Scala analysis: segah-haji_aqa
Iranian Segah Dastgah on setar of Haji Aqa Mohammad Irani (Jean During)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 211.500 cents 211.500000 2: 353.000 cents 353.000000 3: 507.500 cents 507.500000 4: 703.500 cents 703.500000 5: 857.500 cents 857.500000 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 342.5000 cents 342.5000 1: 211.5000 cents 211.5000 2: 141.5000 cents 141.5000 3: 154.5000 cents 154.5000 4: 196.0000 cents 196.0000 5: 154.0000 cents 154.0000 6: 342.5000 cents 342.5000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 141.50000 cents 1: 1 154.00000 cents 1: 1 154.50000 cents 1: 1 196.00000 cents 1: 1 211.50000 cents 1: 1 342.50000 cents 2: 1 296.00000 cents 2: 1 350.00000 cents 2: 1 350.50000 cents 2: 1 353.00000 cents 2: 1 496.50000 cents 2: 1 554.00000 cents 3: 1 492.00000 cents 3: 1 504.50000 cents 3: 1 507.50000 cents 3: 1 692.50000 cents 3: 1 695.50000 cents 3: 1 708.00000 cents 4: 1 646.00000 cents 4: 1 703.50000 cents 4: 1 847.00000 cents 4: 1 849.50000 cents 4: 1 850.00000 cents 4: 1 904.00000 cents 5: 1 857.50000 cents 5: 1 988.50000 cents 5: 1 1004.00000 cents 5: 1 1045.50000 cents 5: 1 1046.00000 cents 5: 1 1058.50000 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 : 211.5 353.0 507.5 703.5 857.5 1200.0 211.5 : 141.5 296.0 492.0 646.0 988.5 1200.0 353.0 : 154.5 350.5 504.5 847.0 1058.5 1200.0 507.5 : 196.0 350.0 692.5 904.0 1045.5 1200.0 703.5 : 154.0 496.5 708.0 849.5 1004.0 1200.0 857.5 : 342.5 554.0 695.5 850.0 1046.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 141.5000 .. 342.5000 cents 201.00000 cents 141.50000 cents 2: 296.0000 .. 554.0000 cents 258.00000 cents -46.50000 cents 3: 492.0000 .. 708.0000 cents 216.00000 cents -62.00000 cents 4: 646.0000 .. 904.0000 cents 258.00000 cents -62.00000 cents 5: 857.5000 .. 1058.5000 cents 201.00000 cents -46.50000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 141.50000 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 342.50000 cents Average / Smallest step : 1.413428 Largest / Average step : 1.712500 Largest / Smallest step : 2.420495 Median interval of one step : 175.25000 cents, amount: 0 Least squares average step : 183.97253 cents, oct.: 1103.83516 cents Scale is not proper Scale is a mode of a 2400-tone equal temperament with octave 2/1 degrees: 423 706 1015 1407 1715 2400 Least number of segments generator : 1201 of 600.500 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1553 of 776.500 cents and inv. generated superset size: 537 = 531 more = 8950.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEF Step pattern size order : EACDBF Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 4.50000 cents Scale diversity : 1.412404 Lumma stability : 0.235833 Lumma impropriety factor : 0.180833 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 : 0.50000 cents Number of recognisable fifths : 4, average 699.8750 cents Formal octave complements present : 1 = 16.6667% -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
6: 1 0 1 1 1 2 N T3 SD: 90.4765 c. M: 153.0000 c. 7: 1 1 1 1 1 2 P M ME SD: 18.5791 c. M: 40.0714 c. 10: 2 1 1 2 1 3 N SD: 19.1311 c. M:-28.5000 c. 17: 3 2 2 3 2 5 N SD: 6.9983 c. M: 13.3824 c. 24: 4 3 3 4 3 7 N SD: 6.6583 c. M: 11.5000 c. 38: 7 4 5 6 5 11 N SD: 6.1707 c. M:-9.5526 c. 41: 7 5 5 7 5 12 N SD: 6.0959 c. M: 9.9390 c. 45: 8 5 6 7 6 13 N SD: 5.2423 c. M: 10.1667 c. 50: 9 6 6 8 7 14 N SD: 5.4772 c. M: 7.5000 c. 56: 10 6 8 9 7 16 N SD: 5.3242 c. M: 10.1429 c. 57: 10 7 7 9 8 16 N SD: 4.8082 c. M: 8.7632 c. 61: 11 7 8 10 8 17 N SD: 4.6224 c. M:-8.0738 c. 62: 11 7 8 10 8 18 N SD: 4.4984 c. M: 6.7258 c. 67: 12 8 8 11 9 19 N SD: 4.1779 c. M: 6.0075 c. 68: 12 8 9 11 9 19 N SD: 3.5558 c. M:-7.2059 c. 78: 14 9 10 13 10 22 N SD: 2.8789 c. M:-4.1923 c. 85: 15 10 11 14 11 24 N SD: 1.8169 c. M:-3.6765 c. 92: 16 11 12 15 12 26 N SD: 1.9170 c. M:-3.3696 c. 102: 18 12 13 17 13 29 N SD: 1.2986 c. M:-2.3824 c. 109: 19 13 14 18 14 31 N SD: 1.2734 c. M: 2.3257 c. 130: 23 15 17 21 17 37 N SD: 1.3190 c. M: 2.2308 c. 147: 26 17 19 24 19 42 N SD: 1.1992 c. M: 1.9796 c. 193: 34 23 25 31 25 55 N SD: 1.1964 c. M:-2.3446 c. 203: 36 24 26 33 26 58 N SD: 0.9511 c. M:-1.6798 c. 210: 37 25 27 34 27 60 N SD: 0.7469 c. M:-1.2857 c. 227: 40 27 29 37 29 65 N SD: 0.6852 c. M:-1.1850 c. 288: 51 34 37 47 37 82 N SD: 0.8361 c. M:-1.1667 c. 295: 52 35 38 48 38 84 N SD: 0.6400 c. M:-0.9746 c. 312: 55 37 40 51 40 89 N SD: 0.3897 c. M:-0.8462 c. 319: 56 38 41 52 41 91 N SD: 0.4515 c. M: 0.8417 c. 329: 58 39 42 54 42 94 N SD: 0.4531 c. M:-0.7994 c. 336: 59 40 43 55 43 96 N SD: 0.4480 c. M: 0.7857 c. 357: 63 42 46 58 46 102 N SD: 0.4404 c. M: 0.9790 c. 421: 74 50 54 69 54 120 N SD: 0.4170 c. M: 0.5736 c. 435: 77 51 56 71 56 124 N SD: 0.4167 c. M:-0.9138 c. 442: 78 52 57 72 57 126 N SD: 0.2570 c. M:-0.4186 c. 459: 81 54 59 75 59 131 N SD: 0.1932 c. M: 0.3105 c. 754: 133 89 97 123 97 215 N SD: 0.2138 c. M:-0.3249 c. 771: 136 91 99 126 99 220 N SD: 0.1547 c. M:-0.3074 c. 778: 137 92 100 127 100 222 N SD: 0.1386 c. M:-0.2134 c. 1163: 205 137 150 190 149 332 N SD: 0.1161 c. M:-0.1973 c. 1237: 218 146 159 202 159 353 N SD: 0.1092 c. M: 0.1855 c. 1475: 260 174 190 241 189 421 N SD: 0.1198 c. M:-0.2288 c. 1482: 261 175 191 242 190 423 N SD: 0.1197 c. M:-0.1923 c. 1499: 264 177 193 245 192 428 N SD: 0.1104 c. M:-0.1691 c. 1520: 268 179 196 248 195 434 N SD: 0.0985 c. M: 0.1316 c. 1605: 283 189 207 262 206 458 N SD: 0.0938 c. M:-0.1636 c. 1622: 286 191 209 265 208 463 N SD: 0.0665 c. M: 0.1023 c. 1629: 287 192 210 266 209 465 N SD: 0.0732 c. M: 0.1455 c. 1934: 341 228 249 316 248 552 N SD: 0.0658 c. M:-0.1194 c. 1941: 342 229 250 317 249 554 N SD: 0.0457 c. M:-0.0734 c. 2400: 423 283 309 392 308 685 N SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 0.7725 cents 3 x x 4 x 5:6 S SD: 9.4914 cents 4 x 5 x 6:7:8 S SD: 29.0535 cents 5 x 6:7 x 8:10 S SD: 23.6407 cents 6:7 x 8:9:10:12 S SD: 12.4565 cents 7:8 x 9 x 11:14 SD: 26.5251 cents 8:9:10:11:12:13:16 SD: 9.6866 cents 14:16:17:19:21:23:28 SD: 5.5945 cents 22:25:27:29:33:36:44 SD: 5.2178 cents 23:26:28:31:35:38:46 SD: 5.0691 cents 26:29:32:35:39:43:52 SD: 4.6573 cents 30:34:37:40:45:49:60 SD: 2.8190 cents 44:50:54:59:66:72:88 SD: 1.8650 cents 53:60:65:71:80:87:106 SD: 1.6618 cents 62:70:76:83:93:102:124 SD: 0.9119 cents 106:120:130:142:159:174:212 SD: 0.6486 cents 164:185:201:220:246:269:328 SD: 0.6069 cents 168:190:206:225:252:276:336 SD: 0.5680 cents 176:199:216:236:264:289:352 SD: 0.4528 cents 200:226:245:268:300:328:400 SD: 0.4398 cents 208:235:255:279:312:341:416 SD: 0.4139 cents 217:245:266:291:326:356:434 SD: 0.3304 cents 261:295:320:350:392:428:522 SD: 0.2605 cents 309:349:379:414:464:507:618 SD: 0.2439 cents 323:365:396:433:485:530:646 SD: 0.0680 cents