Scala analysis: xen18-schulter-archytan-5-26-12
5/26-Archytan temperament
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 150.387 cents 150.386668 2: 214.396 cents 214.396191 3: 278.406 cents 278.405714 4: 428.792 cents 428.792382 5: 492.802 cents 492.801905 6: 643.189 cents 643.188573 7: 707.198 cents 707.198095 8: 857.585 cents 857.584764 9: 921.594 cents 921.594286 10: 985.604 cents 985.603809 11: 1135.990 cents 1135.990477 12: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 64.0095 cents 64.0095 1: 150.3867 cents 150.3867 2: 64.0095 cents 64.0095 3: 64.0095 cents 64.0095 4: 150.3867 cents 150.3867 5: 64.0095 cents 64.0095 6: 150.3867 cents 150.3867 7: 64.0095 cents 64.0095 8: 150.3867 cents 150.3867 9: 64.0095 cents 64.0095 10: 64.0095 cents 64.0095 11: 150.3867 cents 150.3867 12: 64.0095 cents 64.0095
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 64.00952 cents 1: 5 150.38667 cents 2: 2 128.01905 cents 2: 10 214.39619 cents 3: 9 278.40571 cents 3: 3 364.78286 cents 4: 4 342.41524 cents 4: 8 428.79238 cents 5: 11 492.80190 cents 5: 1 579.17905 cents 6: 6 556.81143 cents 6: 6 643.18857 cents 7: 1 620.82095 cents 7: 11 707.19809 cents 8: 8 771.20762 cents 8: 4 857.58476 cents 9: 3 835.21714 cents 9: 9 921.59429 cents 10: 10 985.60381 cents 10: 2 1071.98095 cents 11: 5 1049.61333 cents 11: 7 1135.99048 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 : 150.4 214.4 278.4 428.8 492.8 643.2 707.2 857.6 921.6 985.6 1136.0 1200.0 150.4 : 64.0 128.0 278.4 342.4 492.8 556.8 707.2 771.2 835.2 985.6 1049.6 1200.0 214.4 : 64.0 214.4 278.4 428.8 492.8 643.2 707.2 771.2 921.6 985.6 1136.0 1200.0 278.4 : 150.4 214.4 364.8 428.8 579.2 643.2 707.2 857.6 921.6 1072.0 1136.0 1200.0 428.8 : 64.0 214.4 278.4 428.8 492.8 556.8 707.2 771.2 921.6 985.6 1049.6 1200.0 492.8 : 150.4 214.4 364.8 428.8 492.8 643.2 707.2 857.6 921.6 985.6 1136.0 1200.0 643.2 : 64.0 214.4 278.4 342.4 492.8 556.8 707.2 771.2 835.2 985.6 1049.6 1200.0 707.2 : 150.4 214.4 278.4 428.8 492.8 643.2 707.2 771.2 921.6 985.6 1136.0 1200.0 857.6 : 64.0 128.0 278.4 342.4 492.8 556.8 620.8 771.2 835.2 985.6 1049.6 1200.0 921.6 : 64.0 214.4 278.4 428.8 492.8 556.8 707.2 771.2 921.6 985.6 1136.0 1200.0 985.6 : 150.4 214.4 364.8 428.8 492.8 643.2 707.2 857.6 921.6 1072.0 1136.0 1200.0 1136.0: 64.0 214.4 278.4 342.4 492.8 556.8 707.2 771.2 921.6 985.6 1049.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.0095 .. 150.3867 cents 86.37715 cents 64.00952 cents 2: 128.0190 .. 214.3962 cents 86.37715 cents -22.36762 cents 3: 278.4057 .. 364.7829 cents 86.37714 cents 64.00952 cents 4: 342.4152 .. 428.7924 cents 86.37715 cents -22.36762 cents 5: 492.8019 .. 579.1790 cents 86.37714 cents 64.00952 cents 6: 556.8114 .. 643.1886 cents 86.37715 cents -22.36762 cents 7: 620.8210 .. 707.1981 cents 86.37714 cents -22.36762 cents 8: 771.2076 .. 857.5848 cents 86.37715 cents 64.00952 cents 9: 835.2171 .. 921.5943 cents 86.37715 cents -22.36762 cents 10: 985.6038 .. 1071.9810 cents 86.37715 cents 64.00952 cents 11: 1049.6133 .. 1135.9905 cents 86.37715 cents -22.36762 cents
SHOW DATA
Number of notes : 12 -- Interval properties -- Smallest interval : 64.00952 cents, class 1 Average step (divided formal octave): 100.0000 cents Largest one step interval : 150.38667 cents Average / Smallest step : 1.562268 Largest / Average step : 1.503867 Largest / Smallest step : 2.349442 Median interval of one step : 64.00952 cents, amount: 7 Most common interval of one step : 64.00952 cents, amount: 7 Least squares average step : 102.01547 cents, oct.: 1224.18560 cents Scale is not proper Scale has Myhill's property chromas: 86.37715 cents and 22.36762 cents, ratio: 3.861704 generators: 5 of 492.80190 cents and 7 of 707.19810 cents ET pair of linear temperament : 17&39 Scale is distributional even Scale is a mode of a 1556-tone equal temperament with octave 1200.000 cents degrees: 195 278 361 556 639 834 917 1112 1195 1278 1473 1556 generators: 639 and 917 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 22.36762 cents Ratio Whole / Half tone : 3.349442 Scale diversity : 1.215236 Lumma stability : 0.320048 Lumma impropriety factor : 0.111838 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 : 22.36762 cents Most common intervals : 492.80190 cents & inv., amount: 11 Scale is a chain of 6 triads 0.0 64.010 707.198 cents Most common triad is 0.0 492.802 707.198 cents, amount: 10 Number of recognisable fifths : 11, average 707.1981 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: 30.6800 c. M: 57.5848 c. Twelve-tone Chromatic (1/11-comma) 13: 2 0 1 2 0 2 1 1 1 1 1 1 N D3 SD: 25.0093 c. M:-34.2287 c. 17: 2 1 1 2 1 2 1 2 1 1 2 1 P M ME SD: 5.6080 c. M: 10.5259 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: 2.1064 c. M:-3.9537 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: 0.2354 c. M: 0.4419 c. 207: 26 11 11 26 11 26 11 26 11 11 26 11 N M DE SD: 0.2058 c. M:-0.3863 c. 263: 33 14 14 33 14 33 14 33 14 14 33 14 N M DE SD: 0.1118 c. M:-0.2099 c. 319: 40 17 17 40 17 40 17 40 17 17 40 17 N M DE SD: 0.0509 c. M:-0.0955 c. 375: 47 20 20 47 20 47 20 47 20 20 47 20 N M DE SD: 0.0081 c. M:-0.0152 c. 1181: 148 63 63 148 63 148 63 148 63 63 148 63 N M DE SD: 0.0034 c. M: 0.0064 c. 1556: 195 83 83 195 83 195 83 195 83 83 195 83 N M DE SD: 0.0006 c. M: 0.0012 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: 2.6215 cents 3 x x x x 4 x x 5 x x x 6 S SD: 9.0942 cents 4 x x x 5 x x 6 x x 7 x 8 S SD: 11.4930 cents 5 x x 6 x x 7 x 8 x 9 x 10 S SD: 17.9094 cents 6 x x 7 x 8 x 9:10 x 11 x 12 S SD: 11.7498 cents 7 x 8 x 9 x 10 x 11:12 x x 14 S SD: 13.6967 cents 8 x 9 x 10:11 x 12:13 x 14:15:16 S SD: 11.3301 cents 9 x 10:11 x 12:13:14:15 x 16:17:18 S SD: 11.7771 cents 10:11 x 12:13 x x 15:16:17:18:19:20 SD: 8.4968 cents 11:12 x 13:14:15:16:17:18:19 x 21:22 SD: 7.2687 cents 12:13 x 14:15:16:17:18:20 x 21:23:24 SD: 6.9563 cents 13:14 x 15 x 17:19:20:21:22:23:25:26 SD: 6.9254 cents 14:15:16 x 18:19:20:21:23:24:25:27:28 SD: 5.5471 cents 16:17:18:19 x 21:23:24:26:27:28:31:32 SD: 5.8744 cents 17 x 19:20:22:23:25:26:28:29:30:33:34 SD: 5.2508 cents 18 x 20:21:23:24:26:27:30:31:32:35:36 SD: 4.7367 cents 19:21 x 22:24:25:28:29:31:32:34:37:38 SD: 6.2360 cents 20:22:23 x 26:27:29:30:33:34:35:39:40 SD: 5.1007 cents 21:23:24:25:27:28:30:32:34:36:37:40:42 SD: 4.7280 cents 22:24:25:26:28:29:32:33:36:37:39:42:44 SD: 3.0678 cents 30:33:34:35:38:40:44:45:49:51:53:58:60 SD: 2.9906 cents 31:34:35:36:40:41:45:47:51:53:55:60:62 SD: 2.7270 cents 33:36:37:39:42:44:48:50:54:56:58:64:66 SD: 2.6078 cents 36:39:41:42:46:48:52:54:59:61:64:69:72 SD: 2.3412 cents 40:44:45:47:51:53:58:60:66:68:71:77:80 SD: 2.0619 cents 45:49:51:53:58:60:65:68:74:77:80:87:90 SD: 1.8574 cents 46:50:52:54:59:61:67:69:75:78:81:89:92 SD: 1.6973 cents 53:58:60:62:68:70:77:80:87:90:94:102:106 SD: 1.5057 cents 64:70:72:75:82:85:93:96:105:109:113:123:128 SD: 1.2318 cents 67:73:76:79:86:89:97:101:110:114:118:129:134 SD: 0.9673 cents 85:93:96:100:109:113:123:128:139:145:150:164:170 SD: 0.9258 cents 91:99:103:107:117:121:132:137:149:155:161:175:182 SD: 0.8387 cents 97:106:110:114:124:129:141:146:159:165:171:187:194 SD: 0.7498 cents 107:117:121:126:137:142:155:161:176:182:189:206:214 SD: 0.7326 cents 121:132:137:142:155:161:175:182:199:206:214:233:242 SD: 0.5485 cents 142:155:161:167:182:189:206:214:233:242:251:274:284 SD: 0.5051 cents 167:182:189:196:214:222:242:251:274:284:295:322:334 SD: 0.3176 cents 189:206:214:222:242:251:274:284:310:322:334:364:378 SD: 0.3085 cents 206:225:233:242:264:274:299:310:338:351:364:397:412 SD: 0.3025 cents 242:264:274:284:310:322:351:364:397:412:428:466:484 SD: 0.2767 cents 274:299:310:322:351:364:397:412:450:467:484:528:548 SD: 0.2693 cents 309:337:350:363:396:411:448:465:507:526:546:596:618 SD: 0.1991 cents 349:381:395:410:447:464:506:525:573:594:617:673:698 SD: 0.1979 cents 373:407:422:438:478:496:541:561:612:635:659:719:746 SD: 0.1419 cents 498:543:564:585:638:662:722:749:817:848:880:960:996 SD: 0.1302 cents 516:563:584:606:661:686:748:776:847:879:912:995:1032 SD: 0.1291 cents 538:587:609:632:689:715:780:809:883:916:951:1037:1076 SD: 0.1268 cents 562:613:636:660:720:747:815:846:922:957:993:1083:1124 SD: 0.1003 cents