Scala analysis: CD11_17_Iraq
Suite - Ensemble de Muhammad Al-Qubbbânjî (mansuri, Iraq)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 147.966 cents 147.965600 2: 339.608 cents 339.608373 3: 559.520 cents 559.520399 4: 828.767 cents 828.767333 5: 1043.489 cents 1043.489335 6: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 156.5107 cents 156.5107 1: 147.9656 cents 147.9656 2: 191.6428 cents 191.6428 3: 219.9120 cents 219.9120 4: 269.2469 cents 269.2469 5: 214.7220 cents 214.7220 6: 156.5107 cents 156.5107
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 147.96560 cents 1: 1 156.51066 cents 1: 1 191.64277 cents 1: 1 214.72200 cents 1: 1 219.91203 cents 1: 1 269.24693 cents 2: 1 304.47627 cents 2: 1 339.60837 cents 2: 1 371.23267 cents 2: 1 411.55480 cents 2: 1 483.96894 cents 2: 1 489.15896 cents 3: 1 496.11904 cents 3: 1 519.19827 cents 3: 1 559.52040 cents 3: 1 640.47960 cents 3: 1 680.80173 cents 3: 1 703.88096 cents 4: 1 710.84104 cents 4: 1 716.03106 cents 4: 1 788.44520 cents 4: 1 828.76733 cents 4: 1 860.39163 cents 4: 1 895.52373 cents 5: 1 930.75307 cents 5: 1 980.08797 cents 5: 1 985.27800 cents 5: 1 1008.35723 cents 5: 1 1043.48933 cents 5: 1 1052.03440 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 : 148.0 339.6 559.5 828.8 1043.5 1200.0 148.0 : 191.6 411.6 680.8 895.5 1052.0 1200.0 339.6 : 219.9 489.2 703.9 860.4 1008.4 1200.0 559.5 : 269.2 484.0 640.5 788.4 980.1 1200.0 828.8 : 214.7 371.2 519.2 710.8 930.8 1200.0 1043.5: 156.5 304.5 496.1 716.0 985.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 147.9656 .. 269.2469 cents 121.28133 cents 147.96560 cents 2: 304.4763 .. 489.1590 cents 184.68269 cents 35.22933 cents 3: 496.1190 .. 703.8810 cents 207.76192 cents 6.96008 cents 4: 710.8410 .. 895.5237 cents 184.68269 cents 6.96008 cents 5: 930.7531 .. 1052.0344 cents 121.28133 cents 35.22933 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 147.96560 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 269.24693 cents Average / Smallest step : 1.351666 Largest / Average step : 1.346235 Largest / Smallest step : 1.819659 Median interval of one step : 203.18239 cents, amount: 0 Least squares average step : 200.42043 cents, oct.: 1202.52261 cents Scale is strictly proper Step pattern alph. order: ABCDEF Step pattern size order : ACEFDB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 6.96008 cents Scale diversity : 1.585241 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.316925 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 : 5.19002 cents Number of recognisable fifths : 3, average 710.2510 cents Number of appreciable fifths : 2, average 707.3610 cents Formal octave complements present : 1 = 16.6667% -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 42.2536 c. M:-60.3916 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 7: 1 1 1 2 1 1 P M ME SD: 24.6135 c. M: 45.2347 c. 10: 1 2 2 2 2 1 P D3 I SD: 26.7572 c. M:-40.4796 c. 13: 2 2 2 3 2 2 SP M ME SD: 22.5343 c. M:-36.6498 c. Glacial-6 15: 2 2 3 3 3 2 P SD: 15.1067 c. M: 28.7673 c. 17: 2 3 3 4 3 2 P SD: 11.6937 c. M:-18.2915 c. 22: 3 3 4 5 4 3 P SD: 11.2429 c. M:-15.6708 c. 23: 3 4 4 5 4 3 SP SD: 12.7303 c. M:-25.6090 c. 24: 3 4 4 6 4 3 P SD: 10.7702 c. M:-21.2327 c. 25: 3 4 5 5 5 3 P SD: 10.1640 c. M:-16.4796 c. 28: 3 5 5 6 5 4 SP SD: 11.7232 c. M: 19.3942 c. 30: 4 4 6 7 5 4 N SD: 10.5506 c. M: 19.6084 c. 32: 4 5 6 7 6 4 P SD: 3.5129 c. M:-6.5107 c. 39: 5 6 7 9 7 5 P SD: 3.6332 c. M:-5.8806 c. 56: 7 9 10 13 10 7 P SD: 4.3011 c. M:-6.9470 c. 62: 8 10 11 14 11 8 SP SD: 4.8720 c. M:-8.7787 c. 67: 8 11 12 15 12 9 SP SD: 3.8007 c. M: 4.8867 c. 71: 9 11 13 16 13 9 P SD: 2.6628 c. M:-4.3980 c. 75: 9 12 14 17 13 10 P SD: 2.9326 c. M: 3.9656 c. 84: 10 14 15 19 15 11 SP SD: 2.6690 c. M: 5.1085 c. 88: 11 14 16 20 16 11 P SD: 3.1014 c. M:-6.5107 c. 90: 11 14 17 20 16 12 P SD: 3.1060 c. M: 6.2750 c. 94: 12 15 17 21 17 12 SP SD: 3.4122 c. M:-5.2259 c. 96: 12 15 18 21 17 13 SP SD: 3.3548 c. M: 5.9893 c. 97: 12 15 18 22 17 13 P SD: 3.1100 c. M: 5.5878 c. 98: 12 16 18 22 17 13 SP SD: 2.8248 c. M:-3.8857 c. 99: 12 16 18 22 18 13 SP SD: 2.3001 c. M: 4.5249 c. 107: 13 17 20 24 19 14 P SD: 1.7200 c. M: 3.1598 c. 114: 14 18 21 26 20 15 P SD: 1.8472 c. M:-2.8116 c. 116: 14 19 21 26 21 15 SP SD: 1.6822 c. M: 3.1380 c. 130: 16 21 24 29 23 17 SP SD: 1.8541 c. M:-3.5565 c. 137: 17 22 25 31 24 18 SP SD: 1.7585 c. M:-3.3495 c. 138: 17 22 25 31 25 18 SP SD: 1.6545 c. M: 2.9987 c. 139: 17 22 26 31 25 18 P SD: 1.5200 c. M: 2.9177 c. 145: 18 23 27 32 26 19 SP SD: 1.5002 c. M:-3.2382 c. 146: 18 23 27 33 26 19 P SD: 1.2417 c. M: 2.6221 c. 148: 18 24 27 33 27 19 SP SD: 1.5284 c. M:-2.4566 c. 152: 19 24 28 34 27 20 SP SD: 1.0891 c. M:-2.0344 c. 169: 21 27 31 38 30 22 SP SD: 1.2203 c. M:-2.0019 c. 178: 22 28 33 40 32 23 P SD: 1.2136 c. M: 2.5297 c. 184: 23 29 34 41 33 24 SP SD: 1.0363 c. M:-2.0344 c. 197: 24 32 36 44 35 26 SP SD: 1.2778 c. M: 1.8650 c. 201: 25 32 37 45 36 26 SP SD: 1.1377 c. M:-1.6736 c. 223: 27 36 41 50 40 29 SP SD: 1.1353 c. M: 2.6741 c. 229: 28 37 42 51 41 30 SP SD: 0.9209 c. M: 1.2407 c. 236: 29 38 43 53 42 31 SP SD: 0.6696 c. M: 1.1165 c. 268: 33 43 49 60 48 35 SP SD: 0.3560 c. M:-0.6901 c. 307: 38 49 56 69 55 40 SP SD: 0.3839 c. M:-0.5686 c. 382: 47 61 70 86 68 50 SP SD: 0.4008 c. M: 0.5574 c. 414: 51 66 76 93 74 54 SP SD: 0.2257 c. M: 0.4779 c. 566: 70 90 104 127 101 74 SP SD: 0.3089 c. M:-0.4443 c. 575: 71 92 105 129 103 75 SP SD: 0.2800 c. M:-0.5655 c. 607: 75 97 111 136 109 79 SP SD: 0.3088 c. M: 0.4313 c. 643: 79 103 118 144 115 84 SP SD: 0.2884 c. M: 0.5317 c. 650: 80 104 119 146 116 85 SP SD: 0.2216 c. M: 0.4124 c. 682: 84 109 125 153 122 89 SP SD: 0.0776 c. M: 0.1650 c. 1396: 172 223 256 313 250 182 SP SD: 0.0825 c. M: 0.1146 c. 1403: 173 224 257 315 251 183 SP SD: 0.0649 c. M: 0.1476 c. 1671: 206 267 306 375 299 218 SP SD: 0.0550 c. M: 0.0949 c. 2085: 257 333 382 468 373 272 SP SD: 0.0498 c. M: 0.0959 c. 2117: 261 338 388 475 379 276 SP SD: 0.0486 c. M: 0.0713 c. 2353: 290 376 431 528 421 307 SP SD: 0.0505 c. M: 0.0693 c. 2385: 294 381 437 535 427 311 SP SD: 0.0433 c. M: 0.0881 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 63.4062 cents 3 x x 4:5 x 6 S SD: 27.6277 cents 4 x 5 x 6:7:8 S SD: 38.5984 cents 5 x 6:7:8:9:10 S SD: 8.9464 cents 6 x 7:8:10:11:12 S SD: 22.0861 cents 8:9:10:11:13:15:16 SD: 14.4549 cents 10:11:12:14:16:18:20 S SD: 7.9778 cents 13:14:16:18:21:24:26 S SD: 5.5784 cents 23:25:28:32:37:42:46 SD: 2.3353 cents 42:46:51:58:68:77:84 SD: 2.1547 cents 47:51:57:65:76:86:94 SD: 1.6252 cents 65:71:79:90:105:119:130 SD: 1.2538 cents 78:85:95:108:126:143:156 SD: 1.2395 cents 88:96:107:122:142:161:176 SD: 1.1840 cents 91:99:111:126:147:166:182 SD: 1.1562 cents 102:111:124:141:165:186:204 SD: 0.9524 cents 110:120:134:152:178:201:220 SD: 0.9375 cents 111:121:135:153:179:203:222 SD: 0.7970 cents 133:145:162:184:215:243:266 SD: 0.7319 cents 134:146:163:185:216:245:268 SD: 0.4737 cents 179:195:218:247:289:327:358 SD: 0.4526 cents 189:206:230:261:305:345:378 SD: 0.3600 cents 202:220:246:279:326:369:404 SD: 0.2787 cents 236:257:287:326:381:431:472 SD: 0.2259 cents 370:403:450:511:597:676:740 SD: 0.1772 cents 438:477:533:605:707:800:876 SD: 0.1332 cents 503:548:612:695:812:919:1006 SD: 0.0934 cents