Scala analysis: xen18-schulter-archytan-1-4-12
1/4-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 161.397 cents 161.397167 2: 217.542 cents 217.542048 3: 273.687 cents 273.686929 4: 435.084 cents 435.084095 5: 491.229 cents 491.228976 6: 652.626 cents 652.626143 7: 708.771 cents 708.771024 8: 870.168 cents 870.168191 9: 926.313 cents 926.313071 10: 982.458 cents 982.457952 11: 1143.855 cents 1143.855119 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 56.1449 cents 56.1449 1: 161.3972 cents 161.3972 2: 56.1449 cents 56.1449 3: 56.1449 cents 56.1449 4: 161.3972 cents 161.3972 5: 56.1449 cents 56.1449 6: 161.3972 cents 161.3972 7: 56.1449 cents 56.1449 8: 161.3972 cents 161.3972 9: 56.1449 cents 56.1449 10: 56.1449 cents 56.1449 11: 161.3972 cents 161.3972 12: 56.1449 cents 56.1449
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 56.14488 cents 1: 5 161.39717 cents 2: 2 112.28976 cents 2: 10 217.54205 cents 3: 9 273.68693 cents 3: 3 378.93921 cents 4: 4 329.83181 cents 4: 8 435.08410 cents 5: 11 491.22898 cents 5: 1 596.48126 cents 6: 6 547.37386 cents 6: 6 652.62614 cents 7: 1 603.51874 cents 7: 11 708.77102 cents 8: 8 764.91590 cents 8: 4 870.16819 cents 9: 3 821.06079 cents 9: 9 926.31307 cents 10: 10 982.45795 cents 10: 2 1087.71024 cents 11: 5 1038.60283 cents 11: 7 1143.85512 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 12 0.0 : 161.4 217.5 273.7 435.1 491.2 652.6 708.8 870.2 926.3 982.5 1143.9 1200.0 161.4 : 56.1 112.3 273.7 329.8 491.2 547.4 708.8 764.9 821.1 982.5 1038.6 1200.0 217.5 : 56.1 217.5 273.7 435.1 491.2 652.6 708.8 764.9 926.3 982.5 1143.9 1200.0 273.7 : 161.4 217.5 378.9 435.1 596.5 652.6 708.8 870.2 926.3 1087.7 1143.9 1200.0 435.1 : 56.1 217.5 273.7 435.1 491.2 547.4 708.8 764.9 926.3 982.5 1038.6 1200.0 491.2 : 161.4 217.5 378.9 435.1 491.2 652.6 708.8 870.2 926.3 982.5 1143.9 1200.0 652.6 : 56.1 217.5 273.7 329.8 491.2 547.4 708.8 764.9 821.1 982.5 1038.6 1200.0 708.8 : 161.4 217.5 273.7 435.1 491.2 652.6 708.8 764.9 926.3 982.5 1143.9 1200.0 870.2 : 56.1 112.3 273.7 329.8 491.2 547.4 603.5 764.9 821.1 982.5 1038.6 1200.0 926.3 : 56.1 217.5 273.7 435.1 491.2 547.4 708.8 764.9 926.3 982.5 1143.9 1200.0 982.5 : 161.4 217.5 378.9 435.1 491.2 652.6 708.8 870.2 926.3 1087.7 1143.9 1200.0 1143.9: 56.1 217.5 273.7 329.8 491.2 547.4 708.8 764.9 926.3 982.5 1038.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 56.1449 .. 161.3972 cents 105.25229 cents 56.14488 cents 2: 112.2898 .. 217.5420 cents 105.25229 cents -49.10741 cents 3: 273.6869 .. 378.9392 cents 105.25228 cents 56.14488 cents 4: 329.8318 .. 435.0841 cents 105.25229 cents -49.10741 cents 5: 491.2290 .. 596.4813 cents 105.25229 cents 56.14488 cents 6: 547.3739 .. 652.6261 cents 105.25229 cents -49.10741 cents 7: 603.5187 .. 708.7710 cents 105.25229 cents -49.10740 cents 8: 764.9159 .. 870.1682 cents 105.25229 cents 56.14488 cents 9: 821.0608 .. 926.3131 cents 105.25229 cents -49.10741 cents 10: 982.4580 .. 1087.7102 cents 105.25229 cents 56.14488 cents 11: 1038.6028 .. 1143.8551 cents 105.25229 cents -49.10741 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 56.14488 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 161.39717 cents Average / Smallest step : 1.781106 Largest / Average step : 1.613972 Largest / Smallest step : 2.874655 Median interval of one step : 56.14488 cents, amount: 7 Most common interval of one step : 56.14488 cents, amount: 7 Least squares average step : 102.45589 cents, oct.: 1229.47064 cents Scale is not proper Scale has Myhill's property chromas: 105.25229 cents and 49.10740 cents, ratio: 2.143308 generators: 5 of 491.22898 cents and 7 of 708.77102 cents ET pair of linear temperament : 17&22 Scale is distributional even Step pattern alph. order: ABBABABABBAB Step pattern size order : LSSLSLSLSSLS Scale is a Constant Structure, by a margin of 7.03748 cents Ratio Whole / Half tone : 3.874655 Scale diversity : 1.247012 Lumma stability : 0.280724 Lumma impropriety factor : 0.245537 Rothenberg efficiency : 0.722222 redundancy: 0.277778 Efficiency x scale size : 8.666667 Number of different interval sizes : 22 = 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 : 7.03748 cents Most common intervals : 491.22898 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 56.145 708.771 cents Most common triad is 0.0 491.229 708.771 cents, amount: 10 Number of recognisable fifths : 11, average 708.7710 cents Scale contains two identical disjunct hexachords Formal octave complements present : 7 = 58.3333% Limited inverse transpositions : 11 Inversional symmetry on intervals : 5-6 11-12 -- Rational properties --
FIT/MODE
12: 1 1 0 2 0 2 1 1 1 0 2 1 N T3 SD: 54.9588 c. M: 91.2290 c. 13: 2 0 1 2 0 2 1 1 1 1 1 1 N D3 SD: 25.9698 c. M: 39.3990 c. 14: 2 1 0 2 1 2 0 2 1 0 2 1 N SD: 24.2022 c. M: 39.6008 c. 15: 2 0 1 2 1 2 1 2 0 1 2 1 N SD: 27.9960 c. M: 57.5420 c. 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 12.3122 c. M: 23.1094 c. Twelve-tone Chromatic (2/11-comma positive) 22: 3 1 1 3 1 3 1 3 1 1 3 1 N M DE SD: 1.3634 c. M:-2.5591 c. Twelve-tone Chromatic (1/3-comma positive) 105: 14 5 5 14 5 14 5 14 5 5 14 5 N M DE SD: 0.8507 c. M: 1.5968 c. 127: 17 6 6 17 6 17 6 17 6 6 17 6 N M DE SD: 0.4672 c. M: 0.8769 c. 149: 20 7 7 20 7 20 7 20 7 7 20 7 N M DE SD: 0.1969 c. M: 0.3695 c. 171: 23 8 8 23 8 23 8 23 8 8 23 8 N M DE SD: 0.0039 c. M:-0.0072 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: 3.4080 cents 3 x x x x 4 x x 5 x x x 6 S SD: 5.2475 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 12.7741 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 21.0723 cents 6 x x 7 x 8 x 9:10 x 11 x 12 S SD: 11.5675 cents 7 x 8 x 9 x 10:11 x 12 x x 14 S SD: 13.8462 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 12.7327 cents 9:10 x 11 x 12:13:14:15 x 16:17:18 S SD: 11.9417 cents 10:11 x 12:13 x x 15 x 17:18:19:20 SD: 8.4276 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 7.7999 cents 12:13 x 14:15:16 x 18:20 x 21:23:24 SD: 6.7892 cents 13:14 x 15 x 17:19:20:21:22:23:25:26 SD: 7.6658 cents 14:15:16 x 18:19:20:21:23:24:25:27:28 SD: 6.6143 cents 15:16:17:18:19:20:22:23:25:26 x 29:30 SD: 7.5553 cents 16 x 18:19 x 21:23:24:26:27:28:31:32 SD: 5.7402 cents 17 x 19:20:22:23:25:26:28:29:30:33:34 SD: 4.8514 cents 18:20 x 21:23:24:26:27:30:31:32:35:36 SD: 3.6509 cents 19:21 x 22:24:25:28:29:31:32:34:37:38 SD: 6.0513 cents 20:22:23 x 26:27:29:30:33:34:35:39:40 SD: 4.3770 cents 21:23:24:25:27:28:31:32:35:36:37:41:42 SD: 4.0705 cents 22:24:25:26:28:29:32:33:36:38:39:43:44 SD: 3.6867 cents 24:26:27:28:31:32:35:36:40:41:42:46:48 SD: 3.3393 cents 26:29 x 30:33:35:38:39:43:44:46:50:52 SD: 4.9434 cents 27:30:31:32:35:36:39:41:45:46:48:52:54 SD: 4.1886 cents 28:31:32:33:36:37:41:42:46:48:49:54:56 SD: 2.7575 cents 30:33:34:35:39:40:44:45:50:51:53:58:60 SD: 2.5030 cents 31:34:35:36:40:41:45:47:51:53:55:60:62 SD: 2.2607 cents 42:46:48:49:54:56:61:63:69:72:74:81:84 SD: 2.0317 cents 46:50:52:54:59:61:67:69:76:79:81:89:92 SD: 1.8948 cents 51:56:58:60:66:68:74:77:84:87:90:99:102 SD: 1.6858 cents 52:57:59:61:67:69:76:78:86:89:92:101:104 SD: 1.0888 cents 81:89:92:95:104:108:118:122:134:138:143:157:162 SD: 0.8053 cents 105:115:119:123:135:139:153:158:174:179:185:203:210 SD: 0.7734 cents 112:123:127:131:144:149:163:169:185:191:198:217:224 SD: 0.6434 cents 122:134:138:143:157:162:178:184:202:208:215:236:244 SD: 0.5969 cents 140:154:159:164:180:186:204:211:231:239:247:271:280 SD: 0.4910 cents 144:158:163:169:185:191:210:217:238:246:254:279:288 SD: 0.4712 cents 164:180:186:192:211:218:239:247:271:280:289:318:328 SD: 0.3178 cents 216:237:245:253:278:287:315:325:357:369:381:418:432 SD: 0.2461 cents 297:326:337:348:382:394:433:447:491:507:524:575:594 SD: 0.2298 cents 308:338:349:361:396:409:449:464:509:526:543:596:616 SD: 0.1963 cents 360:395:408:422:463:478:525:542:595:615:635:697:720 SD: 0.1859 cents 409:449:464:479:526:543:596:616:676:698:721:792:818 SD: 0.1683 cents 441:484:500:517:567:586:643:664:729:753:778:854:882 SD: 0.1622 cents 461:506:523:540:593:612:672:694:762:787:813:893:922 SD: 0.1526 cents 472:518:535:553:607:627:688:711:780:806:833:914:944 SD: 0.1390 cents 554:608:628:649:712:736:808:834:916:946:977:1073:1108 SD: 0.1371 cents 561:616:636:657:721:745:818:845:927:958:990:1086:1122 SD: 0.1302 cents 585:642:663:685:752:777:853:881:967:999:1032:1133:1170 SD: 0.1100 cents