Scala analysis: dualhexk
Aaron Johnson's dual-hexany in 1/4-kleismic
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 115.587 cents 115.587047 2: 153.212 cents 153.211740 3: 268.799 cents 268.798786 4: 384.386 cents 384.385833 5: 468.853 cents 468.853027 6: 537.598 cents 537.597573 7: 700.027 cents 700.027120 8: 768.772 cents 768.771666 9: 853.239 cents 853.238860 10: 968.826 cents 968.825906 11: 1084.413 cents 1084.412953 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 115.5870 cents 115.5870 1: 115.5870 cents 115.5870 2: 37.6247 cents 37.6247 3: 115.5870 cents 115.5870 4: 115.5870 cents 115.5870 5: 84.4672 cents 84.4672 6: 68.7445 cents 68.7445 7: 162.4295 cents 162.4295 8: 68.7445 cents 68.7445 9: 84.4672 cents 84.4672 10: 115.5870 cents 115.5870 11: 115.5870 cents 115.5870 12: 115.5870 cents 115.5870
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 37.62469 cents 1: 2 68.74455 cents 1: 2 84.46719 cents 1: 6 115.58705 cents 1: 1 162.42955 cents 2: 4 153.21174 cents 2: 2 200.05424 cents 2: 6 231.17409 cents 3: 5 268.79879 cents 3: 1 299.91864 cents 3: 4 315.64129 cents 3: 2 346.76114 cents 4: 1 353.26598 cents 4: 7 384.38583 cents 4: 3 431.22833 cents 4: 1 462.34819 cents 5: 1 422.01053 cents 5: 2 468.85303 cents 5: 6 499.97288 cents 5: 3 546.81538 cents 6: 1 537.59757 cents 6: 5 584.44007 cents 6: 5 615.55993 cents 6: 1 662.40243 cents 7: 3 653.18462 cents 7: 6 700.02712 cents 7: 2 731.14697 cents 7: 1 777.98947 cents 8: 1 737.65181 cents 8: 3 768.77167 cents 8: 7 815.61417 cents 8: 1 846.73402 cents 9: 2 853.23886 cents 9: 4 884.35871 cents 9: 1 900.08136 cents 9: 5 931.20121 cents 10: 6 968.82591 cents 10: 2 999.94576 cents 10: 4 1046.78826 cents 11: 1 1037.57045 cents 11: 6 1084.41295 cents 11: 2 1115.53281 cents 11: 2 1131.25545 cents 11: 1 1162.37531 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 0.0 : 115.6 153.2 268.8 384.4 468.9 537.6 700.0 768.8 853.2 968.8 1084.4 1200.0 115.6 : 37.6 153.2 268.8 353.3 422.0 584.4 653.2 737.7 853.2 968.8 1084.4 1200.0 153.2 : 115.6 231.2 315.6 384.4 546.8 615.6 700.0 815.6 931.2 1046.8 1162.4 1200.0 268.8 : 115.6 200.1 268.8 431.2 500.0 584.4 700.0 815.6 931.2 1046.8 1084.4 1200.0 384.4 : 84.5 153.2 315.6 384.4 468.9 584.4 700.0 815.6 931.2 968.8 1084.4 1200.0 468.9 : 68.7 231.2 299.9 384.4 500.0 615.6 731.1 846.7 884.4 999.9 1115.5 1200.0 537.6 : 162.4 231.2 315.6 431.2 546.8 662.4 778.0 815.6 931.2 1046.8 1131.3 1200.0 700.0 : 68.7 153.2 268.8 384.4 500.0 615.6 653.2 768.8 884.4 968.8 1037.6 1200.0 768.8 : 84.5 200.1 315.6 431.2 546.8 584.4 700.0 815.6 900.1 968.8 1131.3 1200.0 853.2 : 115.6 231.2 346.8 462.3 500.0 615.6 731.1 815.6 884.4 1046.8 1115.5 1200.0 968.8 : 115.6 231.2 346.8 384.4 500.0 615.6 700.0 768.8 931.2 999.9 1084.4 1200.0 1084.4: 115.6 231.2 268.8 384.4 500.0 584.4 653.2 815.6 884.4 968.8 1084.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.6247 .. 162.4295 cents 124.80485 cents 37.62469 cents 2: 153.2117 .. 231.1741 cents 77.96235 cents -9.21781 cents 3: 268.7988 .. 346.7611 cents 77.96235 cents 37.62469 cents 4: 353.2660 .. 462.3482 cents 109.08221 cents 6.50484 cents 5: 422.0105 .. 546.8154 cents 124.80485 cents -40.33766 cents 6: 537.5976 .. 662.4024 cents 124.80485 cents -9.21781 cents 7: 653.1846 .. 777.9895 cents 124.80485 cents -9.21781 cents 8: 737.6518 .. 846.7340 cents 109.08221 cents -40.33766 cents 9: 853.2389 .. 931.2012 cents 77.96235 cents 6.50484 cents 10: 968.8259 .. 1046.7883 cents 77.96235 cents 37.62469 cents 11: 1037.5705 .. 1162.3753 cents 124.80485 cents -9.21781 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 37.62469 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 162.42955 cents Average / Smallest step : 2.657829 Largest / Average step : 1.624295 Largest / Smallest step : 4.317100 Median interval of one step : 115.58705 cents, amount: 6 Most common interval of one step : 115.58705 cents, amount: 6 Least squares average step : 97.04941 cents, oct.: 1164.59290 cents Scale is not proper Step pattern alph. order: ABAACDEDCAAA Step pattern size order : DADDCBEBCDDD Scale is a Constant Structure, by a margin of 6.50484 cents Scale diversity : 1.463285 Lumma stability : 0.136257 Lumma impropriety factor : 0.097955 Rothenberg efficiency : 0.329624 redundancy: 0.670376 Efficiency x scale size : 3.955483 Number of different interval sizes : 44 = 4.00000 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.00000 = 4 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 6.50484 cents Most common intervals : 384.38583 cents & inv., amount: 7 Most common triad is 0.0 384.386 815.614 cents, amount: 3 Number of recognisable fifths : 6, average 700.0271 cents Formal octave complements present : 3 = 25.0000% -- Rational properties --
FIT/MODE
12: 1 0 1 1 1 1 1 1 1 1 1 2 N T3 SD: 64.8812 c. M: 100.0271 c. 13: 1 1 1 1 1 1 2 0 1 1 2 1 N D3 SD: 25.2933 c. M: 45.7490 c. 14: 1 1 1 1 1 1 2 1 1 1 1 2 P D3 S SD: 27.7948 c. M: 55.8415 c. 16: 1 1 1 2 1 1 2 1 1 2 1 2 P D3 SD: 24.4553 c. M: 43.7988 c. 17: 2 0 2 2 1 1 2 1 1 2 2 1 N D3 SD: 23.1339 c. M:-44.9988 c. 18: 2 0 2 2 1 1 3 1 1 2 1 2 N SD: 19.4357 c. M:-33.3062 c. 19: 2 0 2 2 1 1 3 1 1 2 2 2 N SD: 19.6812 c. M: 32.3344 c. 20: 2 1 1 2 2 1 3 1 1 2 2 2 N T3 SD: 16.0436 c. M: 28.7988 c. 21: 2 1 2 2 1 1 3 1 2 2 2 2 N SD: 14.2717 c. M: 25.9145 c. 22: 2 1 2 2 2 1 3 1 2 2 2 2 P D3 SD: 10.8797 c. M:-22.0561 c. 25: 2 1 3 2 2 1 4 1 2 2 3 2 N SD: 13.0083 c. M:-19.9729 c. 28: 3 1 2 3 2 2 3 2 2 3 2 3 N SD: 11.9293 c. M:-19.5453 c. 31: 3 1 3 3 2 2 4 2 2 3 3 3 N SD: 2.8389 c. M:-5.4219 c. 72: 7 2 7 7 5 4 10 4 5 7 7 7 N SD: 2.2518 c. M: 4.2642 c. 94: 9 3 9 9 7 5 13 5 7 9 9 9 N SD: 1.7377 c. M:-3.4874 c. 103: 10 3 10 10 7 6 14 6 7 10 10 10 N SD: 1.5352 c. M: 2.8336 c. 125: 12 4 12 12 9 7 17 7 9 12 12 12 N SD: 0.7149 c. M:-1.5470 c. 156: 15 5 15 15 11 9 21 9 11 15 15 15 N SD: 0.4432 c. M:-0.8640 c. 228: 22 7 22 22 16 13 31 13 16 22 22 22 N SD: 0.4088 c. M: 0.7555 c. 353: 34 11 34 34 25 20 48 20 25 34 34 34 N SD: 0.2588 c. M: 0.4997 c. 384: 37 12 37 37 27 22 52 22 27 37 37 37 N SD: 0.0664 c. M: 0.1139 c. 924: 89 29 89 89 65 53 125 53 65 89 89 89 N SD: 0.0319 c. M:-0.0648 c. 1308: 126 41 126 126 92 75 177 75 92 126 126 126 N SD: 0.0225 c. M: 0.0457 c. 2201: 212 69 212 212 155 126 298 126 155 212 212 212 N SD: 0.0159 c. M: 0.0302 c.
FIT/HARMONIC
1 x 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 x 4 S SD: 0.9639 cents 3 x x x x 4 x x x 5 x x 6 S SD: 14.2229 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 0.6816 cents 5 x x 6 x x 7 x x 8:9 x 10 S SD: 18.0605 cents 6 x x 7 x 8 x 9 x 10 x 11:12 S SD: 9.2144 cents 7 x x 8 x 9:10 x 11 x 12:13:14 S SD: 14.6820 cents 8 x 9 x 10 x 11:12 x 13:14:15:16 S SD: 6.7805 cents 9 x 10 x 11:12 x 13:14:15:16:17:18 S SD: 10.5968 cents 10 x 11:12 x 13:14:15 x 16:18:19:20 S SD: 10.6742 cents 11 x 12:13:14 x 15:16:17:18:19:21:22 SD: 7.8276 cents 12 x 13:14:15:16 x 18:19:20:21:22:24 S SD: 6.3183 cents 13:14 x 15:16:17:18:19:20:21:23:24:26 SD: 6.8669 cents 14:15 x 16:17:18:19:21:22:23:25:26:28 SD: 7.3823 cents 15:16 x 18:19:20 x 22:23:25:26:28:30 SD: 8.4450 cents 16:17 x 19:20:21:22:24:25:26:28:30:32 SD: 3.3132 cents 22 x 24:26:27:29:30:33:34:36:39:41:44 SD: 4.2438 cents 23 x 25:27:29:30:31:34:36:38:40:43:46 SD: 3.9839 cents 24 x 26:28:30:31:33:36:37:39:42:45:48 SD: 3.6704 cents 25:27 x 29:31:33:34:37:39:41:44:47:50 SD: 3.3976 cents 26:28 x 30:32:34:35:39:41:43:46:49:52 SD: 4.9814 cents 27:29:30:32:34:35:37:40:42:44:47:51:54 SD: 4.5959 cents 28:30:31:33:35:37:38:42:44:46:49:52:56 SD: 3.1739 cents 30:32:33:35:37:39:41:45:47:49:53:56:60 SD: 2.8996 cents 32:34:35:37:40:42:44:48:50:52:56:60:64 SD: 2.3748 cents 37 x 40:43:46:49:50:55:58:61:65:69:74 SD: 3.5655 cents 38:41:42:44:47:50:52:57:59:62:67:71:76 SD: 3.2051 cents 39:42:43:46:49:51:53:58:61:64:68:73:78 SD: 2.8115 cents 40:43:44:47:50:52:55:60:62:65:70:75:80 SD: 2.6706 cents 41:44:45:48:51:54:56:61:64:67:72:77:82 SD: 1.8227 cents 44:47:48:51:55:58:60:66:69:72:77:82:88 SD: 1.7220 cents 52:56:57:61:65:68:71:78:81:85:91:97:104 SD: 1.4788 cents 55:59:60:64:69:72:75:82:86:90:96:103:110 SD: 1.3987 cents 61:65:67:71:76:80:83:91:95:100:107:114:122 SD: 1.3769 cents 64:68:70:75:80:84:87:96:100:105:112:120:128 SD: 1.2983 cents 72:77:79:84:90:94:98:108:112:118:126:135:144 SD: 1.0798 cents 77:82:84:90:96:101:105:115:120:126:135:144:154 SD: 0.8467 cents 88:94:96:103:110:115:120:132:137:144:154:165:176 SD: 0.7568 cents 100:107:109:117:125:131:136:150:156:164:175:187:200 SD: 0.7297 cents 116:124:127:135:145:152:158:174:181:190:203:217:232 SD: 0.6974 cents 118:126:129:138:147:155:161:177:184:193:207:221:236 SD: 0.6680 cents 129:138:141:151:161:169:176:193:201:211:226:241:258 SD: 0.5117 cents 132:141:144:154:165:173:180:198:206:216:231:247:264 SD: 0.4092 cents 173:185:189:202:216:227:236:259:270:283:303:324:346 SD: 0.3226 cents 245:262:268:286:306:321:334:367:382:401:429:458:490 SD: 0.2826 cents 261:279:285:305:326:342:356:391:407:427:457:488:522 SD: 0.2064 cents 347:371:379:405:433:455:473:520:541:568:607:649:694 SD: 0.1956 cents 379:405:414:443:473:497:517:568:591:620:663:709:758 SD: 0.1915 cents 433:463:473:506:541:568:591:649:675:709:758:810:866 SD: 0.1888 cents 434:464:474:507:542:569:592:650:677:710:760:812:868 SD: 0.1788 cents 435:465:475:508:543:570:593:652:678:712:761:814:870 SD: 0.1755 cents 447:478:488:522:558:586:610:670:697:732:782:836:894 SD: 0.1677 cents 463:495:506:541:578:607:632:694:722:758:810:866:926 SD: 0.1505 cents 495:529:541:578:618:649:675:742:772:810:866:926:990 SD: 0.1452 cents 508:543:555:593:634:666:693:761:792:832:889:950:1016 SD: 0.1435 cents 540:577:590:631:674:708:737:809:842:884:945:1010:1080 SD: 0.1404 cents 560:599:612:654:699:734:764:839:873:917:980:1048:1120 SD: 0.1288 cents 595:636:650:695:743:780:812:892:928:974:1041:1113:1190 SD: 0.1264 cents 596:637:651:696:744:781:813:893:929:976:1043:1115:1192 SD: 0.1116 cents