Scala analysis: CD10_11_Egypt
Fin de la messe - 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: 196.601 cents 196.601293 2: 504.485 cents 504.485119 3: 716.962 cents 716.962266 4: 952.983 cents 952.983261 5: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 247.0167 cents 247.0167 1: 196.6013 cents 196.6013 2: 307.8838 cents 307.8838 3: 212.4771 cents 212.4771 4: 236.0210 cents 236.0210 5: 247.0167 cents 247.0167
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 196.60129 cents 1: 1 212.47715 cents 1: 1 236.02099 cents 1: 1 247.01674 cents 1: 1 307.88383 cents 2: 1 443.61803 cents 2: 1 448.49814 cents 2: 1 483.03773 cents 2: 1 504.48512 cents 2: 1 520.36097 cents 3: 1 679.63903 cents 3: 1 695.51488 cents 3: 1 716.96227 cents 3: 1 751.50186 cents 3: 1 756.38197 cents 4: 1 892.11617 cents 4: 1 952.98326 cents 4: 1 963.97901 cents 4: 1 987.52285 cents 4: 1 1003.39871 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 5.00000 = 5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 0.0 : 196.6 504.5 717.0 953.0 1200.0 196.6 : 307.9 520.4 756.4 1003.4 1200.0 504.5 : 212.5 448.5 695.5 892.1 1200.0 717.0 : 236.0 483.0 679.6 987.5 1200.0 953.0 : 247.0 443.6 751.5 964.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 196.6013 .. 307.8838 cents 111.28253 cents 196.60129 cents 2: 443.6180 .. 520.3610 cents 76.74294 cents 135.73421 cents 3: 679.6390 .. 756.3820 cents 76.74294 cents 159.27805 cents 4: 892.1162 .. 1003.3987 cents 111.28253 cents 135.73421 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 196.60129 cents, class 1 Average step (divided formal octave): 240.0000 cents Largest one step interval : 307.88383 cents Average / Smallest step : 1.220745 Largest / Average step : 1.282849 Largest / Smallest step : 1.566032 Median interval of one step : 236.02099 cents, amount: 1 Least squares average step : 239.42530 cents, oct.: 1197.12649 cents Scale is strictly proper Step pattern alph. order: ABCDE Step pattern size order : AEBCD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 135.73421 cents Scale diversity : 1.394460 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.686624 Rothenberg efficiency : 0.400000 redundancy: 0.600000 Efficiency x scale size : 2.000000 Number of different interval sizes : 20 = 5.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 5.00000 = 5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 4.88011 cents Number of recognisable fifths : 2, average 706.2386 cents Number of appreciable fifths : 1, average 695.5149 cents Best fifths form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 20.0000% Limited transpositions with margin 111.2825 cents: 3 Limited inverse transpositions with margin 111.2825 cents: 3 -- Rational properties --
FIT/MODE
5: 1 1 1 1 1 SP B ME I SD: 22.5452 c. M:-43.3987 c. 12: 2 3 2 3 2 SP M ME I SD: 22.4943 c. M:-47.0167 c. Suspended Pentatonic, Raga Madhyamavati, Madhmat Sarang, Megh, Egyptian, Shang, Rui Bin, Jin Yu, Qing Yu: China, Yo: Japan, Ngu Cung Dao: Vietnam, Yematebela wofe: Ethiopia 13: 2 3 3 2 3 SP M ME S SD: 25.8638 c. M: 42.9467 c. 14: 2 4 2 3 3 SP D3 S SD: 19.0194 c. M: 31.2480 c. 17: 3 4 3 4 3 SP M ME I SD: 18.4547 c. M:-35.2520 c. Seventeen-tone Suspended Pentatonic 18: 3 5 3 3 4 SP T3 SD: 17.3084 c. M:-28.8482 c. 19: 3 5 3 4 4 SP D3 S SD: 10.7415 c. M: 22.2254 c. 23: 4 6 4 4 5 SP T3 SD: 12.7858 c. M:-17.2540 c. 24: 4 6 4 5 5 SP D3 S SD: 8.1029 c. M: 16.9623 c. 29: 5 7 5 6 6 SP D3 S SD: 8.4041 c. M: 13.5140 c. 30: 5 8 5 6 6 SP T3 S SD: 7.8832 c. M:-15.5149 c. 35: 6 9 6 7 7 SP T3 S SD: 6.8929 c. M:-9.8006 c. 38: 6 10 7 7 8 SP SD: 5.8382 c. M:-9.3535 c. 43: 7 11 8 8 9 SP SD: 4.4207 c. M:-8.6191 c. 47: 8 12 8 9 10 SP SD: 5.8250 c. M: 8.3024 c. 48: 8 12 9 9 10 SP SD: 4.5863 c. M:-8.0377 c. 50: 8 13 9 10 10 SP SD: 3.9967 c. M:-7.0167 c. 54: 9 14 9 11 11 SP T3 S SD: 4.3888 c. M:-6.6260 c. 55: 9 14 10 11 11 SP SD: 3.6230 c. M:-7.0167 c. 57: 9 15 10 11 12 SP SD: 4.1063 c. M: 7.1276 c. 62: 10 16 11 12 13 SP SD: 2.5583 c. M: 4.5962 c. 67: 11 17 12 13 14 SP SD: 2.1602 c. M: 3.7295 c. 92: 15 24 16 18 19 SP SD: 1.9732 c. M:-4.2105 c. 97: 16 25 17 19 20 SP SD: 1.3950 c. M:-2.7314 c. 117: 19 30 21 23 24 SP SD: 1.2961 c. M: 1.9210 c. 141: 23 36 25 28 29 SP SD: 1.4570 c. M: 2.3575 c. 147: 24 38 26 29 30 SP SD: 1.3864 c. M:-2.1188 c. 152: 25 39 27 30 31 SP SD: 1.3054 c. M:-2.2799 c. 159: 26 41 28 31 33 SP SD: 1.0661 c. M: 2.0399 c. 164: 27 42 29 32 34 SP SD: 0.9164 c. M: 1.7637 c. 166: 27 43 29 33 34 SP SD: 1.2327 c. M:-1.5390 c. 169: 28 43 30 33 35 SP SD: 1.2105 c. M:-2.2153 c. 171: 28 44 30 34 35 SP SD: 0.8900 c. M:-1.4027 c. 209: 34 54 37 41 43 SP SD: 0.7863 c. M: 1.3860 c. 214: 35 55 38 42 44 SP SD: 0.4159 c. M:-0.7947 c. 281: 46 72 50 55 58 SP SD: 0.4530 c. M: 0.6701 c. 335: 55 86 59 66 69 SP SD: 0.4091 c. M:-0.5895 c. 378: 62 97 67 74 78 SP SD: 0.3841 c. M: 0.6023 c. 390: 64 100 69 77 80 SP SD: 0.4163 c. M:-0.8629 c. 433: 71 111 77 85 89 SP SD: 0.4108 c. M:-0.8206 c. 447: 73 115 79 88 92 SP SD: 0.3082 c. M: 0.6281 c. 452: 74 116 80 89 93 SP SD: 0.1082 c. M: 0.1481 c. 1001: 164 257 177 197 206 SP SD: 0.1044 c. M:-0.2102 c. 1068: 175 274 189 210 220 SP SD: 0.0927 c. M: 0.1743 c. 1185: 194 304 210 233 244 SP SD: 0.1088 c. M: 0.1813 c. 1220: 200 313 216 240 251 SP SD: 0.1003 c. M:-0.1315 c. 1282: 210 329 227 252 264 SP SD: 0.0527 c. M: 0.0971 c. 1734: 284 445 307 341 357 SP SD: 0.0340 c. M: 0.0615 c. 2191: 359 562 388 431 451 SP SD: 0.0307 c. M: 0.0579 c.
FIT/HARMONIC
1 x x x x 2 S SD: 0.0000 cents 2 x x 3 x 4 S SD: 7.5036 cents 3 x 4 x 5:6 S SD: 22.9754 cents 4 x 5:6:7:8 S SD: 30.0424 cents 6:7:8:9:10:12 S SD: 19.9137 cents 8:9:11:12:14:16 SD: 10.4364 cents 14:16:19:21:24:28 SD: 9.7988 cents 15:17:20:23:26:30 SD: 6.2495 cents 18:20:24:27:31:36 SD: 4.9351 cents 23:26:31:35:40:46 SD: 4.5577 cents 26:29:35:39:45:52 SD: 3.9780 cents 27:30:36:41:47:54 SD: 3.6125 cents 33:37:44:50:57:66 SD: 1.9538 cents 41:46:55:62:71:82 SD: 1.0953 cents 68:76:91:103:118:136 SD: 0.9257 cents 101:113:135:153:175:202 SD: 0.7950 cents 109:122:146:165:189:218 SD: 0.4570 cents 142:159:190:215:246:284 SD: 0.4457 cents 166:186:222:251:288:332 SD: 0.3873 cents 207:232:277:313:359:414 SD: 0.2814 cents 275:308:368:416:477:550 SD: 0.1506 cents 316:354:423:478:548:632 SD: 0.1234 cents 458:513:613:693:794:916 SD: 0.1074 cents