Scala analysis: hanson11_tuning_95828_95886
Hanson[11] (Kleismic[11]) in 53-et
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 67.925 cents 67.924530 2: 249.057 cents 249.056600 3: 316.981 cents 316.981130 4: 384.906 cents 384.905660 5: 566.038 cents 566.037740 6: 633.962 cents 633.962260 7: 701.887 cents 701.886790 8: 883.019 cents 883.018870 9: 950.943 cents 950.943400 10: 1018.868 cents 1018.867920 11: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 181.1321 cents 181.1321 1: 67.9245 cents 67.9245 2: 181.1321 cents 181.1321 3: 67.9245 cents 67.9245 4: 67.9245 cents 67.9245 5: 181.1321 cents 181.1321 6: 67.9245 cents 67.9245 7: 67.9245 cents 67.9245 8: 181.1321 cents 181.1321 9: 67.9245 cents 67.9245 10: 67.9245 cents 67.9245 11: 181.1321 cents 181.1321
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 67.92453 cents 1: 4 181.13207 cents 2: 3 135.84906 cents 2: 8 249.05660 cents 3: 10 316.98113 cents 3: 1 430.18868 cents 4: 6 384.90566 cents 4: 5 498.11321 cents 5: 2 452.83019 cents 5: 9 566.03774 cents 6: 9 633.96226 cents 6: 2 747.16981 cents 7: 5 701.88679 cents 7: 6 815.09434 cents 8: 1 769.81132 cents 8: 10 883.01887 cents 9: 8 950.94340 cents 9: 3 1064.15094 cents 10: 4 1018.86792 cents 10: 7 1132.07547 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 0.0 : 67.9 249.1 317.0 384.9 566.0 634.0 701.9 883.0 950.9 1018.9 1200.0 67.9 : 181.1 249.1 317.0 498.1 566.0 634.0 815.1 883.0 950.9 1132.1 1200.0 249.1 : 67.9 135.8 317.0 384.9 452.8 634.0 701.9 769.8 950.9 1018.9 1200.0 317.0 : 67.9 249.1 317.0 384.9 566.0 634.0 701.9 883.0 950.9 1132.1 1200.0 384.9 : 181.1 249.1 317.0 498.1 566.0 634.0 815.1 883.0 1064.2 1132.1 1200.0 566.0 : 67.9 135.8 317.0 384.9 452.8 634.0 701.9 883.0 950.9 1018.9 1200.0 634.0 : 67.9 249.1 317.0 384.9 566.0 634.0 815.1 883.0 950.9 1132.1 1200.0 701.9 : 181.1 249.1 317.0 498.1 566.0 747.2 815.1 883.0 1064.2 1132.1 1200.0 883.0 : 67.9 135.8 317.0 384.9 566.0 634.0 701.9 883.0 950.9 1018.9 1200.0 950.9 : 67.9 249.1 317.0 498.1 566.0 634.0 815.1 883.0 950.9 1132.1 1200.0 1018.9: 181.1 249.1 430.2 498.1 566.0 747.2 815.1 883.0 1064.2 1132.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 67.9245 .. 181.1321 cents 113.20754 cents 67.92453 cents 2: 135.8491 .. 249.0566 cents 113.20754 cents -45.28301 cents 3: 316.9811 .. 430.1887 cents 113.20755 cents 67.92453 cents 4: 384.9057 .. 498.1132 cents 113.20755 cents -45.28302 cents 5: 452.8302 .. 566.0377 cents 113.20755 cents -45.28302 cents 6: 633.9623 .. 747.1698 cents 113.20755 cents 67.92452 cents 7: 701.8868 .. 815.0943 cents 113.20755 cents -45.28302 cents 8: 769.8113 .. 883.0189 cents 113.20755 cents -45.28302 cents 9: 950.9434 .. 1064.1509 cents 113.20754 cents 67.92453 cents 10: 1018.8679 .. 1132.0755 cents 113.20755 cents -45.28302 cents
SHOW DATA
Number of notes : 11 -- Interval properties -- Smallest interval : 67.92452 cents, class 1 Average step (divided formal octave): 109.0909 cents Largest one step interval : 181.13207 cents Average / Smallest step : 1.606061 Largest / Average step : 1.660377 Largest / Smallest step : 2.666667 Median interval of one step : 67.92453 cents, amount: 7 Most common interval of one step : 67.92453 cents, amount: 7 Least squares average step : 105.95868 cents, oct.: 1165.54553 cents Scale is not proper Scale has Myhill's property chromas: 113.20754 cents and 45.28301 cents, ratio: 2.500000 generators: 3 of 316.98113 cents and 8 of 883.01887 cents ET pair of linear temperament : 15&19 Scale is distributional even Scale is a mode of a 53-tone equal temperament with octave 2/1 degrees: 3 11 14 17 25 28 31 39 42 45 53 generators: 14 and 39 Number of contiguous 1-step segments: 0 Scale is fully connected major-minor triadic in 53-tone equal temperament Step pattern alph. order: ABAABAABAAB Step pattern size order : SLSSLSSLSSL Interval vector is [ 0 0 7 0 0 3 0 4 0 0 8 0 0 10 0 0 6 0 1 2 0 5 0 0 9 0 ] Scale is a Constant Structure, by a margin of 22.64151 cents Scale diversity : 1.241814 Lumma stability : 0.283019 Lumma impropriety factor : 0.226415 Rothenberg efficiency : 0.727273 redundancy: 0.272727 Efficiency x scale size : 8.000000 Number of different interval sizes : 20 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 22.64151 cents Most common intervals : 316.98113 cents & inv., amount: 10 Scale is a chain of 5 triads 0.0 384.906 883.019 cents Most common triad is 0.0 316.981 883.019 cents, amount: 9 Number of recognisable fifths : 5, average 701.8868 cents Scale contains two identical disjunct hexachords Formal octave complements present : 7 = 63.6364% Limited inverse transpositions : 1 Inversional symmetry on degrees : 6 Inversional symmetry on intervals : 0-1 -- Rational properties -- Prime limit : 2 (not all pitches rational)
FIT/MODE
11: 0 2 0 1 2 0 1 2 0 1 2 N T3 SD: 57.7964 c. M: 98.7993 c. 12: 1 2 0 1 2 0 1 2 1 0 2 N T3 SD: 29.3902 c. M:-50.9434 c. 13: 1 2 0 1 2 1 1 2 0 1 2 N T3 SD: 25.6723 c. M:-40.0581 c. 14: 1 2 1 0 3 0 1 2 1 1 2 N SD: 23.7736 c. M: 42.0485 c. 15: 1 2 1 1 2 1 1 2 1 1 2 P M ME S SD: 11.2956 c. M:-21.1321 c. 19: 1 3 1 1 3 1 1 3 1 1 3 N M DE S SD: 4.4588 c. M: 8.3416 c. 34: 2 5 2 2 5 2 2 5 2 2 5 N M DE S SD: 2.4917 c. M:-4.6615 c. 53: 3 8 3 3 8 3 3 8 3 3 8 N M DE S SD: 0.0000 c. M:-0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x 2 S SD: 0.0000 cents 2 x x x x x x 3 x x x 4 S SD: 0.0341 cents 3 x x x x 4 x x 5 x x 6 S SD: 22.6686 cents 4 x x x 5 x x 6 x 7 x 8 S SD: 4.4845 cents 5 x x 6 x 7 x x 8 x 9:10 S SD: 14.2574 cents 6 x 7 x x 8 x 9:10 x 11:12 S SD: 12.7716 cents 7 x 8 x 9 x 10:11 x 12:13:14 S SD: 16.1087 cents 8 x 9 x 10:11 x 12:13:14 x 16 S SD: 9.4568 cents 9 x 10:11 x 12:13:14:15 x 16:18 S SD: 15.0477 cents 10 x x 12 x 14 x 15 x 17:18:20 SD: 6.0512 cents 11:12 x 13:14:15:16:17:18:19:20:22 S SD: 11.6725 cents 12:13:14 x 15 x 17:18:20:21:22:24 SD: 9.6357 cents 13:14:15 x 16:18:19:20:22 x 23:26 SD: 10.2425 cents 14:15:16:17 x 19:20:21:23:24:25:28 SD: 7.8147 cents 15:16:17:18:19:21:22:23:25:26:27:30 SD: 7.1215 cents 16:17:18:19:20:22:23:24:27:28:29:32 SD: 6.4256 cents 17:18:20 x 21:24:25:26:28:29:31:34 SD: 8.4318 cents 18:19:21:22 x 25:26:27:30:31:32:36 SD: 5.0337 cents 20:21:23:24:25:28:29:30:33:35:36:40 SD: 3.2334 cents 32:33:37:38:40:44:46:48:53:55:58:64 SD: 3.1913 cents 34:35:39:41:42:47:49:51:57:59:61:68 SD: 2.9947 cents 36:37:42:43:45:50:52:54:60:62:65:72 SD: 2.8108 cents 39:41:45:47:49:54:56:58:65:68:70:78 SD: 2.8003 cents 40:42:46:48:50:55:58:60:67:69:72:80 SD: 2.5414 cents 44:46:51:53:55:61:63:66:73:76:79:88 SD: 1.8369 cents 45:47:52:54:56:62:65:67:75:78:81:90 SD: 1.8168 cents 50:52:58:60:62:69:72:75:83:87:90:100 SD: 1.8067 cents 52:54:60:62:65:72:75:78:87:90:94:104 SD: 1.5095 cents 64:67:74:77:80:89:92:96:107:111:115:128 SD: 1.4990 cents 70:73:81:84:87:97:101:105:117:121:126:140 SD: 1.1673 cents 72:75:83:86:90:100:104:108:120:125:130:144 SD: 1.1324 cents 80:83:92:96:100:111:115:120:133:139:144:160 SD: 1.0965 cents 90:94:104:108:112:125:130:135:150:156:162:180 SD: 0.9817 cents 96:100:111:115:120:133:138:144:160:166:173:192 SD: 0.8092 cents 104:108:120:125:130:144:150:156:173:180:187:208 SD: 0.5363 cents 149:155:172:179:186:207:215:223:248:258:268:298 SD: 0.5346 cents 150:156:173:180:187:208:216:225:250:260:270:300 SD: 0.4880 cents 168:175:194:202:210:233:242:252:280:291:303:336 SD: 0.4534 cents 174:181:201:209:217:241:251:261:290:301:313:348 SD: 0.4441 cents 176:183:203:211:220:244:254:264:293:305:317:352 SD: 0.3830 cents 194:202:224:233:242:269:280:291:323:336:349:388 SD: 0.3621 cents 220:229:254:264:275:305:317:330:366:381:396:440 SD: 0.3370 cents 228:237:263:274:285:316:329:342:380:395:411:456 SD: 0.3259 cents 253:263:292:304:316:351:365:379:421:438:456:506 SD: 0.3106 cents 258:268:298:310:322:358:372:387:430:447:465:516 SD: 0.3068 cents 272:283:314:327:340:377:392:408:453:471:490:544 SD: 0.2677 cents 298:310:344:358:372:413:430:447:496:516:537:596 SD: 0.2062 cents 373:388:431:448:466:517:538:559:621:646:672:746 SD: 0.2037 cents 382:397:441:459:477:530:551:573:636:662:688:764 SD: 0.1985 cents 398:414:460:478:497:552:574:597:663:689:717:796 SD: 0.1767 cents 452:470:522:543:565:627:652:678:753:783:814:904 SD: 0.1682 cents 473:492:546:568:591:656:682:709:788:819:852:946 SD: 0.1595 cents 478:497:552:574:597:663:689:717:796:828:861:956 SD: 0.1062 cents 574:597:663:689:717:796:828:861:956:994:1034:1148 SD: 0.1007 cents