Scala analysis: xen18-erlich-wurschmidt-10
3L 7s MOS for Wurschmidt, L=314.10, 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: 350.870 cents 350.870000 3: 387.640 cents 387.640000 4: 424.410 cents 424.410000 5: 738.510 cents 738.510000 6: 775.280 cents 775.280000 7: 812.050 cents 812.050000 8: 848.820 cents 848.820000 9: 1162.920 cents 1162.920000 10: 1199.690 cents 1199.690000
SHOW/INTERVAL
0: 36.7700 cents 36.7700 1: 36.7700 cents 36.7700 2: 314.1000 cents 314.1000 3: 36.7700 cents 36.7700 4: 36.7700 cents 36.7700 5: 314.1000 cents 314.1000 6: 36.7700 cents 36.7700 7: 36.7700 cents 36.7700 8: 36.7700 cents 36.7700 9: 314.1000 cents 314.1000 10: 36.7700 cents 36.7700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 36.77000 cents 1: 3 314.10000 cents 2: 4 73.54000 cents 2: 6 350.87000 cents 3: 1 110.31000 cents 3: 9 387.64000 cents 4: 8 424.41000 cents 4: 2 701.74000 cents 5: 5 461.18000 cents 5: 5 738.51000 cents 6: 2 497.95000 cents 6: 8 775.28000 cents 7: 9 812.05000 cents 7: 1 1089.38000 cents 8: 6 848.82000 cents 8: 4 1126.15000 cents 9: 3 885.59000 cents 9: 7 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 8 9 10 0.0 : 36.8 350.9 387.6 424.4 738.5 775.3 812.0 848.8 1162.9 1199.7 36.8 : 314.1 350.9 387.6 701.7 738.5 775.3 812.1 1126.2 1162.9 1199.7 350.9 : 36.8 73.5 387.6 424.4 461.2 497.9 812.1 848.8 885.6 1199.7 387.6 : 36.8 350.9 387.6 424.4 461.2 775.3 812.1 848.8 1162.9 1199.7 424.4 : 314.1 350.9 387.6 424.4 738.5 775.3 812.0 1126.2 1162.9 1199.7 738.5 : 36.8 73.5 110.3 424.4 461.2 497.9 812.1 848.8 885.6 1199.7 775.3 : 36.8 73.5 387.6 424.4 461.2 775.3 812.1 848.8 1162.9 1199.7 812.0 : 36.8 350.9 387.6 424.4 738.5 775.3 812.1 1126.2 1162.9 1199.7 848.8 : 314.1 350.9 387.6 701.7 738.5 775.3 1089.4 1126.2 1162.9 1199.7 1162.9: 36.8 73.5 387.6 424.4 461.2 775.3 812.1 848.8 885.6 1199.7 1199.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7700 .. 314.1000 cents 277.33000 cents 36.77000 cents 2: 73.5400 .. 350.8700 cents 277.33000 cents -240.56000 cents 3: 110.3100 .. 387.6400 cents 277.33000 cents -240.56000 cents 4: 424.4100 .. 701.7400 cents 277.33000 cents 36.77000 cents 5: 461.1800 .. 738.5100 cents 277.33000 cents -240.56000 cents 6: 497.9500 .. 775.2800 cents 277.33000 cents -240.56000 cents 7: 812.0500 .. 1089.3800 cents 277.33000 cents 36.77000 cents 8: 848.8200 .. 1126.1500 cents 277.33000 cents -240.56000 cents 9: 885.5900 .. 1162.9200 cents 277.33000 cents -240.56000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 36.77000 cents, class 1 Average step (divided formal octave): 119.9690 cents Largest one step interval : 314.10000 cents Average / Smallest step : 3.262687 Largest / Average step : 2.618176 Largest / Smallest step : 8.542290 Median interval of one step : 36.77000 cents, amount: 7 Most common interval of one step : 36.77000 cents, amount: 7 Least squares average step : 121.76984 cents, oct.: 1217.69844 cents Scale is not proper Scale has Myhill's property chromas: 277.33000 cents and 240.56000 cents, ratio: 1.152852 generators: 3 of 387.64000 cents and 7 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: 24 229 253 277 482 506 530 554 759 783 generators: 253 and 530 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAAABA Step pattern size order : SLSSLSSSLS Scale is a Constant Structure, by a margin of 36.77000 cents Scale diversity : 0.993188 Lumma stability : 0.122598 Lumma impropriety factor : 0.693504 Rothenberg efficiency : 0.733333 redundancy: 0.266667 Efficiency x scale size : 7.333333 Number of different interval sizes : 18 = 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: 9 Scale is a chain of 5 triads 0.0 350.870 812.050 cents Most common triad is 0.0 387.640 812.050 cents, amount: 8 Number of recognisable fifths : 2, average 701.7400 cents Number of recognisable fourths : 2, average 497.9500 cents Formal octave complements present : 9 = 90.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 6-7 -- Rational properties --
FIT/MODE
10: 0 3 0 1 2 0 1 0 3 0 N SD: 33.0275 c. M: 55.4660 c. 11: 0 3 1 0 3 0 0 1 3 0 N SD: 30.7468 c. M:-48.6109 c. 13: 0 4 0 1 3 0 1 0 4 0 N SD: 26.0683 c. M:-37.0092 c. 14: 1 3 1 0 4 0 1 0 4 0 N SD: 29.4276 c. M:-48.9221 c. 15: 0 4 1 0 4 1 0 1 4 0 N SD: 25.4401 c. M:-36.7700 c. 17: 0 5 0 1 4 1 0 1 4 1 N SD: 24.6401 c. M: 36.7700 c. 18: 1 4 1 0 5 1 0 1 4 1 N SD: 19.8437 c. M:-29.8794 c. 20: 0 6 0 1 5 1 0 1 5 1 N SD: 20.6251 c. M: 36.7700 c. 21: 1 5 1 0 6 1 0 1 5 1 N SD: 15.7470 c. M:-24.5133 c. 23: 1 6 0 1 6 1 1 0 6 1 N SD: 14.3664 c. M:-22.5170 c. 24: 1 6 1 1 6 1 0 1 6 1 N SD: 14.2446 c. M:-25.4737 c. 25: 1 6 1 1 6 1 1 1 6 1 N M DE SD: 10.9015 c. M: 18.6960 c. 26: 1 7 0 1 7 1 1 0 7 1 N SD: 13.0178 c. M:-18.5046 c. 27: 1 7 1 1 7 0 1 1 7 1 N SD: 12.4001 c. M:-19.9196 c. 28: 1 7 1 1 7 1 1 1 7 1 N M DE SD: 5.9049 c. M: 10.1268 c. 31: 1 8 1 1 8 1 1 1 8 1 N M DE SD: 1.8753 c. M: 3.2161 c. 34: 1 9 1 1 9 1 1 1 9 1 N M DE SD: 1.4432 c. M:-2.4750 c. 65: 2 17 2 2 17 2 2 2 17 2 N M DE SD: 0.1395 c. M: 0.2392 c. 229: 7 60 7 7 60 7 7 7 60 7 N M DE SD: 0.0955 c. M:-0.1638 c. 294: 9 77 9 9 77 9 9 9 77 9 N M DE SD: 0.0435 c. M:-0.0747 c. 359: 11 94 11 11 94 11 11 11 94 11 N M DE SD: 0.0104 c. M:-0.0178 c. 783: 24 205 24 24 205 24 24 24 205 24 N M DE SD: 0.0020 c. M: 0.0035 c. 1142: 35 299 35 35 299 35 35 35 299 35 N M DE SD: 0.0019 c. M:-0.0032 c. 1925: 59 504 59 59 504 59 59 59 504 59 N M DE SD: 0.0003 c. M:-0.0005 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 0.3100 cents 2 x x x x 3 x x x x 4 S SD: 18.2782 cents 3 x x x 4 x x x 5 x 6 S SD: 27.2544 cents 4 x x 5 x 6 x x 7 x 8 S SD: 31.3643 cents 5 x 6 x x x x 8 x x 10 S SD: 11.7560 cents 6 x 7 x 8:9 x x 10 x 12 S SD: 24.5580 cents 7 x x x 9 x 11 x x x 14 SD: 4.2953 cents 8 x x 10 x 12 x x 13 x 16 SD: 9.3771 cents 9:10:11 x 12 x 14 x 15 x 18 S SD: 27.8955 cents 10:11:12 x 13:15 x 16 x x 20 SD: 23.5185 cents 11:12:13 x 14:17 x x 18 x 22 SD: 21.7680 cents 12:13 x 15 x 18 x 19:20:23:24 SD: 17.2476 cents 13:14:16 x 17:20 x 21 x 25:26 SD: 15.2444 cents 14:15:17 x 18:21:22 x 23:27:28 SD: 12.0786 cents 15:16:18 x 19:23 x 24 x 29:30 SD: 12.4231 cents 16:17 x 20 x x 25 x 26:31:32 SD: 11.8401 cents 17:18:21 x 22:26 x 27:28:33:34 SD: 8.9662 cents 18:19:22 x 23 x 28:29 x 35:36 SD: 8.6562 cents 19:20:23:24 x 29:30 x 31:37:38 SD: 7.6641 cents 20:21:24:25:26 x 31:32:33:39:40 SD: 7.9019 cents 21:22 x 26:27:32:33 x 34:41:42 SD: 6.5241 cents 22:23:27 x 28:34 x 35:36:43:44 SD: 5.5823 cents 23:24:28:29 x 35:36:37:38:45:46 SD: 5.3641 cents 24:25:29:30:31:37 x 38:39:47:48 SD: 5.5553 cents 25:26 x 31:32:38:39:40:41:49:50 SD: 4.2891 cents 26:27:32 x 33:40:41:42 x 51:52 SD: 4.9972 cents 27:28:33:34:35:41:42:43:44:53:54 SD: 4.3172 cents 28:29:34:35:36:43:44:45:46:55:56 SD: 3.4823 cents 29:30 x 36:37:44:45:46:47:57:58 SD: 4.3789 cents 30:31:37 x 38:46:47:48:49:59:60 SD: 3.2427 cents 32:33:39:40:41:49:50:51:52:63:64 SD: 2.3780 cents 34:35:42 x 43:52:53:54:56:67:68 SD: 3.9401 cents 35:36:43:44:45:54:55:56:57:69:70 SD: 2.7083 cents 36:37:44:45:46:55:56:58:59:70:72 SD: 2.4930 cents 39:40:48:49:50:60:61:62:64:76:78 SD: 2.2256 cents 40:41:49:50:51:61:63:64:65:78:80 SD: 1.8883 cents 43:44:53:54:55:66:67:69:70:84:86 SD: 1.8225 cents 44:45:54:55:56:67:69:70:72:86:88 SD: 1.6757 cents 55:56:67:69:70:84:86:88:90:108:110 SD: 1.6241 cents 57:58:70:71:73:87:89:91:93:112:114 SD: 1.5559 cents 72:74:88:90:92:110:113:115:118:141:144 SD: 1.4816 cents 75:77:92:94:96:115:117:120:122:147:150 SD: 1.3644 cents 76:78:93:95:97:116:119:121:124:149:152 SD: 1.3188 cents 79:81:97:99:101:121:124:126:129:155:158 SD: 1.1410 cents 85:87:104:106:109:130:133:136:139:166:170 SD: 1.0831 cents 87:89:107:109:111:133:136:139:142:170:174 SD: 1.0166 cents 90:92:110:113:115:138:141:144:147:176:180 SD: 0.8152 cents 120:123:147:150:153:184:188:192:196:235:240 SD: 0.7863 cents 133:136:163:166:170:204:208:213:217:260:266 SD: 0.6667 cents 137:140:168:171:175:210:214:219:224:268:274 SD: 0.6249 cents 139:142:170:174:178:213:218:222:227:272:278 SD: 0.6195 cents 143:146:175:179:183:219:224:229:233:280:286 SD: 0.6069 cents 144:147:176:180:184:221:225:230:235:282:288 SD: 0.5876 cents 147:150:180:184:188:225:230:235:240:288:294 SD: 0.3347 cents 191:195:234:239:244:293:299:305:312:374:382 SD: 0.3346 cents 227:232:278:284:290:348:355:363:371:444:454 SD: 0.3031 cents 267:273:327:334:341:409:418:427:436:523:534 SD: 0.2480 cents 324:331:397:405:414:496:507:518:529:634:648 SD: 0.2247 cents 338:345:414:423:432:518:529:540:552:662:676 SD: 0.2146 cents 370:378:453:463:473:567:579:591:604:724:740 SD: 0.1980 cents 374:382:458:468:478:573:585:598:611:732:748 SD: 0.1554 cents 414:423:507:518:529:634:648:662:676:810:828 SD: 0.1525 cents 471:481:577:589:602:722:737:753:769:922:942 SD: 0.1493 cents 515:526:631:644:658:789:806:823:841:1008:1030 SD: 0.1279 cents 558:570:683:698:713:855:873:892:911:1092:1116 SD: 0.1256 cents 566:578:693:708:723:867:886:905:924:1108:1132 SD: 0.1214 cents