Scala analysis: xen18-schulter-archytan-1-5-12
1/5-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 151.855 cents 151.854735 2: 214.816 cents 214.815638 3: 277.777 cents 277.776542 4: 429.631 cents 429.631277 5: 492.592 cents 492.592181 6: 644.447 cents 644.446915 7: 707.408 cents 707.407819 8: 859.263 cents 859.262554 9: 922.223 cents 922.223458 10: 985.184 cents 985.184362 11: 1137.039 cents 1137.039096 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 62.9609 cents 62.9609 1: 151.8547 cents 151.8547 2: 62.9609 cents 62.9609 3: 62.9609 cents 62.9609 4: 151.8547 cents 151.8547 5: 62.9609 cents 62.9609 6: 151.8547 cents 151.8547 7: 62.9609 cents 62.9609 8: 151.8547 cents 151.8547 9: 62.9609 cents 62.9609 10: 62.9609 cents 62.9609 11: 151.8547 cents 151.8547 12: 62.9609 cents 62.9609
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 62.96090 cents 1: 5 151.85474 cents 2: 2 125.92181 cents 2: 10 214.81564 cents 3: 9 277.77654 cents 3: 3 366.67037 cents 4: 4 340.73745 cents 4: 8 429.63128 cents 5: 11 492.59218 cents 5: 1 581.48601 cents 6: 6 555.55308 cents 6: 6 644.44691 cents 7: 1 618.51399 cents 7: 11 707.40782 cents 8: 8 770.36872 cents 8: 4 859.26255 cents 9: 3 833.32963 cents 9: 9 922.22346 cents 10: 10 985.18436 cents 10: 2 1074.07819 cents 11: 5 1048.14526 cents 11: 7 1137.03910 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 : 151.9 214.8 277.8 429.6 492.6 644.4 707.4 859.3 922.2 985.2 1137.0 1200.0 151.9 : 63.0 125.9 277.8 340.7 492.6 555.6 707.4 770.4 833.3 985.2 1048.1 1200.0 214.8 : 63.0 214.8 277.8 429.6 492.6 644.4 707.4 770.4 922.2 985.2 1137.0 1200.0 277.8 : 151.9 214.8 366.7 429.6 581.5 644.4 707.4 859.3 922.2 1074.1 1137.0 1200.0 429.6 : 63.0 214.8 277.8 429.6 492.6 555.6 707.4 770.4 922.2 985.2 1048.1 1200.0 492.6 : 151.9 214.8 366.7 429.6 492.6 644.4 707.4 859.3 922.2 985.2 1137.0 1200.0 644.4 : 63.0 214.8 277.8 340.7 492.6 555.6 707.4 770.4 833.3 985.2 1048.1 1200.0 707.4 : 151.9 214.8 277.8 429.6 492.6 644.4 707.4 770.4 922.2 985.2 1137.0 1200.0 859.3 : 63.0 125.9 277.8 340.7 492.6 555.6 618.5 770.4 833.3 985.2 1048.1 1200.0 922.2 : 63.0 214.8 277.8 429.6 492.6 555.6 707.4 770.4 922.2 985.2 1137.0 1200.0 985.2 : 151.9 214.8 366.7 429.6 492.6 644.4 707.4 859.3 922.2 1074.1 1137.0 1200.0 1137.0: 63.0 214.8 277.8 340.7 492.6 555.6 707.4 770.4 922.2 985.2 1048.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 151.8547 cents 88.89383 cents 62.96090 cents 2: 125.9218 .. 214.8156 cents 88.89383 cents -25.93293 cents 3: 277.7765 .. 366.6704 cents 88.89383 cents 62.96090 cents 4: 340.7374 .. 429.6313 cents 88.89383 cents -25.93293 cents 5: 492.5922 .. 581.4860 cents 88.89383 cents 62.96090 cents 6: 555.5531 .. 644.4469 cents 88.89383 cents -25.93293 cents 7: 618.5140 .. 707.4078 cents 88.89383 cents -25.93293 cents 8: 770.3687 .. 859.2626 cents 88.89383 cents 62.96090 cents 9: 833.3296 .. 922.2235 cents 88.89383 cents -25.93293 cents 10: 985.1844 .. 1074.0782 cents 88.89383 cents 62.96090 cents 11: 1048.1453 .. 1137.0391 cents 88.89383 cents -25.93293 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 62.96090 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 151.85474 cents Average / Smallest step : 1.588287 Largest / Average step : 1.518547 Largest / Smallest step : 2.411889 Median interval of one step : 62.96090 cents, amount: 7 Most common interval of one step : 62.96090 cents, amount: 7 Least squares average step : 102.07419 cents, oct.: 1224.89027 cents Scale is not proper Scale has Myhill's property chromas: 88.89383 cents and 25.93293 cents, ratio: 3.427836 generators: 5 of 492.59218 cents and 7 of 707.40782 cents ET pair of linear temperament : 17&39 Scale is distributional even Scale is a mode of a 324-tone equal temperament with octave 1200.000 cents degrees: 41 58 75 116 133 174 191 232 249 266 307 324 generators: 133 and 191 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABBABABABBAB Step pattern size order : LSSLSLSLSSLS Scale is a Constant Structure, by a margin of 25.93293 cents Ratio Whole / Half tone : 3.411889 Scale diversity : 1.223683 Lumma stability : 0.314805 Lumma impropriety factor : 0.129665 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 : 25.93293 cents Most common intervals : 492.59218 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 62.961 707.408 cents Most common triad is 0.0 492.592 707.408 cents, amount: 10 Number of recognisable fifths : 11, average 707.4078 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 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 31.5739 c. M: 59.2626 c. Twelve-tone Chromatic (1/11-comma) 13: 2 0 1 2 0 2 1 1 1 1 1 1 N D3 SD: 25.0359 c. M:-32.7606 c. 15: 2 1 0 2 1 2 1 2 1 0 2 1 N SD: 22.5911 c. M: 37.7765 c. 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 6.5019 c. M: 12.2037 c. Twelve-tone Chromatic (2/11-comma positive) 39: 5 2 2 5 2 5 2 5 2 2 5 2 N M DE SD: 1.2126 c. M:-2.2759 c. Twelve-tone Chromatic (1/4-comma positive) 56: 7 3 3 7 3 7 3 7 3 3 7 3 N M DE SD: 1.1293 c. M: 2.1197 c. 95: 12 5 5 12 5 12 5 12 5 5 12 5 N M DE SD: 0.1679 c. M: 0.3152 c. 229: 29 12 12 29 12 29 12 29 12 12 29 12 N M DE SD: 0.0672 c. M:-0.1261 c. 324: 41 17 17 41 17 41 17 41 17 17 41 17 N M DE SD: 0.0018 c. M: 0.0033 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: 2.7264 cents 3 x x x x 4 x x 5 x x x 6 S SD: 8.5606 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.6559 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 18.3274 cents 6 x x 7 x 8 x 9:10 x 11 x 12 S SD: 11.6989 cents 7 x 8 x 9 x 10:11 x 12 x x 14 S SD: 13.7242 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.5047 cents 9:10 x 11 x 12:13:14:15 x 16:17:18 S SD: 11.7716 cents 10:11 x 12:13 x x 15:16:17:18:19:20 SD: 8.6417 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 7.3007 cents 12:13 x 14:15:16:17:18:20 x 21:23:24 SD: 7.0437 cents 13:14 x 15 x 17:19:20:21:22:23:25:26 SD: 6.9883 cents 14:15:16 x 18:19:20:21:23:24:25:27:28 SD: 5.6574 cents 16:17:18:19 x 21:23:24:26:27:28:31:32 SD: 6.0474 cents 17 x 19:20:22:23:25:26:28:29:30:33:34 SD: 5.1608 cents 18:20 x 21:23:24:26:27:30:31:32:35:36 SD: 4.5528 cents 19:21 x 22:24:25:28:29:31:32:34:37:38 SD: 6.1708 cents 20:22:23 x 26:27:29:30:33:34:35:39:40 SD: 4.9607 cents 21:23:24:25:27:28:30:32:34:36:37:41:42 SD: 4.8317 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 3.1802 cents 30:33:34:35:38:40:44:45:49:51:53:58:60 SD: 2.9406 cents 31:34:35:36:40:41:45:47:51:53:55:60:62 SD: 2.5872 cents 36:39:41:42:46:48:52:54:59:61:64:69:72 SD: 2.4806 cents 39:43:44:46:50:52:57:59:64:66:69:75:78 SD: 2.4055 cents 40:44:45:47:51:53:58:60:66:68:71:77:80 SD: 2.0162 cents 45:49:51:53:58:60:65:68:74:77:79:87:90 SD: 1.8478 cents 46:50:52:54:59:61:67:69:76:78:81:89:92 SD: 1.6244 cents 53:58:60:62:68:70:77:80:87:90:94:102:106 SD: 1.4569 cents 64:70:72:75:82:85:93:96:105:109:113:123:128 SD: 1.2368 cents 67:73:76:79:86:89:97:101:110:114:118:129:134 SD: 1.0292 cents 75:82:85:88:96:100:109:113:123:128:132:145:150 SD: 0.9777 cents 85:93:96:100:109:113:123:128:140:145:150:164:170 SD: 0.8362 cents 97:106:110:114:124:129:141:146:159:165:171:187:194 SD: 0.7446 cents 107:117:121:126:137:142:155:161:176:182:189:206:214 SD: 0.7374 cents 109:119:123:128:140:145:158:164:179:186:193:210:218 SD: 0.7367 cents 121:132:137:142:155:161:176:182:199:206:214:233:242 SD: 0.5330 cents 142:155:161:167:182:189:206:214:233:242:251:274:284 SD: 0.4897 cents 166:181:188:195:213:221:241:250:273:283:293:320:332 SD: 0.4526 cents 173:189:196:203:222:230:251:260:284:295:306:334:346 SD: 0.4205 cents 188:205:213:221:241:250:273:283:309:320:332:363:376 SD: 0.3840 cents 206:225:233:242:264:274:299:310:338:351:364:397:412 SD: 0.2910 cents 249:272:282:292:319:331:361:375:409:424:440:480:498 SD: 0.2855 cents 252:275:285:296:323:335:366:379:414:429:445:486:504 SD: 0.2603 cents 295:322:334:346:378:392:428:444:485:503:521:569:590 SD: 0.2431 cents 317:346:359:372:406:421:460:477:521:540:560:611:634 SD: 0.2103 cents 361:394:409:424:463:480:524:543:593:615:638:696:722 SD: 0.2008 cents 380:415:430:446:487:505:551:572:624:647:671:733:760 SD: 0.1900 cents 395:431:447:464:506:525:573:594:649:673:698:762:790 SD: 0.1852 cents 402:439:455:472:515:534:583:605:660:685:710:775:804 SD: 0.1811 cents 408:445:462:479:523:542:592:614:670:695:721:787:816 SD: 0.1720 cents 437:477:495:513:560:581:634:658:718:744:772:843:874 SD: 0.1666 cents 448:489:507:526:574:595:650:674:736:763:791:864:896 SD: 0.1623 cents 459:501:520:539:588:610:666:691:754:782:811:885:918 SD: 0.1533 cents 493:538:558:579:632:655:715:742:810:840:871:951:986 SD: 0.1387 cents 501:547:567:588:642:666:727:754:823:853:885:966:1002 SD: 0.1186 cents 523:571:592:614:670:695:759:787:859:891:924:1009:1046 SD: 0.1000 cents