Scala analysis: jubilee10sym1
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: 380.630 cents 380.630000 4: 483.550 cents 483.550000 5: 599.670 cents 599.670000 6: 702.590 cents 702.590000 7: 805.510 cents 805.510000 8: 980.300 cents 980.300000 9: 1083.220 cents 1083.220000 10: 1199.340 cents 1199.340000
SHOW/INTERVAL
0: 116.1200 cents 116.1200 1: 102.9200 cents 102.9200 2: 102.9200 cents 102.9200 3: 174.7900 cents 174.7900 4: 102.9200 cents 102.9200 5: 116.1200 cents 116.1200 6: 102.9200 cents 102.9200 7: 102.9200 cents 102.9200 8: 174.7900 cents 174.7900 9: 102.9200 cents 102.9200 10: 116.1200 cents 116.1200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 102.92000 cents 1: 2 116.12000 cents 1: 2 174.79000 cents 2: 2 205.84000 cents 2: 4 219.04000 cents 2: 4 277.71000 cents 3: 4 321.96000 cents 3: 4 380.63000 cents 3: 2 393.83000 cents 4: 2 424.88000 cents 4: 2 483.55000 cents 4: 6 496.75000 cents 5: 10 599.67000 cents 6: 6 702.59000 cents 6: 2 715.79000 cents 6: 2 774.46000 cents 7: 2 805.51000 cents 7: 4 818.71000 cents 7: 4 877.38000 cents 8: 4 921.63000 cents 8: 4 980.30000 cents 8: 2 993.50000 cents 9: 2 1024.55000 cents 9: 2 1083.22000 cents 9: 6 1096.42000 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 : 102.9 205.8 380.6 483.6 599.7 702.6 805.5 980.3 1083.2 1199.3 102.9 : 102.9 277.7 380.6 496.7 599.7 702.6 877.4 980.3 1096.4 1199.3 205.8 : 174.8 277.7 393.8 496.7 599.7 774.5 877.4 993.5 1096.4 1199.3 380.6 : 102.9 219.0 322.0 424.9 599.7 702.6 818.7 921.6 1024.5 1199.3 483.6 : 116.1 219.0 322.0 496.7 599.7 715.8 818.7 921.6 1096.4 1199.3 599.7 : 102.9 205.8 380.6 483.6 599.7 702.6 805.5 980.3 1083.2 1199.3 702.6 : 102.9 277.7 380.6 496.7 599.7 702.6 877.4 980.3 1096.4 1199.3 805.5 : 174.8 277.7 393.8 496.8 599.7 774.5 877.4 993.5 1096.4 1199.3 980.3 : 102.9 219.0 322.0 424.9 599.7 702.6 818.7 921.6 1024.5 1199.3 1083.2: 116.1 219.0 322.0 496.7 599.7 715.8 818.7 921.6 1096.4 1199.3 1199.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 102.9200 .. 174.7900 cents 71.87000 cents 102.92000 cents 2: 205.8400 .. 277.7100 cents 71.87000 cents 31.05000 cents 3: 321.9600 .. 393.8300 cents 71.87000 cents 44.25000 cents 4: 424.8800 .. 496.7500 cents 71.87000 cents 31.05000 cents 5: 599.6700 .. 599.6700 cents 1/1, 0.0000 cents 102.92000 cents 6: 702.5900 .. 774.4600 cents 71.87000 cents 102.92000 cents 7: 805.5100 .. 877.3800 cents 71.87000 cents 31.05000 cents 8: 921.6300 .. 993.5000 cents 71.87000 cents 44.25000 cents 9: 1024.5500 .. 1096.4200 cents 71.87000 cents 31.05000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 102.92000 cents, class 1 Average step (divided formal octave): 119.9340 cents Largest one step interval : 174.79000 cents Average / Smallest step : 1.165313 Largest / Average step : 1.457385 Largest / Smallest step : 1.698309 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 : 119.55306 cents, oct.: 1195.53065 cents Scale is strictly proper Scale has 2 repeating blocks of 5 notes Scale is 3-distributional even Step pattern alph. order: AABACAABAC Step pattern size order : SSLSMSSLSM Scale is a Constant Structure, by a margin of 31.05000 cents Scale diversity : 1.260595 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.520603 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 : 599.67000 cents & inv., amount: 10 Number of recognisable fifths : 8, average 705.8900 cents Number of appreciable fifths : 6, average 702.5900 cents Number of recognisable fourths : 8, average 493.4500 cents Number of appreciable fourths : 6, average 496.7500 cents Scale contains two identical disjunct pentachords Formal octave complements present : 2 = 20.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 5 Limited inverse transpositions with margin 71.8700 cents: 5 -- Rational properties --
FIT/MODE
10: 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 19.4717 c. M:-34.0280 c. 12: 1 1 2 1 1 1 1 2 1 1 P B ME I SD: 11.5983 c. M:-19.1500 c. Symmetrical Decatonic 22: 2 2 3 2 2 2 2 3 2 2 SP B ME I SD: 6.8982 c. M:-12.2218 c. Static Symmetrical Major 34: 3 3 5 3 3 3 3 5 3 3 SP B DE I SD: 6.3689 c. M:-10.2959 c. 48: 4 4 7 4 5 4 4 7 4 5 SP B D3 SD: 5.5849 c. M: 8.8113 c. 54: 5 4 8 5 5 5 4 8 5 5 SP B SD: 5.2262 c. M:-8.1300 c. 58: 5 5 8 5 6 5 5 8 5 6 SP B D3 SD: 5.2004 c. M: 8.4210 c. 60: 5 5 9 5 6 5 5 9 5 6 SP B D3 SD: 3.4497 c. M: 5.9500 c. 70: 6 6 10 6 7 6 6 10 6 7 SP B D3 SD: 2.3777 c. M: 3.8140 c. 82: 7 7 12 7 8 7 7 12 7 8 SP B D3 SD: 0.6866 c. M: 1.0746 c. 186: 16 16 27 16 18 16 16 27 16 18 SP B D3 SD: 0.2649 c. M:-0.4981 c. 268: 23 23 39 23 26 23 23 39 23 26 SP B D3 SD: 0.1508 c. M: 0.2423 c. 454: 39 39 66 39 44 39 39 66 39 44 SP B D3 SD: 0.1550 c. M: 0.2226 c. 548: 47 47 80 47 53 47 47 80 47 53 SP B D3 SD: 0.1142 c. M:-0.1823 c. 734: 63 63 107 63 71 63 63 107 63 71 SP B D3 SD: 0.0652 c. M:-0.1075 c. 816: 70 70 119 70 79 70 70 119 70 79 SP B D3 SD: 0.0404 c. M: 0.0709 c. 1002: 86 86 146 86 97 86 86 146 86 97 SP B D3 SD: 0.0188 c. M:-0.0347 c. 1818: 156 156 265 156 176 156 156 265 156 176 SP B D3 SD: 0.0118 c. M:-0.0186 c. 2086: 179 179 304 179 202 179 179 304 179 202 SP B D3 SD: 0.0118 c. M: 0.0193 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.6600 cents 2 x x x x x 3 x x x 4 S SD: 0.4579 cents 3 x x x 4 x x 5 x x 6 S SD: 26.7242 cents 4 x x 5 x x 6 x 7 x 8 S SD: 3.2093 cents 5 x x 6 x 7 x 8:9 x 10 S SD: 15.4612 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 17.7162 cents 7 x 8 x 9:10 x 11:12:13:14 S SD: 11.2452 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 7.6630 cents 9 x 10:11:12:13 x 14:16:17:18 S SD: 9.2226 cents 10 x 11:12:13:14:15:16:18:19:20 S SD: 10.7080 cents 11:12 x 14:15:16:17:18:19:21:22 SD: 14.1380 cents 12:13:14:15:16:17:18:19:21:22:24 SD: 8.1408 cents 14:15:16:17:19:20:21:22:25:26:28 SD: 8.0409 cents 15:16:17:19:20:21:23:24:26:28:30 SD: 6.1475 cents 16:17:18:20:21:23:24:25:28:30:32 SD: 4.7547 cents 22:23:25:27:29:31:33:35:39:41:44 SD: 4.2531 cents 24:25:27:30:32:34:36:38:42:45:48 SD: 3.9423 cents 29:31:33:36:38:41:44:46:51:54:58 SD: 3.5071 cents 30:32:34:37:40:42:45:48:53:56:60 SD: 3.3273 cents 31:33:35:39:41:44:47:49:55:58:62 SD: 3.1821 cents 32:34:36:40:42:45:48:51:56:60:64 SD: 2.1270 cents 46:49:52:57:61:65:69:73:81:86:92 SD: 1.5364 cents 62:66:70:77:82:88:93:99:109:116:124 SD: 1.2560 cents 78:83:88:97:103:110:117:124:137:146:156 SD: 1.0330 cents 94:100:106:117:124:133:141:150:166:176:188 SD: 0.8998 cents 96:102:108:120:127:136:144:153:169:179:192 SD: 0.8802 cents 102:108:115:127:135:144:153:162:180:191:204 SD: 0.8323 cents 114:121:128:142:151:161:171:182:201:213:228 SD: 0.8078 cents 118:125:133:147:156:167:177:188:208:221:236 SD: 0.5152 cents 150:159:169:187:198:212:225:239:264:280:300 SD: 0.5110 cents 164:174:185:204:217:232:246:261:289:307:328 SD: 0.5010 cents 167:177:188:208:221:236:251:266:294:312:334 SD: 0.4498 cents 184:195:207:229:243:260:276:293:324:344:368 SD: 0.4446 cents 196:208:221:244:259:277:294:312:345:366:392 SD: 0.3884 cents 198:210:223:247:262:280:297:315:349:370:396 SD: 0.3600 cents 230:244:259:287:304:325:345:366:405:430:460 SD: 0.3491 cents 244:259:275:304:323:345:366:389:430:456:488 SD: 0.3354 cents 260:276:293:324:344:368:390:414:458:486:520 SD: 0.2594 cents 292:310:329:364:386:413:438:465:514:546:584 SD: 0.2223 cents 326:346:367:406:431:461:489:519:574:609:652 SD: 0.2187 cents 394:418:444:491:521:557:591:627:694:737:788 SD: 0.2179 cents 406:431:457:506:537:574:609:647:715:759:812 SD: 0.2143 cents 420:446:473:523:555:594:630:669:740:785:840 SD: 0.2131 cents 427:453:481:532:565:604:641:680:752:798:854 SD: 0.2041 cents 428:454:482:533:566:605:642:682:754:800:856 SD: 0.1945 cents 444:471:500:553:587:628:666:707:782:830:888 SD: 0.1504 cents 459:487:517:572:607:649:689:731:809:858:918 SD: 0.1449 cents 491:521:553:612:649:694:737:782:865:918:982 SD: 0.1446 cents 537:570:605:669:710:759:806:855:946:1004:1074 SD: 0.1275 cents