Scala analysis: xen18-erlich-hanson-11
4L 7s MOS for Hanson, L=181.09, s=67.99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.990 cents 67.990000 2: 249.080 cents 249.080000 3: 317.070 cents 317.070000 4: 385.060 cents 385.060000 5: 566.150 cents 566.150000 6: 634.140 cents 634.140000 7: 815.230 cents 815.230000 8: 883.220 cents 883.220000 9: 951.210 cents 951.210000 10: 1132.300 cents 1132.300000 11: 1200.290 cents 1200.290000
SHOW/INTERVAL
0: 67.9900 cents 67.9900 1: 67.9900 cents 67.9900 2: 181.0900 cents 181.0900 3: 67.9900 cents 67.9900 4: 67.9900 cents 67.9900 5: 181.0900 cents 181.0900 6: 67.9900 cents 67.9900 7: 181.0900 cents 181.0900 8: 67.9900 cents 67.9900 9: 67.9900 cents 67.9900 10: 181.0900 cents 181.0900 11: 67.9900 cents 67.9900
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 67.99000 cents 1: 4 181.09000 cents 2: 3 135.98000 cents 2: 8 249.08000 cents 3: 10 317.07000 cents 3: 1 430.17000 cents 4: 6 385.06000 cents 4: 5 498.16000 cents 5: 2 453.05000 cents 5: 9 566.15000 cents 6: 9 634.14000 cents 6: 2 747.24000 cents 7: 5 702.13000 cents 7: 6 815.23000 cents 8: 1 770.12000 cents 8: 10 883.22000 cents 9: 8 951.21000 cents 9: 3 1064.31000 cents 10: 4 1019.20000 cents 10: 7 1132.30000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 68.0 249.1 317.1 385.1 566.1 634.1 815.2 883.2 951.2 1132.3 1200.3 68.0 : 181.1 249.1 317.1 498.2 566.1 747.2 815.2 883.2 1064.3 1132.3 1200.3 249.1 : 68.0 136.0 317.1 385.1 566.1 634.1 702.1 883.2 951.2 1019.2 1200.3 317.1 : 68.0 249.1 317.1 498.2 566.1 634.1 815.2 883.2 951.2 1132.3 1200.3 385.1 : 181.1 249.1 430.2 498.2 566.1 747.2 815.2 883.2 1064.3 1132.3 1200.3 566.1 : 68.0 249.1 317.1 385.1 566.1 634.1 702.1 883.2 951.2 1019.2 1200.3 634.1 : 181.1 249.1 317.1 498.2 566.1 634.1 815.2 883.2 951.2 1132.3 1200.3 815.2 : 68.0 136.0 317.1 385.1 453.0 634.1 702.1 770.1 951.2 1019.2 1200.3 883.2 : 68.0 249.1 317.1 385.1 566.2 634.1 702.1 883.2 951.2 1132.3 1200.3 951.2 : 181.1 249.1 317.1 498.2 566.1 634.1 815.2 883.2 1064.3 1132.3 1200.3 1132.3: 68.0 136.0 317.1 385.1 453.0 634.1 702.1 883.2 951.2 1019.2 1200.3 1200.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9900 .. 181.0900 cents 113.10000 cents 67.99000 cents 2: 135.9800 .. 249.0800 cents 113.10000 cents -45.11000 cents 3: 317.0700 .. 430.1700 cents 113.10000 cents 67.99000 cents 4: 385.0600 .. 498.1600 cents 113.10000 cents -45.11000 cents 5: 453.0500 .. 566.1500 cents 113.10000 cents -45.11000 cents 6: 634.1400 .. 747.2400 cents 113.10000 cents 67.99000 cents 7: 702.1300 .. 815.2300 cents 113.10000 cents -45.11000 cents 8: 770.1200 .. 883.2200 cents 113.10000 cents -45.11000 cents 9: 951.2100 .. 1064.3100 cents 113.10000 cents 67.99000 cents 10: 1019.2000 .. 1132.3000 cents 113.10000 cents -45.11000 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 67.99000 cents, class 1 Average step (divided formal octave): 109.1173 cents Largest one step interval : 181.09000 cents Average / Smallest step : 1.604902 Largest / Average step : 1.659591 Largest / Smallest step : 2.663480 Median interval of one step : 67.99000 cents, amount: 7 Most common interval of one step : 67.99000 cents, amount: 7 Least squares average step : 109.78783 cents, oct.: 1207.66609 cents Scale is not proper Scale has Myhill's property chromas: 113.10000 cents and 45.11000 cents, ratio: 2.507205 generators: 3 of 317.07000 cents and 8 of 883.22000 cents ET pair of linear temperament : 15&19 Scale is distributional even Scale is a mode of a 1730-tone equal temperament with octave 1200.290 cents degrees: 98 359 457 555 816 914 1175 1273 1371 1632 1730 generators: 457 and 1273 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABABAABA Step pattern size order : SLSSLSLSSLS Scale is a Constant Structure, by a margin of 22.88000 cents Scale diversity : 1.241543 Lumma stability : 0.283223 Lumma impropriety factor : 0.225496 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 22.88000 cents Most common intervals : 317.07000 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 385.060 883.220 cents Most common triad is 0.0 317.070 883.220 cents, amount: 9 Number of recognisable fifths : 5, average 702.1300 cents Number of recognisable fourths : 5, average 498.1600 cents Scale contains two identical conjunct hexachords Formal octave complements present : 11 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 5-6 -- Rational properties --
FIT/MODE
11: 0 2 0 1 2 0 2 1 0 2 1 N T3 SD: 58.3905 c. M: 98.8355 c. 12: 0 2 1 0 2 1 2 0 1 2 1 N T3 SD: 52.9150 c. M: 84.9875 c. 13: 1 2 0 1 2 1 2 1 0 2 1 N T3 I SD: 24.7668 c. M:-40.0800 c. 15: 1 2 1 1 2 1 2 1 1 2 1 P M ME I SD: 9.5100 c. M: 15.0367 c. 19: 1 3 1 1 3 1 3 1 1 3 1 N M DE I SD: 3.8080 c. M: 6.0211 c. 34: 2 5 2 2 5 2 5 2 2 5 2 N M DE I SD: 2.0676 c. M: 3.2691 c. 53: 3 8 3 3 8 3 8 3 3 8 3 N M DE I SD: 0.0388 c. M: 0.0613 c. 935: 53 141 53 53 141 53 141 53 53 141 53 N M DE I SD: 0.0378 c. M: 0.0598 c. 988: 56 149 56 56 149 56 149 56 56 149 56 N M DE I SD: 0.0337 c. M: 0.0533 c. 1041: 59 157 59 59 157 59 157 59 59 157 59 N M DE I SD: 0.0300 c. M: 0.0475 c. 1094: 62 165 62 62 165 62 165 62 62 165 62 N M DE I SD: 0.0267 c. M: 0.0422 c. 1147: 65 173 65 65 173 65 173 65 65 173 65 N M DE I SD: 0.0237 c. M: 0.0374 c. 1200: 68 181 68 68 181 68 181 68 68 181 68 N M DE I SD: 0.0209 c. M: 0.0330 c. 1253: 71 189 71 71 189 71 189 71 71 189 71 N M DE I SD: 0.0184 c. M: 0.0291 c. 1306: 74 197 74 74 197 74 197 74 74 197 74 N M DE I SD: 0.0161 c. M: 0.0254 c. 1359: 77 205 77 77 205 77 205 77 77 205 77 N M DE I SD: 0.0139 c. M: 0.0220 c. 1412: 80 213 80 80 213 80 213 80 80 213 80 N M DE I SD: 0.0119 c. M: 0.0189 c. 1465: 83 221 83 83 221 83 221 83 83 221 83 N M DE I SD: 0.0101 c. M: 0.0160 c. 1518: 86 229 86 86 229 86 229 86 86 229 86 N M DE I SD: 0.0084 c. M: 0.0133 c. 1571: 89 237 89 89 237 89 237 89 89 237 89 N M DE I SD: 0.0068 c. M: 0.0108 c. 1624: 92 245 92 92 245 92 245 92 92 245 92 N M DE I SD: 0.0053 c. M: 0.0084 c. 1677: 95 253 95 95 253 95 253 95 95 253 95 N M DE I SD: 0.0039 c. M: 0.0062 c. 1730: 98 261 98 98 261 98 261 98 98 261 98 N M DE I SD: 0.0026 c. M: 0.0041 c. 1783: 101 269 101 101 269 101 269 101 101 269 101 N M DE I SD: 0.0014 c. M: 0.0022 c. 1836: 104 277 104 104 277 104 277 104 104 277 104 N M DE I SD: 0.0002 c. M: 0.0004 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.2900 cents 2 x x x x x 3 x x x x 4 S SD: 33.9078 cents 3 x x x x 4 x x 5 x x 6 S SD: 22.7050 cents 4 x x x 5 x 6 x x 7 x 8 S SD: 17.5194 cents 5 x x 6 x 7 x 8 x 9 x 10 S SD: 13.6812 cents 6 x 7 x x 8:9 x 10 x x 12 S SD: 19.5500 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 12.9136 cents 8 x 9 x 10:11:12:13 x 14:15:16 S SD: 12.3427 cents 9 x 10:11 x 12:13:14:15:16:17:18 S SD: 13.8486 cents 10 x x 12:13:14 x 16 x 17:19:20 SD: 11.5709 cents 11:12 x 13:14:15:16 x 18:19:21:22 SD: 11.5746 cents 12:13:14 x 15 x 17:19:20:21:23:24 SD: 9.2990 cents 13:14:15 x 16:18:19:21:22:23:25:26 SD: 8.4522 cents 14:15:16:17 x 19:20:22:23:24:27:28 SD: 8.3656 cents 15:16:17:18:19:21:22:24:25:26:29:30 SD: 6.2582 cents 17:18:20 x 21:24:25:27:28:29:33:34 SD: 7.7394 cents 18:19:21:22 x 25:26:29:30:31:35:36 SD: 4.9759 cents 20:21:23:24:25:28:29:32:33:35:38:40 SD: 3.7474 cents 25:26:29:30:31:35:36:40:42:43:48:50 SD: 2.7060 cents 39:41:45:47:49:54:56:62:65:68:75:78 SD: 2.6386 cents 40:42:46:48:50:55:58:64:67:69:77:80 SD: 2.5431 cents 41:43:47:49:51:57:59:66:68:71:79:82 SD: 2.3567 cents 44:46:51:53:55:61:63:70:73:76:85:88 SD: 2.1746 cents 45:47:52:54:56:62:65:72:75:78:87:90 SD: 1.6240 cents 52:54:60:62:65:72:75:83:87:90:100:104 SD: 1.4979 cents 65:68:75:78:81:90:94:104:108:113:125:130 SD: 1.3150 cents 70:73:81:84:87:97:101:112:117:121:135:140 SD: 1.2524 cents 75:78:87:90:94:104:108:120:125:130:144:150 SD: 0.9970 cents 90:94:104:108:112:125:130:144:150:156:173:180 SD: 0.9832 cents 93:97:107:112:116:129:134:149:155:161:179:186 SD: 0.9141 cents 101:105:117:121:126:140:146:162:168:175:194:202 SD: 0.8490 cents 104:108:120:125:130:144:150:167:173:180:200:208 SD: 0.6368 cents 129:134:149:155:161:179:186:207:215:223:248:258 SD: 0.5445 cents 149:155:172:179:186:207:215:239:248:258:287:298 SD: 0.4822 cents 168:175:194:202:210:233:242:269:280:291:323:336 SD: 0.4050 cents 194:202:224:233:242:269:280:311:323:336:373:388 SD: 0.3490 cents 224:233:259:269:280:311:323:359:373:388:431:448 SD: 0.3332 cents 233:242:269:280:291:323:336:373:388:404:448:466 SD: 0.3018 cents 253:263:292:304:316:351:365:405:421:438:487:506 SD: 0.2752 cents 269:280:311:323:336:373:388:431:448:466:517:538 SD: 0.2711 cents 273:284:315:328:341:379:394:437:455:473:525:546 SD: 0.2696 cents 298:310:344:358:372:413:430:477:496:516:573:596 SD: 0.2327 cents 328:341:379:394:410:455:473:525:546:568:631:656 SD: 0.2246 cents 329:342:380:395:411:456:475:527:548:570:633:658 SD: 0.2205 cents 344:358:397:413:430:477:496:551:573:596:662:688 SD: 0.2196 cents 349:363:403:419:436:484:503:559:581:605:671:698 SD: 0.2040 cents 373:388:431:448:466:517:538:597:621:646:717:746 SD: 0.2027 cents 377:392:435:453:471:523:544:604:628:653:725:754 SD: 0.1912 cents 422:439:487:507:527:585:609:676:703:731:812:844 SD: 0.1863 cents 427:444:493:513:533:592:616:684:711:740:821:854 SD: 0.1749 cents 452:470:522:543:565:627:652:724:753:783:869:904 SD: 0.1569 cents 497:517:574:597:621:689:717:796:828:861:956:994 SD: 0.1108 cents