Scala analysis: jubilee10sym2
A distributionally even scale in jubilee (50/49 planar) temperament, aabacaabac
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: 805.500 cents 805.500000 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: 102.9200 cents 102.9200 8: 71.8600 cents 71.8600 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: 10 599.66000 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: 2.77778 = 25/9
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 102.9 205.8 277.7 380.6 599.7 702.6 805.5 877.4 980.3 1199.3 102.9 : 102.9 174.8 277.7 496.7 599.7 702.6 774.4 877.4 1096.4 1199.3 205.8 : 71.9 174.8 393.8 496.7 599.7 671.5 774.4 993.5 1096.4 1199.3 277.7 : 102.9 322.0 424.9 527.8 599.7 702.6 921.6 1024.5 1127.5 1199.3 380.6 : 219.0 322.0 424.9 496.7 599.7 818.7 921.6 1024.5 1096.4 1199.3 599.7 : 102.9 205.8 277.7 380.6 599.7 702.6 805.5 877.4 980.3 1199.3 702.6 : 102.9 174.8 277.7 496.7 599.7 702.6 774.4 877.4 1096.4 1199.3 805.5 : 71.9 174.8 393.8 496.7 599.7 671.5 774.4 993.5 1096.4 1199.3 877.4 : 102.9 322.0 424.9 527.8 599.7 702.6 921.6 1024.5 1127.5 1199.3 980.3 : 219.0 322.0 424.9 496.7 599.7 818.7 921.6 1024.5 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: 599.6600 .. 599.6600 cents 1/1, 0.0000 cents 71.86000 cents 6: 671.5200 .. 818.7000 cents 147.18000 cents 71.86000 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 : 113.13522 cents, oct.: 1131.35221 cents Scale is not proper Scale has 2 repeating blocks of 5 notes Scale is 3-distributional even Step pattern alph. order: AABACAABAC Step pattern size order : MMSMLMMSML Scale is a Constant Structure, by a margin of 13.20000 cents Scale diversity : 1.329789 Lumma stability : 0.239669 Lumma impropriety factor : 0.221425 Rothenberg efficiency (ambiguous key): 0.330476 redundancy: 0.669524 Efficiency x scale size : 3.304762 Number of different interval sizes : 25 = 2.77778 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.77778 = 25/9 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 13.20000 cents Most common intervals : 599.66000 cents & inv., amount: 10 Number of recognisable fifths : 6, average 702.5800 cents Number of recognisable fourths : 6, average 496.7400 cents Scale contains two identical conjunct hexachords Formal octave complements present : 2 = 20.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 5 -- Rational properties --
FIT/MODE
10: 1 1 0 1 2 1 1 0 1 2 N B D3 SD: 25.7381 c. M: 37.8360 c. 12: 1 1 1 1 2 1 1 1 1 2 P B ME S SD: 13.4230 c. M:-22.1300 c. Messiaen mode 7 22: 2 2 1 2 4 2 2 1 2 4 N B D3 SD: 6.5400 c. M:-12.2182 c. 34: 3 3 2 3 6 3 3 2 3 6 N B D3 SD: 4.8373 c. M:-7.3953 c. 48: 4 4 3 4 9 4 4 3 4 9 N B D3 SD: 4.1588 c. M: 5.9533 c. 60: 5 5 4 5 11 5 5 4 5 11 N B D3 SD: 3.1492 c. M: 5.9533 c. 70: 6 6 4 6 13 6 6 4 6 13 N B D3 SD: 2.2995 c. M: 3.6909 c. 82: 7 7 5 7 15 7 7 5 7 15 N B D3 SD: 0.5675 c. M: 1.0780 c. 186: 16 16 11 16 34 16 16 11 16 34 N B D3 SD: 0.3268 c. M:-0.4946 c. 268: 23 23 16 23 49 23 23 16 23 49 N B D3 SD: 0.1532 c. M: 0.2454 c. 350: 30 30 21 30 64 30 30 21 30 64 N B D3 SD: 0.1809 c. M: 0.2642 c. 466: 40 40 28 40 85 40 40 28 40 85 N B D3 SD: 0.1710 c. M:-0.2799 c. 548: 47 47 33 47 100 47 47 33 47 100 N B D3 SD: 0.1494 c. M:-0.2446 c. 618: 53 53 37 53 113 53 53 37 53 113 N B D3 SD: 0.1554 c. M: 0.2531 c. 630: 54 54 38 54 115 54 54 38 54 115 N B D3 SD: 0.1694 c. M: 0.2423 c. 652: 56 56 39 56 119 56 56 39 56 119 N B D3 SD: 0.1132 c. M:-0.1782 c. 734: 63 63 44 63 134 63 63 44 63 134 N B D3 SD: 0.0550 c. M:-0.0906 c. 816: 70 70 49 70 149 70 70 49 70 149 N B D3 SD: 0.0567 c. M:-0.0837 c. 1002: 86 86 60 86 183 86 86 60 86 183 N B D3 SD: 0.0168 c. M:-0.0313 c. 1818: 156 156 109 156 332 156 156 109 156 332 N B D3 SD: 0.0187 c. M:-0.0303 c. 2086: 179 179 125 179 381 179 179 125 179 381 N B D3 SD: 0.0083 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: 11.3023 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: 13.6209 cents 8 x 9 x 10:11:12:13 x 14:16 S SD: 8.7273 cents 9 x 10 x 11:13 x 14:15:16:18 SD: 10.0657 cents 10 x 11:12 x 14:15:16:17:18:20 S SD: 10.1286 cents 11:12 x 13:14:16:17 x 18:19:22 SD: 12.8427 cents 12:13 x 14:15:17:18:19:20:21:24 SD: 4.5971 cents 13:14 x 15:16:18:20:21:22:23:26 SD: 9.2684 cents 14:15:16 x 17:20:21:22:23:25:28 SD: 7.5493 cents 15:16:17:18:19:21:23:24:25:26:30 SD: 7.1067 cents 16:17:18:19:20:23:24:25:27:28:32 SD: 5.7243 cents 17:18:19:20:21:24:26:27:28:30:34 SD: 4.1625 cents 20:21 x 23:25:28:30:32:33:35:40 SD: 5.2722 cents 22:23:25:26:27:31:33:35:37:39:44 SD: 4.8958 cents 24:25:27:28:30:34:36:38:40:42:48 SD: 3.8527 cents 29:31:33:34:36:41:44:46:48:51:58 SD: 3.1119 cents 32:34:36:38:40:45:48:51:53:56:64 SD: 2.5900 cents 34:36:38:40:42:48:51:54:56:60:68 SD: 2.5389 cents 45:48:51:53:56:64:68:72:75:79:90 SD: 2.5151 cents 46:49:52:54:57:65:69:73:76:81:92 SD: 1.6615 cents 62:66:70:73:77:88:93:99:103:109:124 SD: 1.3538 cents 64:68:72:75:80:90:96:102:106:113:128 SD: 1.3124 cents 79:84:89:93:98:112:119:126:131:139:158 SD: 1.3091 cents 80:85:90:94:100:113:120:127:133:141:160 SD: 0.9132 cents 102:108:115:120:127:144:153:162:169:180:204 SD: 0.9069 cents 110:117:124:129:137:156:165:175:183:194:220 SD: 0.8411 cents 114:121:128:134:142:161:171:182:189:201:228 SD: 0.8001 cents 118:125:133:139:147:167:177:188:196:208:236 SD: 0.7253 cents 126:134:142:148:157:178:189:201:209:222:252 SD: 0.5425 cents 150:159:169:176:187:212:225:239:249:264:300 SD: 0.3391 cents 260:276:293:305:324:368:390:414:432:458:520 SD: 0.3162 cents 276:293:311:324:344:390:414:440:458:486:552 SD: 0.2829 cents 277:294:312:325:345:392:416:441:460:488:554 SD: 0.2653 cents 292:310:329:343:364:413:438:465:485:514:584 SD: 0.2606 cents 294:312:331:345:366:416:441:468:488:518:588 SD: 0.2423 cents 309:328:348:363:385:437:464:492:513:544:618 SD: 0.2210 cents 326:346:367:383:406:461:489:519:541:574:652 SD: 0.2177 cents 374:397:421:439:466:529:561:596:621:659:748 SD: 0.2058 cents 403:428:454:473:502:570:605:642:669:710:806 SD: 0.2005 cents 420:446:473:493:523:594:630:669:697:740:840 SD: 0.1884 cents 427:453:481:501:532:604:641:680:709:752:854 SD: 0.1860 cents 444:471:500:521:553:628:666:707:737:782:888 SD: 0.1700 cents 459:487:517:539:572:649:689:731:762:809:918 SD: 0.1511 cents 553:587:623:649:689:782:830:881:918:974:1106 SD: 0.1433 cents 570:605:642:669:710:806:855:908:946:1004:1140 SD: 0.1327 cents