Scala analysis: xen18-erlich-wurschmidt-07
3L 4s MOS for Wurschmidt, L=350.87, s=36.77
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36.770 cents 36.770000 2: 387.640 cents 387.640000 3: 424.410 cents 424.410000 4: 775.280 cents 775.280000 5: 812.050 cents 812.050000 6: 1162.920 cents 1162.920000 7: 1199.690 cents 1199.690000
SHOW/INTERVAL
0: 36.7700 cents 36.7700 1: 36.7700 cents 36.7700 2: 350.8700 cents 350.8700 3: 36.7700 cents 36.7700 4: 350.8700 cents 350.8700 5: 36.7700 cents 36.7700 6: 350.8700 cents 350.8700 7: 36.7700 cents 36.7700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 36.77000 cents 1: 3 350.87000 cents 2: 1 73.54000 cents 2: 6 387.64000 cents 3: 5 424.41000 cents 3: 2 738.51000 cents 4: 2 461.18000 cents 4: 5 775.28000 cents 5: 6 812.05000 cents 5: 1 1126.15000 cents 6: 3 848.82000 cents 6: 4 1162.92000 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 0.0 : 36.8 387.6 424.4 775.3 812.0 1162.9 1199.7 36.8 : 350.9 387.6 738.5 775.3 1126.2 1162.9 1199.7 387.6 : 36.8 387.6 424.4 775.3 812.1 848.8 1199.7 424.4 : 350.9 387.6 738.5 775.3 812.0 1162.9 1199.7 775.3 : 36.8 387.6 424.4 461.2 812.1 848.8 1199.7 812.0 : 350.9 387.6 424.4 775.3 812.1 1162.9 1199.7 1162.9: 36.8 73.5 424.4 461.2 812.1 848.8 1199.7 1199.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7700 .. 350.8700 cents 314.10000 cents 36.77000 cents 2: 73.5400 .. 387.6400 cents 314.10000 cents -277.33000 cents 3: 424.4100 .. 738.5100 cents 314.10000 cents 36.77000 cents 4: 461.1800 .. 775.2800 cents 314.10000 cents -277.33000 cents 5: 812.0500 .. 1126.1500 cents 314.10000 cents 36.77000 cents 6: 848.8200 .. 1162.9200 cents 314.10000 cents -277.33000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36.77000 cents, class 1 Average step (divided formal octave): 171.3843 cents Largest one step interval : 350.87000 cents Average / Smallest step : 4.660981 Largest / Average step : 2.047271 Largest / Smallest step : 9.542290 Median interval of one step : 36.77000 cents, amount: 4 Most common interval of one step : 36.77000 cents, amount: 4 Least squares average step : 175.87143 cents, oct.: 1231.10000 cents Scale is not proper Scale has Myhill's property chromas: 314.10000 cents and 277.33000 cents, ratio: 1.132586 generators: 2 of 387.64000 cents and 5 of 812.05000 cents ET pair of linear temperament : 31&34 Scale is distributional even Scale is a mode of a 783-tone equal temperament with octave 1199.690 cents degrees: 24 253 277 506 530 759 783 generators: 253 and 530 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABABA Step pattern size order : SLSLSLS Scale is a Constant Structure, by a margin of 36.77000 cents Scale diversity : 0.911531 Lumma stability : 0.122598 Lumma impropriety factor : 0.693504 Rothenberg efficiency : 0.761905 redundancy: 0.238095 Efficiency x scale size : 5.333333 Number of different interval sizes : 12 = 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 : 36.77000 cents Most common intervals : 387.64000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 387.640 775.280 cents Most common triad is 0.0 387.640 812.050 cents, amount: 5 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Scale contains two identical disjunct tetrachords Formal octave complements present : 7 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties --
FIT/MODE
7: 0 2 0 2 0 2 1 N T3 SD: 86.3639 c. M: 134.6143 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 40.9712 c. M:-62.2437 c. 9: 0 3 0 3 0 3 0 N M DE I SD: 24.5133 c. M:-36.7700 c. 17: 0 5 1 5 0 5 1 N T3 SD: 26.6913 c. M: 36.7700 c. 19: 1 5 1 5 1 5 1 N M DE I SD: 17.5811 c. M:-26.3716 c. 22: 1 6 1 6 1 6 1 N M DE I SD: 11.8409 c. M:-17.7614 c. 25: 1 7 1 7 1 7 1 N M DE I SD: 7.4784 c. M:-11.2176 c. 28: 1 8 1 8 1 8 1 N M DE I SD: 4.0507 c. M:-6.0761 c. 31: 1 9 1 9 1 9 1 N M DE I SD: 1.2865 c. M:-1.9297 c. 34: 1 10 1 10 1 10 1 N M DE I SD: 0.9900 c. M:-1.4850 c. 65: 2 19 2 19 2 19 2 N M DE I SD: 0.0957 c. M:-0.1435 c. 229: 7 67 7 67 7 67 7 N M DE I SD: 0.0655 c. M:-0.0983 c. 294: 9 86 9 86 9 86 9 N M DE I SD: 0.0299 c. M:-0.0448 c. 359: 11 105 11 105 11 105 11 N M DE I SD: 0.0071 c. M:-0.0107 c. 783: 24 229 24 229 24 229 24 N M DE I SD: 0.0014 c. M:-0.0021 c. 1142: 35 334 35 334 35 334 35 N M DE I SD: 0.0013 c. M:-0.0019 c. 1925: 59 563 59 563 59 563 59 N M DE I SD: 0.0002 c. M:-0.0003 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.3100 cents 2 x x x 3 x x 4 S SD: 36.6628 cents 3 x x 4 x 5 x 6 S SD: 34.4008 cents 4 x 5 x 6 x x 8 S SD: 24.4459 cents 5 x 6 x x 8 x 10 S SD: 24.0060 cents 6 x x 8:9:10 x 12 S SD: 31.6498 cents 7 x x 9:11 x x 14 SD: 4.2953 cents 8:9:10 x x 13 x 16 SD: 42.3885 cents 9:10:11:12:14 x x 18 SD: 33.6793 cents 10:11 x 13 x 16 x 20 SD: 32.9157 cents 11:12 x 14:17:18 x 22 SD: 24.5972 cents 12:13:15 x x 19:23:24 SD: 21.8881 cents 13:14:16:17:20:21:25:26 SD: 16.2402 cents 14:15 x 18:22 x 27:28 SD: 17.5165 cents 15:16 x 19:23:24:29:30 SD: 14.4945 cents 16:17:20 x 25:26:31:32 SD: 12.6809 cents 17:18:21:22 x 27:33:34 SD: 11.9747 cents 18:19 x 23:28:29:35:36 SD: 10.0824 cents 19:20:24 x 30 x 37:38 SD: 11.5095 cents 20:21:25:26:31:32:39:40 SD: 8.4365 cents 21:22:26:27:33:34:41:42 SD: 7.7100 cents 22:23 x 28:34:35:43:44 SD: 7.8283 cents 23:24:29 x 36:37:45:46 SD: 6.8143 cents 24:25:30:31 x 38:47:48 SD: 7.0163 cents 25:26:31:32:39:40:49:50 SD: 5.0437 cents 26:27 x 33:41:42:51:52 SD: 6.3929 cents 27:28:34:35:42:43:53:54 SD: 5.7251 cents 28:29:35:36:44:45:55:56 SD: 4.2014 cents 30:31 x 38:47:48:59:60 SD: 4.4102 cents 32:33:40:41:50:51:63:64 SD: 2.9473 cents 34:35 x 43:53:54:67:68 SD: 4.7101 cents 35:36:44:45:55:56:69:70 SD: 3.3004 cents 37:38:46:47:58:59:72:74 SD: 3.0031 cents 39:40:49:50:61:62:76:78 SD: 2.4442 cents 40:41:50:51:63:64:78:80 SD: 2.1407 cents 43:44:54:55:67:69:84:86 SD: 1.8683 cents 44:45:55:56:69:70:86:88 SD: 1.7044 cents 48:49:60:61:75:77:94:96 SD: 1.6782 cents 55:56:69:70:86:88:108:110 SD: 1.6675 cents 75:77:94:96:117:120:147:150 SD: 1.6505 cents 76:78:95:97:119:121:149:152 SD: 1.6211 cents 79:81:99:101:124:126:155:158 SD: 1.4974 cents 80:82:100:102:125:128:157:160 SD: 1.2813 cents 83:85:104:106:130:133:162:166 SD: 1.2427 cents 87:89:109:111:136:139:170:174 SD: 0.8458 cents 97:99:121:124:152:155:190:194 SD: 0.8274 cents 136:139:170:174:213:217:266:272 SD: 0.6671 cents 140:143:175:179:219:224:274:280 SD: 0.3566 cents 184:188:230:235:288:294:360:368 SD: 0.2996 cents 234:239:293:299:366:374:458:468 SD: 0.2748 cents 324:331:405:414:507:518:634:648 SD: 0.2280 cents 331:338:414:423:518:529:648:662 SD: 0.1121 cents 558:570:698:713:873:892:1092:1116 SD: 0.1110 cents