Scala analysis: xen18-erlich-wurschmidt-13
3L 10s MOS for Wurschmidt, L=277.33, 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: 73.540 cents 73.540000 3: 350.870 cents 350.870000 4: 387.640 cents 387.640000 5: 424.410 cents 424.410000 6: 461.180 cents 461.180000 7: 738.510 cents 738.510000 8: 775.280 cents 775.280000 9: 812.050 cents 812.050000 10: 848.820 cents 848.820000 11: 1126.150 cents 1126.150000 12: 1162.920 cents 1162.920000 13: 1199.690 cents 1199.690000
SHOW/INTERVAL
0: 36.7700 cents 36.7700 1: 36.7700 cents 36.7700 2: 36.7700 cents 36.7700 3: 277.3300 cents 277.3300 4: 36.7700 cents 36.7700 5: 36.7700 cents 36.7700 6: 36.7700 cents 36.7700 7: 277.3300 cents 277.3300 8: 36.7700 cents 36.7700 9: 36.7700 cents 36.7700 10: 36.7700 cents 36.7700 11: 277.3300 cents 277.3300 12: 36.7700 cents 36.7700 13: 36.7700 cents 36.7700
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 36.77000 cents 1: 3 277.33000 cents 2: 7 73.54000 cents 2: 6 314.10000 cents 3: 4 110.31000 cents 3: 9 350.87000 cents 4: 1 147.08000 cents 4: 12 387.64000 cents 5: 11 424.41000 cents 5: 2 664.97000 cents 6: 8 461.18000 cents 6: 5 701.74000 cents 7: 5 497.95000 cents 7: 8 738.51000 cents 8: 2 534.72000 cents 8: 11 775.28000 cents 9: 12 812.05000 cents 9: 1 1052.61000 cents 10: 9 848.82000 cents 10: 4 1089.38000 cents 11: 6 885.59000 cents 11: 7 1126.15000 cents 12: 3 922.36000 cents 12: 10 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 11 12 13 0.0 : 36.8 73.5 350.9 387.6 424.4 461.2 738.5 775.3 812.0 848.8 1126.2 1162.9 1199.7 36.8 : 36.8 314.1 350.9 387.6 424.4 701.7 738.5 775.3 812.1 1089.4 1126.2 1162.9 1199.7 73.5 : 277.3 314.1 350.9 387.6 665.0 701.7 738.5 775.3 1052.6 1089.4 1126.2 1162.9 1199.7 350.9 : 36.8 73.5 110.3 387.6 424.4 461.2 497.9 775.3 812.1 848.8 885.6 922.4 1199.7 387.6 : 36.8 73.5 350.9 387.6 424.4 461.2 738.5 775.3 812.1 848.8 885.6 1162.9 1199.7 424.4 : 36.8 314.1 350.9 387.6 424.4 701.7 738.5 775.3 812.0 848.8 1126.2 1162.9 1199.7 461.2 : 277.3 314.1 350.9 387.6 665.0 701.7 738.5 775.3 812.1 1089.4 1126.2 1162.9 1199.7 738.5 : 36.8 73.5 110.3 387.6 424.4 461.2 497.9 534.7 812.1 848.8 885.6 922.4 1199.7 775.3 : 36.8 73.5 350.9 387.6 424.4 461.2 498.0 775.3 812.1 848.8 885.6 1162.9 1199.7 812.0 : 36.8 314.1 350.9 387.6 424.4 461.2 738.5 775.3 812.1 848.8 1126.2 1162.9 1199.7 848.8 : 277.3 314.1 350.9 387.6 424.4 701.7 738.5 775.3 812.1 1089.4 1126.2 1162.9 1199.7 1126.2: 36.8 73.5 110.3 147.1 424.4 461.2 497.9 534.7 812.1 848.8 885.6 922.4 1199.7 1162.9: 36.8 73.5 110.3 387.6 424.4 461.2 498.0 775.3 812.1 848.8 885.6 1162.9 1199.7 1199.7
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.7700 .. 277.3300 cents 240.56000 cents 36.77000 cents 2: 73.5400 .. 314.1000 cents 240.56000 cents -203.79000 cents 3: 110.3100 .. 350.8700 cents 240.56000 cents -203.79000 cents 4: 147.0800 .. 387.6400 cents 240.56000 cents -203.79000 cents 5: 424.4100 .. 664.9700 cents 240.56000 cents 36.77000 cents 6: 461.1800 .. 701.7400 cents 240.56000 cents -203.79000 cents 7: 497.9500 .. 738.5100 cents 240.56000 cents -203.79000 cents 8: 534.7200 .. 775.2800 cents 240.56000 cents -203.79000 cents 9: 812.0500 .. 1052.6100 cents 240.56000 cents 36.77000 cents 10: 848.8200 .. 1089.3800 cents 240.56000 cents -203.79000 cents 11: 885.5900 .. 1126.1500 cents 240.56000 cents -203.79000 cents 12: 922.3600 .. 1162.9200 cents 240.56000 cents -203.79000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 36.77000 cents, class 1 Average step (divided formal octave): 92.2838 cents Largest one step interval : 277.33000 cents Average / Smallest step : 2.509759 Largest / Average step : 3.005185 Largest / Smallest step : 7.542290 Median interval of one step : 36.77000 cents, amount: 10 Most common interval of one step : 36.77000 cents, amount: 10 Least squares average step : 93.75247 cents, oct.: 1218.78206 cents Scale is not proper Scale has Myhill's property chromas: 240.56000 cents and 203.79000 cents, ratio: 1.180431 generators: 4 of 387.64000 cents and 9 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 48 229 253 277 301 482 506 530 554 735 759 783 generators: 253 and 530 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAAABAAABAA Step pattern size order : SSLSSSLSSSLSS Scale is a Constant Structure, by a margin of 36.77000 cents Scale diversity : 1.123675 Lumma stability : 0.122598 Lumma impropriety factor : 0.693504 Rothenberg efficiency : 0.717949 redundancy: 0.282051 Efficiency x scale size : 9.333333 Number of different interval sizes : 24 = 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: 12 Scale is a chain of 6 triads 0.0 387.640 775.280 cents Most common triad is 0.0 387.640 812.050 cents, amount: 11 Number of recognisable fifths : 5, average 701.7400 cents Number of recognisable fourths : 5, average 497.9500 cents Formal octave complements present : 13 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 6-7 -- Rational properties --
FIT/MODE
13: 0 1 3 0 1 0 3 0 1 0 3 1 0 N I SD: 24.0165 c. M:-37.0092 c. 16: 0 1 4 0 1 0 4 0 1 0 4 1 0 N I SD: 21.0144 c. M:-36.7700 c. 17: 1 0 4 0 1 1 3 1 1 0 4 0 1 N I SD: 23.0151 c. M:-34.7900 c. 18: 1 0 4 1 0 1 4 1 0 1 4 0 1 N I SD: 17.6755 c. M:-29.8794 c. 20: 1 0 5 0 1 1 4 1 1 0 5 0 1 N I SD: 17.2912 c. M:-27.7330 c. 21: 1 0 5 1 0 1 5 1 0 1 5 0 1 N I SD: 15.2811 c. M:-24.5133 c. 28: 1 1 6 1 1 1 6 1 1 1 6 1 1 N M DE I SD: 7.5782 c. M: 12.1521 c. 31: 1 1 7 1 1 1 7 1 1 1 7 1 1 N M DE I SD: 2.4067 c. M: 3.8594 c. 34: 1 1 8 1 1 1 8 1 1 1 8 1 1 N M DE I SD: 1.8521 c. M: 2.9700 c. 65: 2 2 15 2 2 2 15 2 2 2 15 2 2 N M DE I SD: 0.1790 c. M: 0.2871 c. 229: 7 7 53 7 7 7 53 7 7 7 53 7 7 N M DE I SD: 0.1225 c. M: 0.1965 c. 294: 9 9 68 9 9 9 68 9 9 9 68 9 9 N M DE I SD: 0.0559 c. M: 0.0896 c. 359: 11 11 83 11 11 11 83 11 11 11 83 11 11 N M DE I SD: 0.0133 c. M: 0.0214 c. 783: 24 24 181 24 24 24 181 24 24 24 181 24 24 N M DE I SD: 0.0026 c. M: 0.0042 c. 1142: 35 35 264 35 35 35 264 35 35 35 264 35 35 N M DE I SD: 0.0024 c. M: 0.0038 c. 1925: 59 59 445 59 59 59 445 59 59 59 445 59 59 N M DE I SD: 0.0003 c. M: 0.0006 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 0.3100 cents 2 x x x x x x 3 x x x x x 4 S SD: 18.2782 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 17.0689 cents 4 x x x 5 x x 6 x x 7 x x 8 S SD: 31.3643 cents 5 x x 6 x x 7 x x 8 x x x 10 S SD: 31.5885 cents 6 x x 7 x x 8:9 x x 10 x x 12 S SD: 20.9898 cents 7 x x x x 9 x x 11 x x 13 x 14 SD: 13.9881 cents 8 x 9 x 10 x x 12 x x 13:15 x 16 SD: 23.4747 cents 9 x 10:11 x x 12 x 14 x 15:17 x 18 SD: 17.6260 cents 10 x 11:12 x x 13:15 x 16 x 19 x 20 SD: 15.1306 cents 11 x 12:13 x 14 x 17 x x 18:21 x 22 SD: 14.3438 cents 12 x 13 x 15 x 16:18 x 19:20:23 x 24 SD: 11.4982 cents 13 x 14:16 x x 17:20 x 21 x 25 x 26 SD: 8.4549 cents 14 x 15:17 x 18 x 21:22 x 23:27 x 28 SD: 7.9630 cents 15 x 16:18 x 19:20:23 x 24 x 29 x 30 SD: 8.4071 cents 16 x 17 x 20 x 21 x 25 x 26 x 31:32 SD: 5.4895 cents 17 x 18:21 x x 22:26 x 27:28 x 33:34 SD: 5.0955 cents 18 x 19:22 x 23 x x 28:29 x x 35:36 SD: 4.1505 cents 19 x 20:23:24 x 25:29:30 x 31:36:37:38 SD: 4.3236 cents 20 x 21:24:25 x 26 x 31:32:33:38:39:40 SD: 4.7810 cents 21 x 22 x 26:27 x 32:33 x 34:40:41:42 SD: 3.4609 cents 22 x 23:27 x 28:29:34 x 35:36:42:43:44 SD: 2.6973 cents 23 x 24:28:29 x 30:35:36:37:38:44:45:46 SD: 2.8449 cents 24 x 25:29:30 x 31:37 x 38:39:46:47:48 SD: 3.6574 cents 25 x 26 x 31:32:33:38:39:40:41:48:49:50 SD: 2.7899 cents 26 x 27:32 x 33:34:40:41:42 x 50:51:52 SD: 2.9923 cents 27 x 28:33:34 x 35:41:42:43:44:52:53:54 SD: 2.7056 cents 28 x 29:34:35:36:37:43:44:45:46:54:55:56 SD: 3.0901 cents 29 x 30 x 36:37:38:44:45:46:47:56:57:58 SD: 3.5329 cents 30 x 31:37 x 38:39:46:47:48:49:57:59:60 SD: 2.8823 cents 31:32 x 38:39:40 x 47:49:50:51:59:61:62 SD: 4.0415 cents 32:33 x 39:40:41:42:49:50:51:52:61:63:64 SD: 2.2723 cents 33:34 x 40:41:42:43:51:52:53:54:63:65:66 SD: 3.0602 cents 34:35 x 42 x 43:44:52:53:54:56:65:67:68 SD: 3.5153 cents 35:36:37:43:44:45:46:54:55:56:57:67:69:70 SD: 2.8720 cents 36:37:38:44:45:46:47:55:56:58:59:69:70:72 SD: 2.4618 cents 39:40:41:48:49:50:51:60:61:62:64:75:76:78 SD: 2.0516 cents 40:41:42:49:50:51:52:61:63:64:65:77:78:80 SD: 1.8581 cents 43:44:45:53:54:55:56:66:67:69:70:82:84:86 SD: 1.6280 cents 49:50:51:60:61:63:64:75:77:78:80:94:96:98 SD: 1.3742 cents 68:69:71:83:85:87:89:104:106:109:111:130:133:136 SD: 1.3188 cents 71:73:74:87:89:91:93:109:111:113:116:136:139:142 SD: 1.2982 cents 72:74:75:88:90:92:94:110:113:115:118:138:141:144 SD: 1.1614 cents 84:86:88:103:105:107:110:129:131:134:137:161:164:168 SD: 1.1502 cents 85:87:89:104:106:109:111:130:133:136:139:163:166:170 SD: 0.9608 cents 88:90:92:108:110:112:115:135:138:141:144:169:172:176 SD: 0.9533 cents 89:91:93:109:111:114:116:136:139:142:145:171:174:178 SD: 0.9145 cents 92:94:96:113:115:118:120:141:144:147:150:176:180:184 SD: 0.7269 cents 115:117:120:141:144:147:150:176:180:184:188:220:225:230 SD: 0.6776 cents 133:136:139:163:166:170:174:204:208:213:217:255:260:266 SD: 0.6400 cents 134:137:140:164:168:171:175:205:210:214:219:257:262:268 SD: 0.5627 cents 137:140:143:168:171:175:179:210:214:219:224:263:268:274 SD: 0.5498 cents 141:144:147:173:176:180:184:216:221:225:230:270:276:282 SD: 0.5494 cents 144:147:150:176:180:184:188:221:225:230:235:276:282:288 SD: 0.5041 cents 147:150:153:180:184:188:192:225:230:235:240:282:288:294 SD: 0.4472 cents 179:183:187:219:224:229:234:274:280:286:292:343:350:358 SD: 0.4332 cents 180:184:188:220:225:230:235:276:282:288:294:345:352:360 SD: 0.4291 cents 183:187:191:224:229:234:239:280:286:293:299:351:358:366 SD: 0.4000 cents 184:188:192:225:230:235:240:282:288:294:300:353:360:368 SD: 0.3661 cents 187:191:195:229:234:239:244:286:293:299:305:358:366:374 SD: 0.3649 cents 191:195:199:234:239:244:249:293:299:305:312:366:374:382 SD: 0.3600 cents 226:231:236:277:283:289:295:346:354:361:369:433:442:452 SD: 0.3312 cents 227:232:237:278:284:290:296:348:355:363:371:435:444:454 SD: 0.2803 cents 275:281:287:337:344:351:359:421:430:440:449:527:538:550 SD: 0.2795 cents 276:282:288:338:345:353:360:423:432:441:451:529:540:552 SD: 0.2416 cents 299:305:312:366:374:382:390:458:468:478:488:573:585:598 SD: 0.2395 cents 321:328:335:393:402:410:419:492:502:513:524:615:628:642 SD: 0.2279 cents 324:331:338:397:405:414:423:496:507:518:529:621:634:648 SD: 0.1778 cents 370:378:386:453:463:473:483:567:579:591:604:709:724:740 SD: 0.1555 cents 458:468:478:561:573:585:598:702:717:732:748:878:897:916 SD: 0.1522 cents 511:522:533:626:639:653:667:783:800:817:834:979:1000:1022 SD: 0.1367 cents 515:526:537:631:644:658:672:789:806:823:841:987:1008:1030 SD: 0.1366 cents 547:559:571:670:684:699:714:838:856:874:893:1048:1071:1094 SD: 0.1315 cents 551:563:575:675:689:704:719:844:862:881:900:1056:1079:1102 SD: 0.1271 cents 597:610:623:731:747:763:779:915:934:954:975:1144:1169:1194 SD: 0.1217 cents