Scala analysis: CD10_09_Egypt
Bénédiction des chérubins - Mîkhâ'îl Jirjis al-Batânûnî (unknown maqam, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 234.591 cents 234.591053 2: 498.858 cents 498.857703 3: 744.448 cents 744.448256 4: 859.225 cents 859.225056 5: 1040.996 cents 1040.996262 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 159.0037 cents 159.0037 1: 234.5911 cents 234.5911 2: 264.2667 cents 264.2667 3: 245.5906 cents 245.5906 4: 114.7768 cents 114.7768 5: 181.7712 cents 181.7712 6: 159.0037 cents 159.0037
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 114.77680 cents 1: 1 159.00374 cents 1: 1 181.77121 cents 1: 1 234.59105 cents 1: 1 245.59055 cents 1: 1 264.26665 cents 2: 1 296.54801 cents 2: 1 340.77494 cents 2: 1 360.36735 cents 2: 1 393.59479 cents 2: 1 498.85770 cents 2: 1 509.85720 cents 3: 1 455.55174 cents 3: 1 542.13856 cents 3: 1 575.36600 cents 3: 1 624.63400 cents 3: 1 657.86144 cents 3: 1 744.44826 cents 4: 1 690.14280 cents 4: 1 701.14230 cents 4: 1 806.40521 cents 4: 1 839.63265 cents 4: 1 859.22506 cents 4: 1 903.45199 cents 5: 1 935.73335 cents 5: 1 954.40945 cents 5: 1 965.40895 cents 5: 1 1018.22879 cents 5: 1 1040.99626 cents 5: 1 1085.22320 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 234.6 498.9 744.4 859.2 1041.0 1200.0 234.6 : 264.3 509.9 624.6 806.4 965.4 1200.0 498.9 : 245.6 360.4 542.1 701.1 935.7 1200.0 744.4 : 114.8 296.5 455.6 690.1 954.4 1200.0 859.2 : 181.8 340.8 575.4 839.6 1085.2 1200.0 1041.0: 159.0 393.6 657.9 903.5 1018.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 114.7768 .. 264.2667 cents 149.48985 cents 114.77680 cents 2: 296.5480 .. 509.8572 cents 213.30920 cents 32.28136 cents 3: 455.5517 .. 744.4483 cents 288.89651 cents -54.30546 cents 4: 690.1428 .. 903.4520 cents 213.30920 cents -54.30546 cents 5: 935.7333 .. 1085.2232 cents 149.48985 cents 32.28136 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 114.77680 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 264.26665 cents Average / Smallest step : 1.742512 Largest / Average step : 1.321333 Largest / Smallest step : 2.302440 Median interval of one step : 208.18113 cents, amount: 0 Least squares average step : 212.17069 cents, oct.: 1273.02414 cents Scale is not proper Step pattern alph. order: ABCDEF Step pattern size order : DFEACB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 32.28136 cents Scale diversity : 1.727511 Lumma stability : 0.245097 Lumma impropriety factor : 0.090509 Rothenberg efficiency : 0.333333 redundancy: 0.666667 Efficiency x scale size : 2.000000 Number of different interval sizes : 30 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 6 Mean interval variety : 6.00000 = 6 Median interval variety : 6 Lowest interval variety : 6 Smallest interval difference : 10.99950 cents Number of recognisable fifths : 2, average 695.6425 cents Formal octave complements present : 1 = 16.6667% -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 78.5525 c. M: 144.4483 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 2 1 1 1 1 P M ME SD: 36.1384 c. M: 63.1625 c. 10: 2 2 2 1 2 1 P D3 SD: 21.8841 c. M:-39.0037 c. 14: 3 3 3 1 2 2 N SD: 16.4988 c. M:-26.9803 c. 15: 3 3 3 2 2 2 P SD: 15.3578 c. M: 24.4483 c. 20: 4 4 4 2 3 3 P SD: 17.2870 c. M: 24.4483 c. 21: 4 5 4 2 3 3 N SD: 8.5196 c. M:-15.4280 c. 24: 5 5 5 2 4 3 N SD: 8.5218 c. M:-15.4089 c. 29: 6 6 6 3 4 4 N SD: 7.4166 c. M:-13.6848 c. 31: 6 7 6 3 5 4 N SD: 5.4799 c. M: 8.9644 c. 45: 9 10 9 4 7 6 N SD: 4.6702 c. M:-7.8090 c. 53: 10 12 11 5 8 7 N SD: 3.5683 c. M: 8.1760 c. 60: 12 13 12 6 9 8 N SD: 2.9423 c. M:-5.4089 c. 77: 15 17 16 7 12 10 N SD: 2.1606 c. M:-3.6037 c. 82: 16 18 17 8 12 11 N SD: 2.1176 c. M:-4.1896 c. 92: 18 20 19 9 14 12 N SD: 1.8311 c. M: 3.2055 c. 98: 19 22 20 9 15 13 N SD: 2.0190 c. M:-3.1831 c. 106: 21 23 22 10 16 14 N SD: 1.8001 c. M:-3.1448 c. 113: 22 25 23 11 17 15 N SD: 0.7258 c. M: 1.0854 c. 190: 37 42 39 18 29 25 N SD: 0.6833 c. M:-1.1090 c. 219: 43 48 45 21 33 29 N SD: 0.6815 c. M:-1.0489 c. 250: 49 55 51 24 38 33 N SD: 0.4191 c. M:-0.6089 c. 332: 65 73 68 32 50 44 N SD: 0.4426 c. M:-1.0159 c. 363: 71 80 74 35 55 48 N SD: 0.3455 c. M: 0.6466 c. 469: 92 103 96 45 71 62 N SD: 0.4137 c. M:-0.8034 c. 476: 93 105 97 46 72 63 N SD: 0.3870 c. M: 0.7508 c. 522: 102 115 107 50 79 69 N SD: 0.3161 c. M:-0.5451 c. 553: 108 122 113 53 84 73 N SD: 0.2868 c. M:-0.5951 c. 640: 125 141 131 61 97 85 N SD: 0.2668 c. M: 0.4751 c. 666: 130 147 136 64 101 88 N SD: 0.2975 c. M:-0.4452 c. 680: 133 150 139 65 103 90 N SD: 0.2750 c. M:-0.5541 c. 722: 141 159 148 69 109 96 N SD: 0.2735 c. M: 0.5530 c. 732: 143 161 150 70 111 97 N SD: 0.2424 c. M: 0.4970 c. 746: 146 164 153 71 113 99 N SD: 0.2353 c. M:-0.3239 c. 753: 147 166 154 72 114 100 N SD: 0.2443 c. M: 0.3588 c. 777: 152 171 159 74 118 103 N SD: 0.2315 c. M: 0.5378 c. 859: 168 189 176 82 130 114 N SD: 0.1408 c. M: 0.2512 c. 890: 174 196 182 85 135 118 N SD: 0.1651 c. M: 0.3487 c. 972: 190 214 199 93 147 129 N SD: 0.1122 c. M: 0.2555 c. 1070: 209 236 219 102 162 142 N SD: 0.1916 c. M: 0.2486 c. 1080: 211 238 221 103 164 143 N SD: 0.1574 c. M: 0.3362 c. 1085: 212 239 222 104 164 144 N SD: 0.1386 c. M: 0.2589 c. 1109: 217 244 227 106 168 147 N SD: 0.0965 c. M:-0.2151 c. 1162: 227 256 238 111 176 154 N SD: 0.0915 c. M: 0.1676 c. 1222: 239 269 250 117 185 162 N SD: 0.0672 c. M:-0.1062 c. 1412: 276 311 289 135 214 187 N SD: 0.0377 c. M:-0.0802 c. 2271: 444 500 465 217 344 301 N SD: 0.0435 c. M:-0.0696 c. 2384: 466 525 488 228 361 316 N SD: 0.0295 c. M: 0.0567 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 21.2466 cents 3 x 4 x 5 x 6 S SD: 8.3823 cents 4 x 5:6 x 7:8 S SD: 35.0717 cents 5:6:7 x 8:9:10 S SD: 25.4468 cents 6:7:8:9:10:11:12 H SD: 9.9304 cents 13:15:17:20:21:24:26 SD: 8.5260 cents 15:17:20:23:25:27:30 SD: 6.4983 cents 19:22:25:29:31:35:38 SD: 6.4545 cents 20:23:27:31:33:36:40 SD: 5.9946 cents 21:24:28:32:34:38:42 SD: 5.4652 cents 22:25:29:34:36:40:44 SD: 4.6102 cents 27:31:36:42:44:49:54 SD: 4.4567 cents 28:32:37:43:46:51:56 SD: 2.8396 cents 33:38:44:51:54:60:66 SD: 2.6781 cents 39:45:52:60:64:71:78 SD: 2.3130 cents 47:54:63:72:77:86:94 SD: 2.2735 cents 48:55:64:74:79:88:96 SD: 1.7282 cents 56:64:75:86:92:102:112 SD: 1.4032 cents 69:79:92:106:113:126:138 SD: 0.9406 cents 84:96:112:129:138:153:168 SD: 0.8156 cents 104:119:139:160:171:190:208 SD: 0.7967 cents 117:134:156:180:192:213:234 SD: 0.7407 cents 123:141:164:189:202:224:246 SD: 0.6457 cents 132:151:176:203:217:241:264 SD: 0.4589 cents 165:189:220:254:271:301:330 SD: 0.4324 cents 171:196:228:263:281:312:342 SD: 0.3527 cents 207:237:276:318:340:378:414 SD: 0.3503 cents 221:253:295:340:363:403:442 SD: 0.3410 cents 227:260:303:349:373:414:454 SD: 0.2440 cents 255:292:340:392:419:465:510 SD: 0.2217 cents 296:339:395:455:486:540:592 SD: 0.1786 cents 428:490:571:658:703:781:856 SD: 0.0892 cents 599:686:799:921:984:1093:1198 SD: 0.0749 cents