Scala analysis: xen13-chalmers-13tet-5L3S
5L+3S Eight-Tone Moment of Symmetry (MOS)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184.615 cents 184.615385 2: 369.231 cents 369.230769 3: 461.538 cents 461.538462 4: 646.154 cents 646.153846 5: 830.769 cents 830.769231 6: 923.077 cents 923.076923 7: 1107.692 cents 1107.692308 8: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 92.3077 cents 92.3077 1: 184.6154 cents 184.6154 2: 184.6154 cents 184.6154 3: 92.3077 cents 92.3077 4: 184.6154 cents 184.6154 5: 184.6154 cents 184.6154 6: 92.3077 cents 92.3077 7: 184.6154 cents 184.6154 8: 92.3077 cents 92.3077
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 92.30769 cents 1: 5 184.61539 cents 2: 6 276.92308 cents 2: 2 369.23077 cents 3: 1 369.23077 cents 3: 7 461.53846 cents 4: 4 553.84615 cents 4: 4 646.15385 cents 5: 7 738.46154 cents 5: 1 830.76923 cents 6: 2 830.76923 cents 6: 6 923.07692 cents 7: 5 1015.38461 cents 7: 3 1107.69231 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 0.0 : 184.6 369.2 461.5 646.2 830.8 923.1 1107.7 1200.0 184.6 : 184.6 276.9 461.5 646.2 738.5 923.1 1015.4 1200.0 369.2 : 92.3 276.9 461.5 553.8 738.5 830.8 1015.4 1200.0 461.5 : 184.6 369.2 461.5 646.2 738.5 923.1 1107.7 1200.0 646.2 : 184.6 276.9 461.5 553.8 738.5 923.1 1015.4 1200.0 830.8 : 92.3 276.9 369.2 553.8 738.5 830.8 1015.4 1200.0 923.1 : 184.6 276.9 461.5 646.2 738.5 923.1 1107.7 1200.0 1107.7: 92.3 276.9 461.5 553.8 738.5 923.1 1015.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.3077 .. 184.6154 cents 92.30769 cents 92.30769 cents 2: 276.9231 .. 369.2308 cents 92.30769 cents 92.30769 cents 3: 369.2308 .. 461.5385 cents 92.30769 cents 1/1, 0.0000 cents 4: 553.8462 .. 646.1538 cents 92.30769 cents 92.30769 cents 5: 738.4615 .. 830.7692 cents 92.30769 cents 92.30769 cents 6: 830.7692 .. 923.0769 cents 92.30769 cents 1/1, 0.0000 cents 7: 1015.3846 .. 1107.6923 cents 92.30769 cents 92.30769 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 92.30769 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 184.61539 cents Average / Smallest step : 1.625000 Largest / Average step : 1.230769 Largest / Smallest step : 2.000000 Median interval of one step : 184.61539 cents, amount: 5 Most common interval of one step : 184.61539 cents, amount: 5 Least squares average step : 156.56109 cents, oct.: 1252.48869 cents Scale is proper Scale has Myhill's property chromas: 92.30769 cents and 0.00000 cents, ratio: 92307732.954128 generators: 3 of 461.53846 cents and 738.46154 cents Scale is maximally even in 13-tone equal temperament ET pair of linear temperament : 13&200000000 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 13-tone equal temperament with octave 1200.000 cents degrees: 2 4 5 7 9 10 12 13 generators: 5 and 8 Number of contiguous 1-step segments: 3 Step pattern alph. order: AABAABAB Step pattern size order : LLSLLSLS Interval vector is [ 3 5 6 3 7 4 ] Scale is not a Constant Structure Scale diversity : 1.233480 Rothenberg stability : 0.892857 = 25/28 Lumma stability : 0.461538 Rothenberg efficiency : 0.758929 redundancy: 0.241071 Efficiency x scale size : 6.071429 Number of different interval sizes : 12 = 1.71429 / 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 : 92.30769 cents Most common intervals : 461.53846 cents & inv., amount: 7 Scale is a chain of 4 triads 0.0 184.615 738.462 cents Most common triad is 0.0 461.538 738.462 cents, amount: 6 Number of recognisable fifths : 0 Scale contains two identical conjunct tetrachords Formal octave complements present : 3 = 37.5000% Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties --
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 48.2688 c. M: 80.7692 c. 9: 1 2 0 2 1 1 1 1 P D3 SD: 36.2619 c. M: 61.5385 c. 10: 2 1 1 1 2 1 1 1 P B ME SD: 31.3031 c. M:-55.3846 c. 13: 2 2 1 2 2 1 2 1 P M ME SD: 0.0000 c. M: 0.0000 c. Dylathian, False Father
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 27.9006 cents 3 x x 4 x x 5 x 6 S SD: 17.7383 cents 4 x 5 x 6 x 7 x 8 S SD: 18.5381 cents 5 x 6 x 7:8 x 9:10 S SD: 24.7639 cents 6:7 x 8:9 x 10:11:12 S SD: 21.1567 cents 7:8 x 9:10:11:12:13:14 S SD: 12.3026 cents 8:9:10 x 12:13:14:15:16 S SD: 11.3779 cents 9:10:11:12:13 x 15:17:18 SD: 8.3886 cents 11:12 x 14:16:18:19:21:22 SD: 9.3119 cents 13:14:16:17:19:21:22:25:26 SD: 8.0423 cents 16:18:20:21:23:26:27:30:32 SD: 5.3589 cents 17:19:21:22:25:27:29:32:34 SD: 5.3356 cents 20:22:25:26:29:32:34:38:40 SD: 4.0740 cents 26:29:32:34:38:42:44:49:52 SD: 2.8048 cents 37:41:46:48:54:60:63:70:74 SD: 2.3458 cents 42:47:52:55:61:68:72:80:84 SD: 2.1824 cents 46:51:57:60:67:74:78:87:92 SD: 1.8683 cents 55:61:68:72:80:89:94:104:110 SD: 1.3312 cents 71:79:88:93:103:115:121:135:142 SD: 1.1391 cents 88:98:109:115:128:142:150:167:176 SD: 0.5833 cents 135:150:167:176:196:218:230:256:270 SD: 0.4639 cents 177:197:219:231:257:286:302:336:354 SD: 0.3727 cents 203:226:251:265:295:328:346:385:406 SD: 0.2966 cents 223:248:276:291:324:360:380:423:446 SD: 0.2664 cents 294:327:364:384:427:475:501:557:588 SD: 0.2301 cents 328:365:406:428:476:530:559:622:656 SD: 0.2164 cents 354:394:438:462:514:572:603:671:708 SD: 0.2111 cents 383:426:474:500:556:619:653:726:766 SD: 0.1644 cents 416:463:515:543:604:672:709:789:832 SD: 0.1540 cents 471:524:583:615:684:761:803:893:942 SD: 0.0872 cents