Scala analysis: CD02_09_Egypt
L'astre pour qui je me sacrifierai est apparu - Darwîsh Muhammad al-Harîrî (sikah arabi, Egypt)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 131.468 cents 131.467847 2: 346.366 cents 346.366141 3: 484.590 cents 484.589733 4: 627.658 cents 627.658323 5: 833.794 cents 833.794451 6: 968.669 cents 968.669344 7: 1088.518 cents 1088.517718 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 111.4823 cents 111.4823 1: 131.4678 cents 131.4678 2: 214.8983 cents 214.8983 3: 138.2236 cents 138.2236 4: 143.0686 cents 143.0686 5: 206.1361 cents 206.1361 6: 134.8749 cents 134.8749 7: 119.8484 cents 119.8484 8: 111.4823 cents 111.4823
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 111.48228 cents 1: 1 119.84837 cents 1: 1 131.46785 cents 1: 1 134.87489 cents 1: 1 138.22359 cents 1: 1 143.06859 cents 1: 1 206.13613 cents 1: 1 214.89829 cents 2: 1 231.33066 cents 2: 1 242.95013 cents 2: 1 254.72327 cents 2: 1 281.29218 cents 2: 1 341.01102 cents 2: 1 346.36614 cents 2: 1 349.20472 cents 2: 1 353.12189 cents 3: 1 362.79850 cents 3: 1 366.20555 cents 3: 1 457.84842 cents 3: 1 460.85940 cents 3: 1 484.07961 cents 3: 1 484.58973 cents 3: 1 487.42831 cents 3: 1 496.19048 cents 4: 1 497.67340 cents 4: 1 572.34168 cents 4: 1 577.69680 cents 4: 1 596.07201 cents 4: 1 603.92799 cents 4: 1 622.30320 cents 4: 1 627.65832 cents 4: 1 702.32660 cents 5: 1 703.80952 cents 5: 1 712.57169 cents 5: 1 715.41027 cents 5: 1 715.92039 cents 5: 1 739.14060 cents 5: 1 742.15158 cents 5: 1 833.79445 cents 5: 1 837.20150 cents 6: 1 846.87811 cents 6: 1 850.79528 cents 6: 1 853.63386 cents 6: 1 858.98898 cents 6: 1 918.70782 cents 6: 1 945.27673 cents 6: 1 957.04987 cents 6: 1 968.66934 cents 7: 1 985.10171 cents 7: 1 993.86387 cents 7: 1 1056.93141 cents 7: 1 1061.77641 cents 7: 1 1065.12511 cents 7: 1 1068.53215 cents 7: 1 1080.15163 cents 7: 1 1088.51772 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 8.00000 = 8
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 131.5 346.4 484.6 627.7 833.8 968.7 1088.5 1200.0 131.5 : 214.9 353.1 496.2 702.3 837.2 957.0 1068.5 1200.0 346.4 : 138.2 281.3 487.4 622.3 742.2 853.6 985.1 1200.0 484.6 : 143.1 349.2 484.1 603.9 715.4 846.9 1061.8 1200.0 627.7 : 206.1 341.0 460.9 572.3 703.8 918.7 1056.9 1200.0 833.8 : 134.9 254.7 366.2 497.7 712.6 850.8 993.9 1200.0 968.7 : 119.8 231.3 362.8 577.7 715.9 859.0 1065.1 1200.0 1088.5: 111.5 243.0 457.8 596.1 739.1 945.3 1080.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.4823 .. 214.8983 cents 103.41601 cents 111.48228 cents 2: 231.3307 .. 353.1219 cents 121.79123 cents 16.43236 cents 3: 362.7985 .. 496.1905 cents 133.39197 cents 9.67662 cents 4: 497.6734 .. 702.3266 cents 204.65321 cents 1.48292 cents 5: 703.8095 .. 837.2015 cents 133.39197 cents 1.48292 cents 6: 846.8781 .. 968.6693 cents 121.79123 cents 9.67662 cents 7: 985.1017 .. 1088.5177 cents 103.41601 cents 16.43236 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 111.48228 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 214.89829 cents Average / Smallest step : 1.345505 Largest / Average step : 1.432655 Largest / Smallest step : 1.927645 Median interval of one step : 136.54924 cents, amount: 0 Least squares average step : 156.80988 cents, oct.: 1254.47902 cents Scale is strictly proper Step pattern alph. order: ABCDEFGH Step pattern size order : CHEFGDBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 1.48292 cents Scale diversity : 1.431204 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.231790 Rothenberg efficiency : 0.250000 redundancy: 0.750000 Efficiency x scale size : 2.000000 Number of different interval sizes : 56 = 8.00000 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 8.00000 = 8 Median interval variety : 8 Lowest interval variety : 8 Smallest interval difference : 0.51012 cents Number of recognisable fifths : 5, average 710.0077 cents Number of appreciable fifths : 3, average 706.2359 cents Formal octave complements present : 1 = 12.5000% Limited inverse transpositions with margin 129.9849 cents: 6 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 47.0044 c. M: 83.7945 c. 9: 1 2 1 1 1 1 1 1 P M ME SD: 34.7236 c. M:-53.6339 c. 10: 1 2 1 1 2 1 1 1 P D3 S SD: 12.6968 c. M: 27.6583 c. 23: 3 4 2 3 4 3 2 2 P SD: 14.8975 c. M:-25.0539 c. 25: 3 4 3 3 4 3 3 2 SP SD: 10.7846 c. M: 17.7945 c. 27: 3 5 3 3 5 3 3 2 P SD: 10.2641 c. M:-22.5934 c. 30: 3 6 3 4 5 3 3 3 N SD: 9.1991 c. M:-13.6339 c. 32: 4 5 4 4 5 4 3 3 SP S SD: 8.9849 c. M:-18.5322 c. 35: 4 6 4 4 6 4 4 3 SP SD: 7.4610 c. M: 10.9373 c. 42: 5 7 5 5 7 5 4 4 SP S SD: 4.8332 c. M:-11.3893 c. 52: 6 9 6 6 9 6 5 5 SP S SD: 3.4395 c. M:-6.9937 c. 72: 8 13 8 9 12 8 7 7 P SD: 3.1932 c. M:-5.6750 c. 76: 8 14 9 9 13 8 8 7 N SD: 3.6632 c. M: 5.5114 c. 77: 8 14 9 9 13 9 8 7 P SD: 4.3555 c. M: 7.8204 c. 79: 9 14 9 9 14 9 8 7 SP SD: 3.6027 c. M:-5.2410 c. 82: 9 15 9 10 14 9 8 8 P SD: 2.9215 c. M: 5.5909 c. 84: 9 15 10 10 14 10 8 8 P SD: 2.8625 c. M: 5.2230 c. 89: 10 16 10 11 15 10 9 8 P SD: 3.3240 c. M:-6.0495 c. 94: 10 17 11 11 16 11 9 9 P SD: 2.5546 c. M: 4.0072 c. 99: 11 18 11 12 17 11 10 9 P SD: 2.5107 c. M:-5.1490 c. 107: 12 19 12 13 18 12 11 10 SP SD: 2.5019 c. M: 4.1834 c. 109: 12 19 13 13 19 12 11 10 P SD: 2.1409 c. M: 5.0817 c. 118: 13 21 14 14 20 13 12 11 P SD: 1.8825 c. M:-3.5459 c. 119: 13 21 14 14 21 13 12 11 P SD: 1.9218 c. M: 3.5090 c. 121: 13 22 14 14 21 14 12 11 P SD: 2.0547 c. M:-3.2315 c. 128: 14 23 15 15 22 14 13 12 P SD: 1.5666 c. M: 3.0443 c. 151: 17 27 17 18 26 17 15 14 SP SD: 1.7807 c. M:-3.6315 c. 161: 18 28 19 19 28 18 16 15 SP SD: 1.7031 c. M: 3.5090 c. 163: 18 29 19 19 28 19 16 15 SP SD: 1.6144 c. M:-3.1098 c. 164: 18 29 19 20 28 18 17 15 P SD: 1.6776 c. M: 2.8157 c. 166: 18 30 19 20 28 19 17 15 P SD: 1.5507 c. M:-3.0485 c. 170: 19 30 20 20 29 19 17 16 SP SD: 1.5466 c. M:-2.6498 c. 174: 19 31 20 21 30 19 18 16 P SD: 1.4839 c. M: 3.1521 c. 176: 19 32 20 21 30 20 18 16 P SD: 1.4057 c. M:-2.3914 c. 180: 20 32 21 21 31 20 18 17 SP SD: 1.4369 c. M:-2.0769 c. 181: 20 32 21 22 31 20 18 17 P SD: 1.2966 c. M:-2.1759 c. 183: 20 33 21 22 31 21 18 17 P SD: 1.0995 c. M:-1.8499 c. 191: 21 34 22 23 33 21 19 18 P SD: 1.0643 c. M:-1.8076 c. 193: 21 35 22 23 33 22 19 18 P SD: 0.9081 c. M:-1.8204 c. 235: 26 42 27 28 40 27 23 22 SP SD: 1.0075 c. M:-1.5434 c. 239: 26 43 28 28 41 27 24 22 P SD: 1.0060 c. M:-2.4396 c. 245: 27 44 28 29 42 28 24 23 SP SD: 0.9413 c. M:-1.3890 c. 258: 28 46 30 31 44 29 26 24 P SD: 1.1265 c. M: 2.1801 c. 260: 28 47 30 31 45 29 26 24 N SD: 1.0249 c. M: 2.2371 c. 268: 29 48 31 32 46 30 27 25 P SD: 1.1281 c. M: 1.6171 c. 270: 30 48 31 32 47 30 27 25 SP SD: 0.9914 c. M:-1.8655 c. 275: 30 49 32 33 47 31 27 26 P SD: 0.9718 c. M: 1.9723 c. 281: 31 50 32 34 48 32 28 26 SP SD: 0.9362 c. M: 2.0275 c. 291: 32 52 34 34 50 33 29 27 SP SD: 0.8540 c. M:-2.0082 c. 292: 32 52 34 35 50 33 29 27 P SD: 0.7581 c. M:-1.1937 c. 302: 33 54 35 36 52 34 30 28 P SD: 0.4793 c. M:-0.8671 c. 312: 34 56 36 37 54 35 31 29 P SD: 0.5083 c. M:-0.8209 c. 354: 39 63 41 42 61 40 35 33 SP SD: 0.5066 c. M:-0.8222 c. 357: 39 64 41 43 61 40 36 33 P SD: 0.5015 c. M:-0.9131 c. 367: 40 66 42 44 63 41 37 34 P SD: 0.4670 c. M: 0.8219 c. 409: 45 73 47 49 70 46 41 38 SP SD: 0.3740 c. M:-0.5615 c. 419: 46 75 48 50 72 47 42 39 SP SD: 0.3966 c. M: 0.6503 c. 530: 58 95 61 63 91 60 53 49 SP SD: 0.3625 c. M: 0.5869 c. 602: 66 108 69 72 103 68 60 56 SP SD: 0.2956 c. M: 0.5719 c. 658: 72 118 76 78 113 74 66 61 SP SD: 0.2888 c. M:-0.5166 c. 669: 73 120 77 80 115 75 67 62 P SD: 0.2668 c. M: 0.5261 c. 711: 78 127 82 85 122 80 71 66 SP SD: 0.1836 c. M: 0.3746 c. 721: 79 129 83 86 124 81 72 67 SP SD: 0.1340 c. M: 0.2624 c. 914: 100 164 105 109 157 103 91 85 SP SD: 0.1592 c. M:-0.2584 c. 1151: 126 206 133 137 198 129 115 107 SP SD: 0.1569 c. M:-0.2629 c. 1203: 132 215 139 143 207 135 120 112 SP SD: 0.1821 c. M: 0.2384 c. 1216: 133 218 140 145 209 137 121 113 SP SD: 0.1685 c. M:-0.4096 c. 1271: 139 228 146 152 218 143 127 118 SP SD: 0.1542 c. M: 0.2467 c. 1323: 145 237 152 158 227 149 132 123 SP SD: 0.1303 c. M: 0.2360 c. 1344: 147 241 155 160 231 151 134 125 SP SD: 0.1349 c. M:-0.2317 c. 1369: 150 245 158 163 235 154 137 127 SP SD: 0.1166 c. M: 0.1933 c. 1560: 171 279 180 186 268 175 156 145 SP SD: 0.1123 c. M: 0.2123 c. 1570: 172 281 181 187 270 176 157 146 SP SD: 0.1248 c. M: 0.2617 c. 1625: 178 291 187 194 279 183 162 151 SP SD: 0.0938 c. M:-0.1922 c. 1635: 179 293 188 195 281 184 163 152 SP SD: 0.1064 c. M: 0.1861 c. 1681: 184 301 194 200 289 189 168 156 SP SD: 0.1094 c. M: 0.1747 c. 1743: 191 312 201 208 299 196 174 162 SP SD: 0.0937 c. M:-0.2246 c. 1753: 192 314 202 209 301 197 175 163 SP SD: 0.0525 c. M: 0.0979 c. 2055: 225 368 237 245 353 231 205 191 SP SD: 0.0737 c. M:-0.0898 c. 2283: 250 409 263 272 392 257 228 212 SP SD: 0.0698 c. M: 0.1545 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 37.1483 cents 3 x x 4 x 5 x x 6 S SD: 17.4413 cents 4 x 5 x 6 x 7 x 8 S SD: 21.0888 cents 5 x 6 x 7:8:9 x 10 S SD: 15.2058 cents 6 x 7:8:9:10 x 11:12 S SD: 21.1544 cents 7:8 x 9:10:11:12:13:14 S SD: 18.4465 cents 8:9:10:11:12:13:14:15:16 H SD: 16.2316 cents 9:10:11:12:13:15:16:17:18 SD: 9.9392 cents 12:13:15:16:17:19:21:23:24 SD: 9.1227 cents 13:14:16:17:19:21:23:24:26 SD: 6.3230 cents 16:17:20:21:23:26:28:30:32 SD: 6.2939 cents 21:23:26:28:30:34:37:39:42 SD: 5.4955 cents 22:24:27:29:32:36:38:41:44 SD: 5.4357 cents 23:25:28:30:33:37:40:43:46 SD: 4.0844 cents 27:29:33:36:39:44:47:51:54 SD: 3.2999 cents 36:39:44:48:52:58:63:68:72 SD: 2.8937 cents 37:40:45:49:53:60:65:69:74 SD: 1.9792 cents 49:53:60:65:70:79:86:92:98 SD: 1.9408 cents 50:54:61:66:72:81:87:94:100 SD: 1.5441 cents 64:69:78:85:92:104:112:120:128 SD: 1.2932 cents 77:83:94:102:111:125:135:144:154 SD: 1.2333 cents 87:94:106:115:125:141:152:163:174 SD: 0.8127 cents 103:111:126:136:148:167:180:193:206 SD: 0.7638 cents 112:121:137:148:161:181:196:210:224 SD: 0.6136 cents 139:150:170:184:200:225:243:261:278 SD: 0.5370 cents 167:180:204:221:240:270:292:313:334 SD: 0.3949 cents 176:190:215:233:253:285:308:330:352 SD: 0.2258 cents 343:370:419:454:493:555:600:643:686 SD: 0.1758 cents 393:424:480:520:565:636:688:737:786 SD: 0.1527 cents 456:492:557:603:655:738:798:855:912 SD: 0.1469 cents 483:521:590:639:694:782:845:906:966 SD: 0.1006 cents