Scala analysis: jubilee10asym2
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: 380.630 cents 380.630000 4: 483.550 cents 483.550000 5: 599.670 cents 599.670000 6: 702.590 cents 702.590000 7: 877.380 cents 877.380000 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: 174.7900 cents 174.7900 8: 102.9200 cents 102.9200 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: 1 527.80000 cents 5: 8 599.67000 cents 5: 1 671.54000 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: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 0.0 : 102.9 205.8 380.6 483.6 599.7 702.6 877.4 980.3 1083.2 1199.3 102.9 : 102.9 277.7 380.6 496.7 599.7 774.5 877.4 980.3 1096.4 1199.3 205.8 : 174.8 277.7 393.8 496.7 671.5 774.5 877.4 993.5 1096.4 1199.3 380.6 : 102.9 219.0 322.0 496.7 599.7 702.6 818.7 921.6 1024.5 1199.3 483.6 : 116.1 219.0 393.8 496.7 599.7 715.8 818.7 921.6 1096.4 1199.3 599.7 : 102.9 277.7 380.6 483.6 599.7 702.6 805.5 980.3 1083.2 1199.3 702.6 : 174.8 277.7 380.6 496.7 599.7 702.6 877.4 980.3 1096.4 1199.3 877.4 : 102.9 205.8 322.0 424.9 527.8 702.6 805.5 921.6 1024.5 1199.3 980.3 : 102.9 219.0 322.0 424.9 599.7 702.6 818.7 921.6 1096.4 1199.3 1083.2: 116.1 219.0 322.0 496.7 599.7 715.8 818.7 993.5 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: 527.8000 .. 671.5400 cents 143.74000 cents 31.05000 cents 6: 702.5900 .. 774.4600 cents 71.87000 cents 31.05000 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 : 120.85979 cents, oct.: 1208.59792 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABACABAAC Step pattern size order : SSLSMSLSSM Scale is a Constant Structure, by a margin of 31.05000 cents Scale diversity : 1.312710 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.400754 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 : 599.67000 cents & inv., amount: 8 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 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 1 1 1 1 1 1 1 1 SP B ME I SD: 20.1633 c. M: 37.8420 c. 12: 1 1 2 1 1 1 2 1 1 1 P D3 SD: 13.4139 c. M:-22.1250 c. 22: 2 2 3 2 2 2 3 2 2 2 SP D3 SD: 5.9399 c. M:-12.2218 c. Standard Pentachordal Major 34: 3 3 5 3 3 3 5 3 3 3 SP D3 SD: 6.2612 c. M:-10.2959 c. 48: 4 4 7 4 5 4 7 4 4 5 SP T3 SD: 5.3356 c. M: 8.8113 c. 60: 5 5 9 5 6 5 9 5 5 6 SP T3 SD: 2.9693 c. M: 5.9500 c. 70: 6 6 10 6 7 6 10 6 6 7 SP T3 SD: 2.6317 c. M: 3.8140 c. 82: 7 7 12 7 8 7 12 7 7 8 SP T3 SD: 0.5995 c. M: 1.0746 c. 186: 16 16 27 16 18 16 27 16 16 18 SP T3 SD: 0.2549 c. M:-0.4981 c. 268: 23 23 39 23 26 23 39 23 23 26 SP T3 SD: 0.1703 c. M: 0.2507 c. 548: 47 47 80 47 53 47 80 47 47 53 SP T3 SD: 0.1321 c. M:-0.2392 c. 630: 54 54 92 54 61 54 92 54 54 61 SP T3 SD: 0.1285 c. M: 0.2389 c. 652: 56 56 95 56 63 56 95 56 56 63 SP T3 SD: 0.1417 c. M:-0.2329 c. 734: 63 63 107 63 71 63 107 63 63 71 SP T3 SD: 0.0672 c. M:-0.1075 c. 816: 70 70 119 70 79 70 119 70 70 79 SP T3 SD: 0.0418 c. M:-0.0783 c. 1002: 86 86 146 86 97 86 146 86 86 97 SP T3 SD: 0.0164 c. M:-0.0347 c. 1818: 156 156 265 156 176 156 265 156 156 176 SP T3 SD: 0.0136 c. M:-0.0250 c. 2086: 179 179 304 179 202 179 304 179 179 202 SP T3 SD: 0.0119 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: 5.3670 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: 19.9662 cents 6 x 7 x 8 x 9:10 x 11:12 S SD: 11.9382 cents 7 x 8 x 9:10:11 x 12:13:14 S SD: 15.6823 cents 8 x 9:10 x 11:12:13:14:15:16 S SD: 7.7963 cents 9 x 10:11:12:13:14:15:16:17:18 S SD: 9.7683 cents 10 x 11:12:13:14:15:17:18:19:20 SD: 11.6127 cents 11:12 x 14:15:16:17:18:19:21:22 SD: 13.4202 cents 12:13:14:15:16:17:18:20:21:22:24 S SD: 8.1098 cents 14:15:16:17:19:20:21:23:25:26:28 SD: 7.9103 cents 15:16:17:19:20:21:23:25:26:28:30 SD: 6.1327 cents 16:17:18:20:21:23:24:27:28:30:32 SD: 4.4618 cents 24:25:27:30:32:34:36:40:42:45:48 SD: 3.8779 cents 29:31:33:36:38:41:44:48:51:54:58 SD: 3.4765 cents 30:32:34:37:40:42:45:50:53:56:60 SD: 3.2999 cents 31:33:35:39:41:44:47:51:55:58:62 SD: 3.2966 cents 32:34:36:40:42:45:48:53:56:60:64 SD: 2.1574 cents 46:49:52:57:61:65:69:76:81:86:92 SD: 1.6321 cents 62:66:70:77:82:88:93:103:109:116:124 SD: 1.1737 cents 80:85:90:100:106:113:120:133:141:150:160 SD: 0.9518 cents 94:100:106:117:124:133:141:156:166:176:188 SD: 0.8271 cents 102:108:115:127:135:144:153:169:180:191:204 SD: 0.7653 cents 114:121:128:142:151:161:171:189:201:213:228 SD: 0.7125 cents 118:125:133:147:156:167:177:196:208:221:236 SD: 0.5203 cents 150:159:169:187:198:212:225:249:264:280:300 SD: 0.5022 cents 167:177:188:208:221:236:251:277:294:312:334 SD: 0.4676 cents 176:187:198:219:233:249:264:292:310:329:352 SD: 0.4492 cents 183:194:206:228:242:259:275:304:322:342:366 SD: 0.4480 cents 196:208:221:244:259:277:294:325:345:366:392 SD: 0.4260 cents 198:210:223:247:262:280:297:329:349:370:396 SD: 0.3617 cents 215:228:242:268:284:304:323:357:379:402:430 SD: 0.3536 cents 230:244:259:287:304:325:345:382:405:430:460 SD: 0.3391 cents 244:259:275:304:323:345:366:405:430:456:488 SD: 0.2727 cents 261:277:294:325:345:369:392:433:460:488:522 SD: 0.2424 cents 276:293:311:344:365:390:414:458:486:516:552 SD: 0.2128 cents 391:415:440:487:517:553:587:649:689:731:782 SD: 0.2004 cents 394:418:444:491:521:557:591:654:694:737:788 SD: 0.1829 cents 406:431:457:506:537:574:609:674:715:759:812 SD: 0.1758 cents 444:471:500:553:587:628:666:737:782:830:888 SD: 0.1499 cents 459:487:517:572:607:649:689:762:809:858:918 SD: 0.1453 cents 491:521:553:612:649:694:737:815:865:918:982 SD: 0.1431 cents 553:587:623:689:731:782:830:918:974:1034:1106 SD: 0.1185 cents