Scala analysis: jubilee12sym
A distributionally even scale in jubilee (50/49 planar) temperament, aabaacaabaac
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: 483.540 cents 483.540000 6: 599.660 cents 599.660000 7: 702.580 cents 702.580000 8: 805.500 cents 805.500000 9: 877.360 cents 877.360000 10: 980.280 cents 980.280000 11: 1083.200 cents 1083.200000 12: 1199.320 cents 1199.320000
SHOW/INTERVAL
0: 116.1200 cents 116.1200 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: 102.9200 cents 102.9200 6: 116.1200 cents 116.1200 7: 102.9200 cents 102.9200 8: 102.9200 cents 102.9200 9: 71.8600 cents 71.8600 10: 102.9200 cents 102.9200 11: 102.9200 cents 102.9200 12: 116.1200 cents 116.1200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 71.86000 cents 1: 8 102.92000 cents 1: 2 116.12000 cents 2: 4 174.78000 cents 2: 4 205.84000 cents 2: 4 219.04000 cents 3: 6 277.70000 cents 3: 6 321.96000 cents 4: 4 380.62000 cents 4: 4 393.82000 cents 4: 4 424.88000 cents 5: 2 483.54000 cents 5: 8 496.74000 cents 5: 2 527.80000 cents 6: 12 599.66000 cents 7: 2 671.52000 cents 7: 8 702.58000 cents 7: 2 715.78000 cents 8: 4 774.44000 cents 8: 4 805.50000 cents 8: 4 818.70000 cents 9: 6 877.36000 cents 9: 6 921.62000 cents 10: 4 980.28000 cents 10: 4 993.48000 cents 10: 4 1024.54000 cents 11: 2 1083.20000 cents 11: 8 1096.40000 cents 11: 2 1127.46000 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 2.63636 = 29/11
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 102.9 205.8 277.7 380.6 483.5 599.7 702.6 805.5 877.4 980.3 1083.2 1199.3 102.9 : 102.9 174.8 277.7 380.6 496.7 599.7 702.6 774.4 877.4 980.3 1096.4 1199.3 205.8 : 71.9 174.8 277.7 393.8 496.7 599.7 671.5 774.4 877.4 993.5 1096.4 1199.3 277.7 : 102.9 205.8 322.0 424.9 527.8 599.7 702.6 805.5 921.6 1024.5 1127.5 1199.3 380.6 : 102.9 219.0 322.0 424.9 496.7 599.7 702.6 818.7 921.6 1024.5 1096.4 1199.3 483.5 : 116.1 219.0 322.0 393.8 496.7 599.7 715.8 818.7 921.6 993.5 1096.4 1199.3 599.7 : 102.9 205.8 277.7 380.6 483.5 599.7 702.6 805.5 877.4 980.3 1083.2 1199.3 702.6 : 102.9 174.8 277.7 380.6 496.7 599.7 702.6 774.4 877.4 980.3 1096.4 1199.3 805.5 : 71.9 174.8 277.7 393.8 496.7 599.7 671.5 774.4 877.4 993.5 1096.4 1199.3 877.4 : 102.9 205.8 322.0 424.9 527.8 599.7 702.6 805.5 921.6 1024.5 1127.5 1199.3 980.3 : 102.9 219.0 322.0 424.9 496.7 599.7 702.6 818.7 921.6 1024.5 1096.4 1199.3 1083.2: 116.1 219.0 322.0 393.8 496.7 599.7 715.8 818.7 921.6 993.5 1096.4 1199.3 1199.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 71.8600 .. 116.1200 cents 44.26000 cents 71.86000 cents 2: 174.7800 .. 219.0400 cents 44.26000 cents 58.66000 cents 3: 277.7000 .. 321.9600 cents 44.26000 cents 58.66000 cents 4: 380.6200 .. 424.8800 cents 44.26000 cents 58.66000 cents 5: 483.5400 .. 527.8000 cents 44.26000 cents 58.66000 cents 6: 599.6600 .. 599.6600 cents 1/1, 0.0000 cents 71.86000 cents 7: 671.5200 .. 715.7800 cents 44.26000 cents 71.86000 cents 8: 774.4400 .. 818.7000 cents 44.26000 cents 58.66000 cents 9: 877.3600 .. 921.6200 cents 44.26000 cents 58.66000 cents 10: 980.2800 .. 1024.5400 cents 44.26000 cents 58.66000 cents 11: 1083.2000 .. 1127.4600 cents 44.26000 cents 58.66000 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 71.86000 cents, class 1 Average step (divided formal octave): 99.9433 cents Largest one step interval : 116.12000 cents Average / Smallest step : 1.390806 Largest / Average step : 1.161858 Largest / Smallest step : 1.615920 Median interval of one step : 102.92000 cents, amount: 8 Most common interval of one step : 102.92000 cents, amount: 8 Least squares average step : 98.85228 cents, oct.: 1186.22732 cents Scale is strictly proper Scale has 2 repeating blocks of 6 notes Scale is 3-distributional even Step pattern alph. order: AABAACAABAAC Step pattern size order : MMSMMLMMSMML Scale is a Constant Structure, by a margin of 58.66000 cents Scale diversity : 1.271072 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.630958 Rothenberg efficiency (ambiguous key): 0.337975 redundancy: 0.662025 Efficiency x scale size : 4.055700 Number of different interval sizes : 29 = 2.63636 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 2.63636 = 29/11 Median interval variety : 3 Lowest interval variety : 1 Smallest interval difference : 13.20000 cents Most common intervals : 599.66000 cents & inv., amount: 12 Number of recognisable fifths : 10, average 705.2200 cents Number of appreciable fifths : 8, average 702.5800 cents Number of recognisable fourths : 10, average 494.1000 cents Number of appreciable fourths : 8, average 496.7400 cents Scale contains two identical disjunct hexachords Best fifths form a closed circle Formal octave complements present : 2 = 16.6667% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 6 Limited inverse transpositions : 5 11 Inversional symmetry on intervals : 2-3 5-6 8-9 11-12 -- Rational properties --
FIT/MODE
12: 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 13.9199 c. M:-22.1300 c. Twelve-tone Chromatic (1/11-comma) 22: 2 2 1 2 2 2 2 2 1 2 2 2 SP B ME SD: 6.6350 c. M:-12.2182 c. Jubilee-12 34: 3 3 2 3 3 3 3 3 2 3 3 3 SP B ME SD: 6.0969 c. M:-10.2976 c. Jubilee-12 48: 4 4 3 4 4 5 4 4 3 4 4 5 SP B D3 SD: 5.2294 c. M: 8.8092 c. 60: 5 5 4 5 5 6 5 5 4 5 5 6 SP B D3 SD: 3.2690 c. M: 5.9533 c. 70: 6 6 4 6 6 7 6 6 4 6 6 7 SP B D3 SD: 2.6131 c. M: 3.8120 c. 82: 7 7 5 7 7 8 7 7 5 7 7 8 SP B D3 SD: 0.6320 c. M: 1.0780 c. 186: 16 16 11 16 16 18 16 16 11 16 16 18 SP B D3 SD: 0.2992 c. M:-0.4946 c. 268: 23 23 16 23 23 26 23 23 16 23 23 26 SP B D3 SD: 0.1689 c. M: 0.2454 c. 548: 47 47 33 47 47 53 47 47 33 47 47 53 SP B D3 SD: 0.1460 c. M:-0.2446 c. 630: 54 54 38 54 54 61 54 54 38 54 54 61 SP B D3 SD: 0.1546 c. M: 0.2423 c. 652: 56 56 39 56 56 63 56 56 39 56 56 63 SP B D3 SD: 0.1410 c. M:-0.2348 c. 734: 63 63 44 63 63 71 63 63 44 63 63 71 SP B D3 SD: 0.0672 c. M:-0.1095 c. 816: 70 70 49 70 70 79 70 70 49 70 70 79 SP B D3 SD: 0.0519 c. M:-0.0837 c. 1002: 86 86 60 86 86 97 86 86 60 86 86 97 SP B D3 SD: 0.0170 c. M:-0.0313 c. 1818: 156 156 109 156 156 176 156 156 109 156 156 176 SP B D3 SD: 0.0180 c. M:-0.0303 c. 2086: 179 179 125 179 179 202 179 179 125 179 179 202 SP B D3 SD: 0.0104 c. M: 0.0174 c.
FIT/HARMONIC
1 x x x x x x x x x x x 2 S SD: 0.6800 cents 2 x x x x x x 3 x x x x 4 S SD: 0.4618 cents 3 x x x x 4 x x x 5 x x 6 S SD: 5.3732 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 3.2061 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 11.3023 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 6.5031 cents 7 x 8 x x 9:10 x 11 x 12:13:14 S SD: 11.2421 cents 8 x 9 x 10 x 11:12:13 x 14:15:16 S SD: 7.6626 cents 9 x 10 x 11:12:13 x 14:15:16:17:18 S SD: 8.2353 cents 10 x 11:12 x 13:14:15:16:17:18:19:20 S SD: 9.0607 cents 11:12 x 13:14:15:16:17 x 18:19:21:22 SD: 12.1341 cents 12:13 x 14:15:16:17:18:19:20:21:22:24 S SD: 5.0347 cents 13:14 x 15:16:17:18:20:21:22:23:24:26 S SD: 8.0276 cents 14:15:16 x 17:19:20:21:22:23:25:26:28 SD: 7.4893 cents 15:16:17:18:19:20:21:23:24:25:26:28:30 SD: 6.0484 cents 16:17:18:19:20:21:23:24:25:27:28:30:32 SD: 4.9056 cents 17:18:19:20:21:22:24:26:27:28:30:32:34 S SD: 4.7545 cents 20:21 x 23:25:26:28:30:32:33:35:37:40 SD: 5.3332 cents 21:22:24:25:26:28:30:32:33:35:37:39:42 SD: 5.1323 cents 22:23:25:26:27:29:31:33:35:37:39:41:44 SD: 4.1286 cents 24:25:27:28:30:32:34:36:38:40:42:45:48 SD: 3.4565 cents 29:31:33:34:36:38:41:44:46:48:51:54:58 SD: 2.9576 cents 32:34:36:38:40:42:45:48:51:53:56:60:64 SD: 2.4428 cents 34:36:38:40:42:45:48:51:54:56:60:64:68 S SD: 2.3391 cents 44:47:50:52:55:58:62:66:70:73:78:82:88 SD: 2.2777 cents 46:49:52:54:57:61:65:69:73:76:81:86:92 SD: 1.4476 cents 62:66:70:73:77:82:88:93:99:103:109:116:124 SD: 1.1345 cents 80:85:90:94:100:106:113:120:127:133:141:150:160 SD: 0.9220 cents 94:100:106:110:117:124:133:141:150:156:166:176:188 SD: 0.8837 cents 97:103:109:114:121:128:137:146:154:161:171:181:194 SD: 0.8676 cents 102:108:115:120:127:135:144:153:162:169:180:191:204 SD: 0.8041 cents 109:116:123:128:136:144:154:164:174:181:192:204:218 SD: 0.7862 cents 114:121:128:134:142:151:161:171:182:189:201:213:228 SD: 0.7194 cents 118:125:133:139:147:156:167:177:188:196:208:221:236 SD: 0.6579 cents 126:134:142:148:157:167:178:189:201:209:222:236:252 SD: 0.6307 cents 130:138:146:153:162:172:184:195:207:216:229:243:260 SD: 0.5959 cents 142:151:160:167:177:188:201:213:226:236:250:265:284 SD: 0.5786 cents 143:152:161:168:178:189:202:215:228:237:252:267:286 SD: 0.5548 cents 150:159:169:176:187:198:212:225:239:249:264:280:300 SD: 0.4319 cents 167:177:188:196:208:221:236:251:266:277:294:312:334 SD: 0.3927 cents 196:208:221:230:244:259:277:294:312:325:345:366:392 SD: 0.3625 cents 214:227:241:251:267:283:303:321:341:355:377:400:428 SD: 0.3583 cents 229:243:258:269:285:303:324:344:365:380:403:428:458 SD: 0.3519 cents 230:244:259:270:287:304:325:345:366:382:405:430:460 SD: 0.3017 cents 260:276:293:305:324:344:368:390:414:432:458:486:520 SD: 0.2809 cents 276:293:311:324:344:365:390:414:440:458:486:516:552 SD: 0.2374 cents 292:310:329:343:364:386:413:438:465:485:514:546:584 SD: 0.2211 cents 326:346:367:383:406:431:461:489:519:541:574:609:652 SD: 0.2124 cents 373:396:420:438:465:493:527:560:594:619:657:697:746 SD: 0.2077 cents 391:415:440:459:487:517:553:587:623:649:689:731:782 SD: 0.1871 cents 420:446:473:493:523:555:594:630:669:697:740:785:840 SD: 0.1823 cents 444:471:500:521:553:587:628:666:707:737:782:830:888 SD: 0.1429 cents 459:487:517:539:572:607:649:689:731:762:809:858:918 SD: 0.1297 cents 553:587:623:649:689:731:782:830:881:918:974:1034:1106 SD: 0.1265 cents