997: 182 157 168 310 164 177 157 324 358 N SD: 0.0735 c. M:-0.1245 c. 2237: 204 176 188 347 184 198 176 363 401 N SD: 0.0779 c. M:-0.1219 c. 2325: 212 183 195 361 191 206 183 377 417 N SD: 0.0756 c. M:-0.1330 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x 3 x x 4 S SD: 3.1179 cents 3 x x x 4 x x 5 x 6 S SD: 31.5171 cents 4 x x 5 x x 6 x 7:8 S SD: 20.8802 cents 5 x x 6 x 7 x 8:9:10 S SD: 8.4957 cents 6 x x 7:8 x 9 x 11:12 SD: 15.0737 cents 7 x 8 x 9:10 x 11:12:14 S SD: 14.3117 cents 8 x 9:10 x 11:12:13:14:16 S SD: 14.9690 cents 9 x 10:11:12:13 x 14:16:18 S SD: 10.4212 cents 10 x 11:12:13:14:15:16:18:20 S SD: 8.5573 cents 11:12 x 13:15 x 16:17:19:22 SD: 13.6258 cents 12:13 x 14:16:17:18:19:21:24 SD: 6.6545 cents 15:16:17:18:20:21:22:24:26:30 SD: 6.1664 cents 16:17:18:19:21:22:24:25:28:32 SD: 5.5883 cents 22:23:25:26:29:31:33:35:39:44 SD: 5.0154 cents 24:26:27:29:32:34:36:38:42:48 SD: 4.8990 cents 25:27:28:30:33:35:37:39:44:50 SD: 4.4993 cents 27:29:30:32:36:38:40:43:48:54 SD: 4.2021 cents 30:32:34:36:40:42:45:47:53:60 SD: 2.7230 cents 31:33:35:37:41:44:46:49:55:62 SD: 2.7118 cents 40:43:45:48:53:56:60:63:71:80 SD: 2.6363 cents 42:45:47:50:56:59:63:66:74:84 SD: 2.1029 cents 46:49:52:55:61:65:69:73:81:92 SD: 2.0426 cents 47:50:53:56:62:66:70:74:83:94 SD: 1.6146 cents 57:61:64:68:76:80:85:90:101:114 SD: 1.5000 cents 64:68:72:76:85:90:96:101:113:128 SD: 1.1598 cents 73:78:82:87:97:103:109:115:129:146 SD: 1.0757 cents 79:84:89:94:105:111:118:125:140:158 SD: 1.0321 cents 89:95:100:106:118:125:133:140:157:178 SD: 0.9165 cents 104:111:117:124:138:146:155:164:184:208 SD: 0.8115 cents 119:127:134:142:158:167:178:188:210:238 SD: 0.6175 cents 150:160:169:179:199:211:224:237:265:300 SD: 0.5524 cents 168:179:189:200:223:236:251:265:297:336 SD: 0.4056 cents 202:215:227:241:268:284:302:319:357:404 SD: 0.3578 cents 214:228:241:255:284:301:320:338:378:428 SD: 0.3413 cents 249:265:280:297:331:350:372:393:440:498 SD: 0.3163 cents 291:310:327:347:386:409:435:459:514:582 SD: 0.3103 cents 296:315:333:353:393:416:442:467:523:592 SD: 0.2789 cents 311:331:350:371:413:437:465:491:549:622 SD: 0.2575 cents 338:360:380:403:449:475:505:533:597:676 SD: 0.2357 cents 354:377:398:422:470:498:529:559:625:708 SD: 0.2286 cents 368:392:414:439:489:517:550:581:650:736 SD: 0.2116 cents 384:409:432:458:510:540:574:606:678:768 SD: 0.1328 cents 552:588:621:658:733:776:825:871:975:1104 SD: 0.0804 cents