Scala analysis: xen18-erlich-magic-13
3L 10s MOS for Magic, L=204.16, s=58.88
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 58.880 cents 58.880000 2: 117.760 cents 117.760000 3: 321.920 cents 321.920000 4: 380.800 cents 380.800000 5: 439.680 cents 439.680000 6: 498.560 cents 498.560000 7: 702.720 cents 702.720000 8: 761.600 cents 761.600000 9: 820.480 cents 820.480000 10: 879.360 cents 879.360000 11: 1083.520 cents 1083.520000 12: 1142.400 cents 1142.400000 13: 1201.280 cents 1201.280000
SHOW/INTERVAL
0: 58.8800 cents 58.8800 1: 58.8800 cents 58.8800 2: 58.8800 cents 58.8800 3: 204.1600 cents 204.1600 4: 58.8800 cents 58.8800 5: 58.8800 cents 58.8800 6: 58.8800 cents 58.8800 7: 204.1600 cents 204.1600 8: 58.8800 cents 58.8800 9: 58.8800 cents 58.8800 10: 58.8800 cents 58.8800 11: 204.1600 cents 204.1600 12: 58.8800 cents 58.8800 13: 58.8800 cents 58.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 58.88000 cents 1: 3 204.16000 cents 2: 7 117.76000 cents 2: 6 263.04000 cents 3: 4 176.64000 cents 3: 9 321.92000 cents 4: 1 235.52000 cents 4: 12 380.80000 cents 5: 11 439.68000 cents 5: 2 584.96000 cents 6: 8 498.56000 cents 6: 5 643.84000 cents 7: 5 557.44000 cents 7: 8 702.72000 cents 8: 2 616.32000 cents 8: 11 761.60000 cents 9: 12 820.48000 cents 9: 1 965.76000 cents 10: 9 879.36000 cents 10: 4 1024.64000 cents 11: 6 938.24000 cents 11: 7 1083.52000 cents 12: 3 997.12000 cents 12: 10 1142.40000 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 : 58.9 117.8 321.9 380.8 439.7 498.6 702.7 761.6 820.5 879.4 1083.5 1142.4 1201.3 58.9 : 58.9 263.0 321.9 380.8 439.7 643.8 702.7 761.6 820.5 1024.6 1083.5 1142.4 1201.3 117.8 : 204.2 263.0 321.9 380.8 585.0 643.8 702.7 761.6 965.8 1024.6 1083.5 1142.4 1201.3 321.9 : 58.9 117.8 176.6 380.8 439.7 498.6 557.4 761.6 820.5 879.4 938.2 997.1 1201.3 380.8 : 58.9 117.8 321.9 380.8 439.7 498.6 702.7 761.6 820.5 879.4 938.2 1142.4 1201.3 439.7 : 58.9 263.0 321.9 380.8 439.7 643.8 702.7 761.6 820.5 879.4 1083.5 1142.4 1201.3 498.6 : 204.2 263.0 321.9 380.8 585.0 643.8 702.7 761.6 820.5 1024.6 1083.5 1142.4 1201.3 702.7 : 58.9 117.8 176.6 380.8 439.7 498.6 557.4 616.3 820.5 879.4 938.2 997.1 1201.3 761.6 : 58.9 117.8 321.9 380.8 439.7 498.6 557.4 761.6 820.5 879.4 938.2 1142.4 1201.3 820.5 : 58.9 263.0 321.9 380.8 439.7 498.6 702.7 761.6 820.5 879.4 1083.5 1142.4 1201.3 879.4 : 204.2 263.0 321.9 380.8 439.7 643.8 702.7 761.6 820.5 1024.6 1083.5 1142.4 1201.3 1083.5: 58.9 117.8 176.6 235.5 439.7 498.6 557.4 616.3 820.5 879.4 938.2 997.1 1201.3 1142.4: 58.9 117.8 176.6 380.8 439.7 498.6 557.4 761.6 820.5 879.4 938.2 1142.4 1201.3 1201.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.8800 .. 204.1600 cents 145.28000 cents 58.88000 cents 2: 117.7600 .. 263.0400 cents 145.28000 cents -86.40000 cents 3: 176.6400 .. 321.9200 cents 145.28000 cents -86.40000 cents 4: 235.5200 .. 380.8000 cents 145.28000 cents -86.40000 cents 5: 439.6800 .. 584.9600 cents 145.28000 cents 58.88000 cents 6: 498.5600 .. 643.8400 cents 145.28000 cents -86.40000 cents 7: 557.4400 .. 702.7200 cents 145.28000 cents -86.40000 cents 8: 616.3200 .. 761.6000 cents 145.28000 cents -86.40000 cents 9: 820.4800 .. 965.7600 cents 145.28000 cents 58.88000 cents 10: 879.3600 .. 1024.6400 cents 145.28000 cents -86.40000 cents 11: 938.2400 .. 1083.5200 cents 145.28000 cents -86.40000 cents 12: 997.1200 .. 1142.4000 cents 145.28000 cents -86.40000 cents
SHOW DATA
Number of notes : 13 -- Interval properties -- Smallest interval : 58.88000 cents, class 1 Average step (divided formal octave): 92.4062 cents Largest one step interval : 204.16000 cents Average / Smallest step : 1.569398 Largest / Average step : 2.209377 Largest / Smallest step : 3.467391 Median interval of one step : 58.88000 cents, amount: 10 Most common interval of one step : 58.88000 cents, amount: 10 Least squares average step : 93.29309 cents, oct.: 1212.81016 cents Scale is not proper Scale has Myhill's property chromas: 145.28000 cents and 86.40000 cents, ratio: 1.681481 generators: 4 of 380.80000 cents and 9 of 820.48000 cents ET pair of linear temperament : 19&41 Scale is distributional even Scale is a mode of a 1571-tone equal temperament with octave 1201.280 cents degrees: 77 154 421 498 575 652 919 996 1073 1150 1417 1494 1571 generators: 498 and 1073 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 27.52000 cents Scale diversity : 1.220120 Lumma stability : 0.196058 Lumma impropriety factor : 0.509856 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 : 27.52000 cents Most common intervals : 380.80000 cents & inv., amount: 12 Scale is a chain of 6 triads 0.0 380.800 761.600 cents Most common triad is 0.0 380.800 820.480 cents, amount: 11 Number of recognisable fifths : 8, average 702.7200 cents Number of recognisable fourths : 8, average 498.5600 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 2 1 0 1 2 1 0 1 2 1 1 N T3 SD: 48.5092 c. M: 81.2308 c. 14: 1 0 3 0 1 1 2 1 1 0 3 0 1 N I SD: 24.7766 c. M: 37.5771 c. 15: 1 0 3 1 0 1 3 0 1 1 2 1 1 N SD: 25.9472 c. M: 42.4107 c. 16: 1 1 2 1 1 1 2 1 1 1 2 1 1 P M ME I SD: 20.2049 c. M: 32.4000 c. 17: 1 1 3 0 1 1 3 1 1 0 3 1 1 N I SD: 20.3702 c. M:-31.3976 c. 18: 1 1 3 1 1 0 4 0 1 1 3 1 1 N I SD: 19.8979 c. M: 31.3956 c. 19: 1 1 3 1 1 1 3 1 1 1 3 1 1 N M DE I SD: 5.4195 c. M: 8.6905 c. 22: 1 1 4 1 1 1 4 1 1 1 4 1 1 N M DE I SD: 5.3336 c. M: 8.5527 c. 41: 2 2 7 2 2 2 7 2 2 2 7 2 2 N M DE I SD: 0.3504 c. M: 0.5620 c. 183: 9 9 31 9 9 9 31 9 9 9 31 9 9 N M DE I SD: 0.2486 c. M: 0.3987 c. 224: 11 11 38 11 11 11 38 11 11 11 38 11 11 N M DE I SD: 0.1390 c. M: 0.2229 c. 265: 13 13 45 13 13 13 45 13 13 13 45 13 13 N M DE I SD: 0.0633 c. M: 0.1014 c. 306: 15 15 52 15 15 15 52 15 15 15 52 15 15 N M DE I SD: 0.0078 c. M: 0.0125 c. 959: 47 47 163 47 47 47 163 47 47 47 163 47 47 N M DE I SD: 0.0075 c. M: 0.0120 c. 1265: 62 62 215 62 62 62 215 62 62 62 215 62 62 N M DE I SD: 0.0038 c. M: 0.0061 c. 1571: 77 77 267 77 77 77 267 77 77 77 267 77 77 N M DE I SD: 0.0015 c. M: 0.0024 c. 1877: 92 92 319 92 92 92 319 92 92 92 319 92 92 N M DE I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x x x x 2 S SD: 1.2800 cents 2 x x x x x x 3 x x x x x 4 S SD: 0.7456 cents 3 x x x x x 4 x x x 5 x x 6 S SD: 1.7285 cents 4 x x x 5 x x 6 x x 7 x x 8 S SD: 22.4120 cents 5 x x 6 x x 7 x x 8 x 9 x 10 S SD: 21.4300 cents 6 x x 7 x x 8:9 x x 10:11 x 12 S SD: 10.8328 cents 7 x x 8 x 9 x x 11 x 12:13 x 14 SD: 18.0469 cents 8 x 9 x 10 x 11:12 x 13 x 15 x 16 SD: 14.7512 cents 9 x 10:11 x x 12 x 14 x 15:17 x 18 SD: 10.2753 cents 10 x 11:12 x 13 x 15 x 16:17:19 x 20 SD: 8.6965 cents 11 x 12:13 x 14:15 x 17 x 18 x 21:22 SD: 9.2060 cents 12 x 13:14:15 x 16:18 x 19:20:22:23:24 S SD: 7.4618 cents 13 x 14 x 16:17 x x 20:21:22:24:25:26 SD: 6.1940 cents 14 x 15:17 x 18:19:21:22 x 23:26:27:28 SD: 4.6229 cents 15 x 16:18:19 x 20 x 23:24:25:28:29:30 SD: 3.7871 cents 16 x 17:19:20 x 21:24:25:26:27:30:31:32 SD: 4.8272 cents 17 x 18:20:21:22:23 x 26:27:28:32:33:34 SD: 5.9963 cents 18 x 19:22 x 23:24:27:28:29:30:34:35:36 SD: 3.9816 cents 19 x 20:23:24 x 25:29:30:31:32:36:37:38 SD: 6.8384 cents 20:21 x 24:25:26:27:30:31:32:33:37:39:40 SD: 3.8354 cents 21:22 x 25:26:27:28:32:33:34:35:39:41:42 SD: 4.3782 cents 22:23:24 x 27:28:29:33:34:35:37:41:43:44 SD: 5.3496 cents 23:24:25:28:29:30:31:35:36:37:38:43:44:46 SD: 4.6811 cents 24:25:26:29:30:31:32:36:37:39:40:45:46:48 SD: 2.9855 cents 28:29:30:34:35:36:37:42:43:45:47:52:54:56 SD: 2.8223 cents 29:30:31:35:36:37:39:44:45:47:48:54:56:58 SD: 2.7747 cents 30:31:32:36:37:39:40:45:47:48:50:56:58:60 SD: 2.3506 cents 38:39:41:46:47:49:51:57:59:61:63:71:74:76 SD: 2.3032 cents 44:46:47:53:55:57:59:66:68:71:73:82:85:88 SD: 2.0407 cents 45:47:48:54:56:58:60:68:70:72:75:84:87:90 SD: 1.8654 cents 48:50:51:58:60:62:64:72:75:77:80:90:93:96 SD: 1.8225 cents 53:55:57:64:66:68:71:80:82:85:88:99:103:106 SD: 1.6464 cents 54:56:58:65:67:70:72:81:84:87:90:101:104:108 SD: 1.3860 cents 56:58:60:67:70:72:75:84:87:90:93:105:108:112 SD: 1.3268 cents 58:60:62:70:72:75:77:87:90:93:96:108:112:116 SD: 1.2784 cents 60:62:64:72:75:77:80:90:93:96:100:112:116:120 SD: 1.2485 cents 69:71:74:83:86:89:92:104:107:111:115:129:133:138 SD: 1.1927 cents 82:85:88:99:102:106:109:123:127:132:136:153:159:164 SD: 1.0611 cents 83:86:89:100:103:107:111:125:129:133:138:155:161:166 SD: 1.0209 cents 84:87:90:101:105:108:112:126:130:135:140:157:163:168 SD: 0.9532 cents 86:89:92:104:107:111:115:129:134:138:143:161:166:172 SD: 0.9315 cents 89:92:95:107:111:115:119:134:138:143:148:166:172:178 SD: 0.8941 cents 94:97:101:113:117:121:125:141:146:151:156:176:182:188 SD: 0.8630 cents 110:114:118:132:137:142:147:165:171:177:183:206:213:220 SD: 0.8053 cents 112:116:120:135:140:144:149:168:174:180:186:209:217:224 SD: 0.7850 cents 114:118:122:137:142:147:152:171:177:183:189:213:221:228 SD: 0.5498 cents 138:143:148:166:172:178:184:207:214:222:229:258:267:276 SD: 0.5126 cents 142:147:152:171:177:183:189:213:220:228:236:266:275:284 SD: 0.5093 cents 168:174:180:202:209:217:224:252:261:270:279:314:325:336 SD: 0.4872 cents 170:176:182:205:212:219:227:255:264:273:283:318:329:340 SD: 0.3931 cents 200:207:214:241:249:258:267:300:311:321:332:374:387:400 SD: 0.3703 cents 201:208:215:242:250:259:268:302:312:323:334:376:389:402 SD: 0.3460 cents 228:236:244:275:284:294:304:342:354:366:379:426:441:456 SD: 0.2843 cents 260:269:278:313:324:335:347:390:404:418:432:486:503:520 SD: 0.2792 cents 284:294:304:342:354:366:379:426:441:456:472:531:549:568 SD: 0.2082 cents 353:365:378:425:440:455:471:530:548:567:587:660:683:707 SD: 0.1909 cents 402:416:430:484:501:518:536:603:624:646:668:752:778:805 SD: 0.1867 cents 411:425:440:495:512:530:548:617:638:660:683:769:795:823 SD: 0.1586 cents 467:483:500:562:582:602:623:701:725:750:776:873:903:935 SD: 0.1576 cents 470:486:503:566:586:606:627:705:730:755:781:879:909:941 SD: 0.1561 cents 485:502:519:584:604:625:647:728:753:779:806:907:938:971 SD: 0.1339 cents 553:572:592:666:689:713:738:830:859:888:919:1034:1070:1107 SD: 0.1260 cents 581:601:622:700:724:749:775:872:902:933:966:1086:1124:1163 SD: 0.1107 cents