Scala analysis: CD05_08_rast_Egypt
Elle a trop duré, la froideur de mon Aimé - ‘Abduh al-Ḥāmūlī (rast, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 212.703 cents 212.702935 2: 356.323 cents 356.323465 3: 491.402 cents 491.401517 4: 699.112 cents 699.112372 5: 813.652 cents 813.652302 6: 1096.271 cents 1096.271375 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 103.7286 cents 103.7286 1: 212.7029 cents 212.7029 2: 143.6205 cents 143.6205 3: 135.0781 cents 135.0781 4: 207.7109 cents 207.7109 5: 114.5399 cents 114.5399 6: 282.6191 cents 282.6191 7: 103.7286 cents 103.7286
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 103.72863 cents 1: 1 114.53993 cents 1: 1 135.07805 cents 1: 1 143.62053 cents 1: 1 207.71086 cents 1: 1 212.70294 cents 1: 1 282.61907 cents 2: 1 278.69858 cents 2: 1 316.43156 cents 2: 1 322.25078 cents 2: 1 342.78891 cents 2: 1 356.32346 cents 2: 1 386.34770 cents 2: 1 397.15900 cents 3: 1 457.32884 cents 3: 1 460.05209 cents 3: 1 486.40944 cents 3: 1 491.40152 cents 3: 1 500.88763 cents 3: 1 599.05063 cents 3: 1 604.86986 cents 4: 1 595.13014 cents 4: 1 600.94937 cents 4: 1 699.11237 cents 4: 1 708.59848 cents 4: 1 713.59056 cents 4: 1 739.94791 cents 4: 1 742.67116 cents 5: 1 802.84100 cents 5: 1 813.65230 cents 5: 1 843.67654 cents 5: 1 857.21109 cents 5: 1 877.74922 cents 5: 1 883.56844 cents 5: 1 921.30142 cents 6: 1 917.38093 cents 6: 1 987.29706 cents 6: 1 992.28914 cents 6: 1 1056.37947 cents 6: 1 1064.92195 cents 6: 1 1085.46007 cents 6: 1 1096.27138 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 : 212.7 356.3 491.4 699.1 813.7 1096.3 1200.0 212.7 : 143.6 278.7 486.4 600.9 883.6 987.3 1200.0 356.3 : 135.1 342.8 457.3 739.9 843.7 1056.4 1200.0 491.4 : 207.7 322.3 604.9 708.6 921.3 1064.9 1200.0 699.1 : 114.5 397.2 500.9 713.6 857.2 992.3 1200.0 813.7 : 282.6 386.3 599.1 742.7 877.7 1085.5 1200.0 1096.3: 103.7 316.4 460.1 595.1 802.8 917.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 103.7286 .. 282.6191 cents 178.89045 cents 103.72863 cents 2: 278.6986 .. 397.1590 cents 118.46042 cents -3.92049 cents 3: 457.3288 .. 604.8699 cents 147.54102 cents 60.16983 cents 4: 595.1301 .. 742.6712 cents 147.54102 cents -9.73972 cents 5: 802.8410 .. 921.3014 cents 118.46042 cents 60.16983 cents 6: 917.3809 .. 1096.2714 cents 178.89045 cents -3.92049 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 103.72863 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 282.61907 cents Average / Smallest step : 1.652664 Largest / Average step : 1.648611 Largest / Smallest step : 2.724601 Median interval of one step : 143.62053 cents, amount: 1 Least squares average step : 173.15638 cents, oct.: 1212.09468 cents Scale is not proper Step pattern alph. order: ABCDEFG Step pattern size order : FDCEBGA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.89873 cents Scale diversity : 1.539340 Lumma stability : 0.273164 Lumma impropriety factor : 0.014651 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 : 1.89873 cents Number of recognisable fifths : 3, average 707.1005 cents Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 178.8904 cents: 4 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 35.9818 c. M: 67.6999 c. Lebeng 9: 2 1 1 1 1 2 1 N D3 S SD: 35.2411 c. M:-53.9637 c. 10: 2 1 1 2 1 2 1 P M ME S SD: 18.0630 c. M:-27.2971 c. Sethares Neutral, Beatles-7, Dichotic-7 17: 3 2 2 3 2 4 1 N SD: 18.0468 c. M:-33.4065 c. 19: 3 3 2 3 2 4 2 SP D3 SD: 16.1585 c. M: 23.2293 c. Nineteen-tone Harmonic Major 21: 4 2 3 3 2 5 2 N SD: 14.3137 c. M:-22.8842 c. 22: 4 3 2 4 2 5 2 P SD: 10.8830 c. M:-25.4947 c. Twenty-two tone Harmonic Major 24: 4 3 3 4 2 6 2 P S SD: 8.2493 c. M: 13.6523 c. Maqam Suznak (Soznak) 34: 6 4 4 6 3 8 3 P S SD: 3.2455 c. M:-6.7700 c. 58: 10 7 7 10 5 14 5 P S SD: 4.5656 c. M: 6.7558 c. 60: 11 7 7 10 6 14 5 P SD: 5.2872 c. M:-8.5985 c. 61: 11 7 7 11 5 15 5 N S SD: 5.0767 c. M:-9.0843 c. 67: 12 8 7 12 6 16 6 N SD: 4.5192 c. M: 7.8194 c. 69: 12 8 8 12 7 16 6 N SD: 4.3811 c. M: 8.4974 c. 71: 13 8 8 12 7 17 6 N SD: 3.8116 c. M:-7.0154 c. 74: 13 9 8 13 7 18 6 N SD: 3.3944 c. M:-6.4313 c. 78: 14 9 9 13 8 18 7 P SD: 3.3629 c. M: 6.8047 c. 80: 14 10 9 14 7 19 7 P SD: 3.4515 c. M:-5.8876 c. 81: 14 10 9 14 8 19 7 N SD: 2.5136 c. M: 5.2955 c. 83: 15 10 9 14 8 20 7 N SD: 3.6346 c. M: 5.1365 c. 84: 15 10 9 15 8 20 7 N SD: 2.6889 c. M: 5.6872 c. 91: 16 11 10 16 9 21 8 N SD: 2.1974 c. M:-3.9301 c. 105: 19 12 12 18 10 25 9 N SD: 2.1860 c. M:-4.4399 c. 108: 19 13 12 19 10 26 9 N SD: 2.0903 c. M:-3.7286 c. 112: 20 13 13 19 11 26 10 P SD: 2.1199 c. M: 3.4142 c. 115: 20 14 13 20 11 27 10 N SD: 1.6826 c. M: 4.0073 c. 117: 21 14 13 20 11 28 10 N SD: 2.0955 c. M: 3.3959 c. 118: 21 14 13 21 11 28 10 N SD: 1.7875 c. M: 3.2659 c. 124: 22 15 14 21 12 29 11 P SD: 1.7371 c. M: 2.7230 c. 125: 22 15 14 22 12 29 11 N SD: 1.6313 c. M:-2.3477 c. 149: 26 18 17 26 14 35 13 N SD: 1.6133 c. M: 3.3070 c. 151: 27 18 17 26 14 36 13 N SD: 1.5328 c. M: 3.0563 c. 158: 28 19 18 27 15 37 14 P SD: 1.3863 c. M: 2.6005 c. 175: 31 21 20 30 17 41 15 N SD: 1.2983 c. M:-2.3477 c. 186: 33 22 21 32 18 44 16 N SD: 1.1765 c. M: 2.3382 c. 196: 35 23 22 34 19 46 17 N SD: 1.0974 c. M: 1.6056 c. 208: 37 25 23 36 20 49 18 N SD: 0.8111 c. M:-1.3688 c. 220: 39 26 25 38 21 52 19 N SD: 0.8564 c. M: 1.7780 c. 232: 41 28 26 40 22 55 20 N SD: 0.7575 c. M: 1.5833 c. 242: 43 29 27 42 23 57 21 N SD: 0.4401 c. M:-0.7013 c. 357: 63 43 40 62 34 84 31 N SD: 0.4730 c. M: 0.9382 c. 417: 74 50 47 72 40 98 36 N SD: 0.4438 c. M:-0.7362 c. 462: 82 55 52 80 44 109 40 N SD: 0.4128 c. M: 0.6653 c. 518: 92 62 58 90 49 122 45 N SD: 0.4214 c. M: 0.5249 c. 525: 93 63 59 91 50 124 45 N SD: 0.3670 c. M:-0.8715 c. 599: 106 72 67 104 57 141 52 N SD: 0.3432 c. M: 0.5835 c. 603: 107 72 68 104 58 142 52 N SD: 0.2900 c. M: 0.6049 c. 637: 113 76 72 110 61 150 55 N SD: 0.1962 c. M: 0.2795 c. 879: 156 105 99 152 84 207 76 N SD: 0.1163 c. M:-0.2663 c. 913: 162 109 103 158 87 215 79 N SD: 0.1337 c. M:-0.2215 c. 994: 176 119 112 172 95 234 86 N SD: 0.1273 c. M: 0.2281 c. 1236: 219 148 139 214 118 291 107 N SD: 0.0932 c. M: 0.1549 c. 1653: 293 198 186 286 158 389 143 N SD: 0.0811 c. M:-0.1408 c. 1687: 299 202 190 292 161 397 146 N SD: 0.0900 c. M: 0.1244 c. 1761: 312 211 198 305 168 415 152 N SD: 0.0813 c. M:-0.1511 c. 1873: 332 224 211 324 179 441 162 N SD: 0.0664 c. M: 0.1268 c. 1919: 340 230 216 332 183 452 166 N SD: 0.0832 c. M:-0.1122 c. 2115: 375 253 238 366 202 498 183 N SD: 0.0650 c. M: 0.1053 c. 2149: 381 257 242 372 205 506 186 N SD: 0.0639 c. M: 0.1336 c. 2398: 425 287 270 415 229 565 207 N SD: 0.0576 c. M:-0.1423 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: 1.4213 cents 3 x x 4 x 5 x 6 S SD: 23.6726 cents 4 x 5 x 6 x x 8 S SD: 10.0416 cents 5 x 6:7 x 8:9:10 S SD: 25.4134 cents 6:7 x 8:9:10:11:12 S SD: 16.8211 cents 7:8 x 9:10:11:13:14 SD: 18.0663 cents 8:9:10:11:12:13:15:16 SD: 10.4599 cents 12:14:15:16:18:19:23:24 SD: 10.2181 cents 14:16:17:19:21:22:26:28 SD: 8.7153 cents 15:17:18:20:22:24:28:30 SD: 8.1598 cents 16:18:20:21:24:26:30:32 SD: 6.6950 cents 18:20:22:24:27:29:34:36 SD: 4.9834 cents 22:25:27:29:33:35:41:44 SD: 3.7740 cents 30:34:37:40:45:48:57:60 SD: 2.6206 cents 40:45:49:53:60:64:75:80 SD: 1.9796 cents 52:59:64:69:78:83:98:104 SD: 1.2288 cents 70:79:86:93:105:112:132:140 SD: 0.6803 cents 122:138:150:162:183:195:230:244 SD: 0.5657 cents 153:173:188:203:229:245:288:306 SD: 0.4052 cents 183:207:225:243:274:293:345:366 SD: 0.3541 cents 207:234:254:275:310:331:390:414 SD: 0.3448 cents 223:252:274:296:334:357:420:446 SD: 0.2704 cents 275:311:338:365:412:440:518:550 SD: 0.2389 cents 320:362:393:425:479:512:603:640 SD: 0.2008 cents 360:407:442:478:539:576:678:720 SD: 0.1909 cents 368:416:452:489:551:589:693:736 SD: 0.1825 cents 390:441:479:518:584:624:735:780 SD: 0.1400 cents 420:475:516:558:629:672:791:840 SD: 0.0946 cents