Scala analysis: jubilee10asym4
A distributionally even scale in jubilee (50/49 planar) temperament, aabaacabac
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 102.920 cents 102.920000 2: 205.840 cents 205.840000 3: 277.700 cents 277.700000 4: 380.620 cents 380.620000 5: 599.660 cents 599.660000 6: 702.580 cents 702.580000 7: 774.440 cents 774.440000 8: 877.360 cents 877.360000 9: 980.280 cents 980.280000 10: 1199.320 cents 1199.320000
SHOW/INTERVAL
0: 219.0400 cents 219.0400 1: 102.9200 cents 102.9200 2: 102.9200 cents 102.9200 3: 71.8600 cents 71.8600 4: 102.9200 cents 102.9200 5: 219.0400 cents 219.0400 6: 102.9200 cents 102.9200 7: 71.8600 cents 71.8600 8: 102.9200 cents 102.9200 9: 102.9200 cents 102.9200 10: 219.0400 cents 219.0400
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 71.86000 cents 1: 6 102.92000 cents 1: 2 219.04000 cents 2: 4 174.78000 cents 2: 2 205.84000 cents 2: 4 321.96000 cents 3: 4 277.70000 cents 3: 2 393.82000 cents 3: 4 424.88000 cents 4: 2 380.62000 cents 4: 6 496.74000 cents 4: 2 527.80000 cents 5: 1 568.60000 cents 5: 8 599.66000 cents 5: 1 630.72000 cents 6: 2 671.52000 cents 6: 6 702.58000 cents 6: 2 818.70000 cents 7: 4 774.44000 cents 7: 2 805.50000 cents 7: 4 921.62000 cents 8: 4 877.36000 cents 8: 2 993.48000 cents 8: 4 1024.54000 cents 9: 2 980.28000 cents 9: 6 1096.40000 cents 9: 2 1127.46000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 102.9 205.8 277.7 380.6 599.7 702.6 774.4 877.4 980.3 1199.3 102.9 : 102.9 174.8 277.7 496.7 599.7 671.5 774.4 877.4 1096.4 1199.3 205.8 : 71.9 174.8 393.8 496.7 568.6 671.5 774.4 993.5 1096.4 1199.3 277.7 : 102.9 322.0 424.9 496.7 599.7 702.6 921.6 1024.5 1127.5 1199.3 380.6 : 219.0 322.0 393.8 496.7 599.7 818.7 921.6 1024.5 1096.4 1199.3 599.7 : 102.9 174.8 277.7 380.6 599.7 702.6 805.5 877.4 980.3 1199.3 702.6 : 71.9 174.8 277.7 496.7 599.7 702.6 774.4 877.4 1096.4 1199.3 774.4 : 102.9 205.8 424.9 527.8 630.7 702.6 805.5 1024.5 1127.5 1199.3 877.4 : 102.9 322.0 424.9 527.8 599.7 702.6 921.6 1024.5 1096.4 1199.3 980.3 : 219.0 322.0 424.9 496.7 599.7 818.7 921.6 993.5 1096.4 1199.3 1199.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.8600 .. 219.0400 cents 147.18000 cents 71.86000 cents 2: 174.7800 .. 321.9600 cents 147.18000 cents -44.26000 cents 3: 277.7000 .. 424.8800 cents 147.18000 cents -44.26000 cents 4: 380.6200 .. 527.8000 cents 147.18000 cents -44.26000 cents 5: 568.6000 .. 630.7200 cents 62.12000 cents 40.80000 cents 6: 671.5200 .. 818.7000 cents 147.18000 cents 40.80000 cents 7: 774.4400 .. 921.6200 cents 147.18000 cents -44.26000 cents 8: 877.3600 .. 1024.5400 cents 147.18000 cents -44.26000 cents 9: 980.2800 .. 1127.4600 cents 147.18000 cents -44.26000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 71.86000 cents, class 1 Average step (divided formal octave): 119.9320 cents Largest one step interval : 219.04000 cents Average / Smallest step : 1.668967 Largest / Average step : 1.826368 Largest / Smallest step : 3.048149 Median interval of one step : 102.92000 cents, amount: 6 Most common interval of one step : 102.92000 cents, amount: 6 Least squares average step : 112.57049 cents, oct.: 1125.70494 cents Scale is not proper Scale has trivalence property Step pattern alph. order: AABACABAAC Step pattern size order : MMSMLMSMML Scale is a Constant Structure, by a margin of 13.20000 cents Scale diversity : 1.363792 Lumma stability : 0.187873 Lumma impropriety factor : 0.221425 Rothenberg efficiency : 0.478413 redundancy: 0.521587 Efficiency x scale size : 4.784127 Number of different interval sizes : 27 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 13.20000 cents Most common intervals : 599.66000 cents & inv., amount: 8 Number of recognisable fifths : 6, average 702.5800 cents Number of recognisable fourths : 6, average 496.7400 cents Formal octave complements present : 2 = 20.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 9 Inversional symmetry on intervals : 4-5 9-10 -- Rational properties --
FIT/MODE
10: 1 1 0 1 2 1 0 1 1 2 N T3 SD: 29.1121 c. M: 54.8480 c. 11: 1 1 1 0 3 0 1 1 1 2 N SD: 33.1057 c. M:-54.5145 c. 12: 1 1 1 1 2 1 1 1 1 2 P B ME S SD: 15.4812 c. M:-25.1067 c. Messiaen mode 7 22: 2 2 1 2 4 2 1 2 2 4 N T3 SD: 6.3615 c. M:-12.2182 c. 34: 3 3 2 3 6 3 2 3 3 6 N T3 SD: 4.5036 c. M:-7.3953 c. 48: 4 4 3 4 9 4 3 4 4 9 N T3 SD: 3.7084 c. M: 5.9533 c. 60: 5 5 4 5 11 5 4 5 5 11 N T3 SD: 2.9987 c. M: 5.9533 c. 70: 6 6 4 6 13 6 4 6 6 13 N T3 SD: 2.5438 c. M: 3.6909 c. 82: 7 7 5 7 15 7 5 7 7 15 N T3 SD: 0.5091 c. M: 1.0780 c. 186: 16 16 11 16 34 16 11 16 16 34 N T3 SD: 0.3595 c. M: 0.6852 c. 268: 23 23 16 23 49 23 16 23 23 49 N T3 SD: 0.1727 c. M: 0.2521 c. 350: 30 30 21 30 64 30 21 30 30 64 N T3 SD: 0.1640 c. M: 0.2642 c. 618: 53 53 37 53 113 53 37 53 53 113 N T3 SD: 0.1546 c. M: 0.2531 c. 652: 56 56 39 56 119 56 39 56 56 119 N T3 SD: 0.0988 c. M:-0.1782 c. 734: 63 63 44 63 134 63 44 63 63 134 N T3 SD: 0.0562 c. M:-0.0906 c. 1002: 86 86 60 86 183 86 60 86 86 183 N T3 SD: 0.0163 c. M:-0.0313 c. 2086: 179 179 125 179 381 179 125 179 179 381 N T3 SD: 0.0073 c. M: 0.0123 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.6800 cents 2 x x x x x 3 x x x 4 S SD: 0.4618 cents 3 x x x x 4 x x 5 x 6 S SD: 33.9527 cents 4 x x x 5 x 6 x x 7:8 S SD: 3.2061 cents 5 x x 6 x 7 x 8 x 9:10 S SD: 13.6628 cents 6 x x 7 x 8:9 x 10:11:12 S SD: 20.5920 cents 7 x 8 x 9:10 x 11 x 12:14 S SD: 13.1387 cents 8 x 9 x 10:11:12 x 13:14:16 S SD: 8.8776 cents 9 x 10 x 11:13 x 14:15:16:18 SD: 8.3401 cents 10 x 11:12 x 14:15:16:17:18:20 S SD: 11.2075 cents 11:12 x 13:14:16 x 17:18:19:22 SD: 11.4440 cents 12:13 x 14:15:17:18:19:20:21:24 SD: 5.0418 cents 13:14 x 15:16:18 x 20:22:23:26 SD: 9.0999 cents 14:15:16 x 17:20:21:22:23:25:28 SD: 7.1594 cents 15:16:17:18:19:21 x 23:25:26:30 SD: 7.6728 cents 16:17:18:19:20:23:24:25:27:28:32 SD: 4.6899 cents 20:21 x 23:25:28:30:31:33:35:40 SD: 5.4790 cents 21:22:24:25:26:30:32:33:35:37:42 SD: 5.4644 cents 22:23:25:26:27:31:33:34:37:39:44 SD: 5.3168 cents 24:25:27:28:30:34:36:38:40:42:48 SD: 4.2796 cents 28:30:32:33:35:40:42:44:46:49:56 SD: 4.2759 cents 29:31:33:34:36:41:44:45:48:51:58 SD: 3.3352 cents 30:32:34:35:37:42:45:47:50:53:60 SD: 3.1570 cents 32:34:36:38:40:45:48:50:53:56:64 SD: 2.5925 cents 34:36:38:40:42:48:51:53:56:60:68 SD: 2.5656 cents 45:48:51:53:56:64:68:70:75:79:90 SD: 2.5618 cents 46:49:52:54:57:65:69:72:76:81:92 SD: 1.5546 cents 62:66:70:73:77:88:93:97:103:109:124 SD: 1.2706 cents 80:85:90:94:100:113:120:125:133:141:160 SD: 0.7590 cents 114:121:128:134:142:161:171:178:189:201:228 SD: 0.7346 cents 126:134:142:148:157:178:189:197:209:222:252 SD: 0.4559 cents 150:159:169:176:187:212:225:235:249:264:300 SD: 0.4290 cents 200:212:225:235:249:283:300:313:332:352:400 SD: 0.4203 cents 212:225:239:249:264:300:318:332:352:373:424 SD: 0.4043 cents 229:243:258:269:285:324:344:358:380:403:458 SD: 0.3807 cents 230:244:259:270:287:325:345:360:382:405:460 SD: 0.3550 cents 247:262:278:290:308:349:371:386:410:435:494 SD: 0.3417 cents 264:280:297:310:329:373:396:413:438:465:528 SD: 0.2938 cents 276:293:311:324:344:390:414:432:458:486:552 SD: 0.2412 cents 294:312:331:345:366:416:441:460:488:518:588 SD: 0.2391 cents 326:346:367:383:406:461:489:510:541:574:652 SD: 0.2149 cents 362:384:408:425:451:512:543:566:601:638:724 SD: 0.2118 cents 374:397:421:439:466:529:561:585:621:659:748 SD: 0.1651 cents 459:487:517:539:572:649:689:718:762:809:918 SD: 0.1510 cents 541:574:609:635:674:765:812:846:898:953:1082 SD: 0.1375 cents 553:587:623:649:689:782:830:865:918:974:1106 SD: 0.1231 cents