Scala analysis: xen18-erlich-magic-10
3L 7s MOS for Magic, L=263.04, 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: 321.920 cents 321.920000 3: 380.800 cents 380.800000 4: 439.680 cents 439.680000 5: 498.560 cents 498.560000 6: 761.600 cents 761.600000 7: 820.480 cents 820.480000 8: 879.360 cents 879.360000 9: 1142.400 cents 1142.400000 10: 1201.280 cents 1201.280000
SHOW/INTERVAL
0: 58.8800 cents 58.8800 1: 58.8800 cents 58.8800 2: 263.0400 cents 263.0400 3: 58.8800 cents 58.8800 4: 58.8800 cents 58.8800 5: 58.8800 cents 58.8800 6: 263.0400 cents 263.0400 7: 58.8800 cents 58.8800 8: 58.8800 cents 58.8800 9: 263.0400 cents 263.0400 10: 58.8800 cents 58.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 7 58.88000 cents 1: 3 263.04000 cents 2: 4 117.76000 cents 2: 6 321.92000 cents 3: 1 176.64000 cents 3: 9 380.80000 cents 4: 8 439.68000 cents 4: 2 643.84000 cents 5: 5 498.56000 cents 5: 5 702.72000 cents 6: 2 557.44000 cents 6: 8 761.60000 cents 7: 9 820.48000 cents 7: 1 1024.64000 cents 8: 6 879.36000 cents 8: 4 1083.52000 cents 9: 3 938.24000 cents 9: 7 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 0.0 : 58.9 321.9 380.8 439.7 498.6 761.6 820.5 879.4 1142.4 1201.3 58.9 : 263.0 321.9 380.8 439.7 702.7 761.6 820.5 1083.5 1142.4 1201.3 321.9 : 58.9 117.8 176.6 439.7 498.6 557.4 820.5 879.4 938.2 1201.3 380.8 : 58.9 117.8 380.8 439.7 498.6 761.6 820.5 879.4 1142.4 1201.3 439.7 : 58.9 321.9 380.8 439.7 702.7 761.6 820.5 1083.5 1142.4 1201.3 498.6 : 263.0 321.9 380.8 643.8 702.7 761.6 1024.6 1083.5 1142.4 1201.3 761.6 : 58.9 117.8 380.8 439.7 498.6 761.6 820.5 879.4 938.2 1201.3 820.5 : 58.9 321.9 380.8 439.7 702.7 761.6 820.5 879.4 1142.4 1201.3 879.4 : 263.0 321.9 380.8 643.8 702.7 761.6 820.5 1083.5 1142.4 1201.3 1142.4: 58.9 117.8 380.8 439.7 498.6 557.4 820.5 879.4 938.2 1201.3 1201.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.8800 .. 263.0400 cents 204.16000 cents 58.88000 cents 2: 117.7600 .. 321.9200 cents 204.16000 cents -145.28000 cents 3: 176.6400 .. 380.8000 cents 204.16000 cents -145.28000 cents 4: 439.6800 .. 643.8400 cents 204.16000 cents 58.88000 cents 5: 498.5600 .. 702.7200 cents 204.16000 cents -145.28000 cents 6: 557.4400 .. 761.6000 cents 204.16000 cents -145.28000 cents 7: 820.4800 .. 1024.6400 cents 204.16000 cents 58.88000 cents 8: 879.3600 .. 1083.5200 cents 204.16000 cents -145.28000 cents 9: 938.2400 .. 1142.4000 cents 204.16000 cents -145.28000 cents
SHOW DATA
Number of notes : 10 -- Interval properties -- Smallest interval : 58.88000 cents, class 1 Average step (divided formal octave): 120.1280 cents Largest one step interval : 263.04000 cents Average / Smallest step : 2.040217 Largest / Average step : 2.189664 Largest / Smallest step : 4.467391 Median interval of one step : 58.88000 cents, amount: 7 Most common interval of one step : 58.88000 cents, amount: 7 Least squares average step : 118.80229 cents, oct.: 1188.02286 cents Scale is not proper Scale has Myhill's property chromas: 204.16000 cents and 145.28000 cents, ratio: 1.405286 generators: 3 of 380.80000 cents and 7 of 820.48000 cents ET pair of linear temperament : 19&41 Scale is distributional even Scale is a mode of a 1265-tone equal temperament with octave 1201.280 cents degrees: 62 339 401 463 525 802 864 926 1203 1265 generators: 401 and 864 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAAABAABA Step pattern size order : SLSSSLSSLS Scale is a Constant Structure, by a margin of 58.88000 cents Scale diversity : 1.267099 Lumma stability : 0.196058 Lumma impropriety factor : 0.509856 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 : 58.88000 cents Most common intervals : 380.80000 cents & inv., amount: 9 Scale is a chain of 5 triads 0.0 321.920 820.480 cents Most common triad is 0.0 380.800 820.480 cents, amount: 8 Number of recognisable fifths : 5, average 702.7200 cents Number of recognisable fourths : 5, average 498.5600 cents Formal octave complements present : 9 = 90.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 8-9 -- Rational properties --
FIT/MODE
10: 0 2 1 0 1 2 1 0 2 1 N T3 SD: 49.4784 c. M: 81.6640 c. 12: 1 2 1 0 1 3 0 1 2 1 N SD: 28.6153 c. M: 41.2267 c. 13: 0 3 1 1 0 3 1 0 3 1 N SD: 33.8350 c. M: 58.8800 c. 14: 1 3 0 1 1 3 1 0 3 1 N SD: 23.8190 c. M: 37.5771 c. 15: 1 3 1 0 1 3 1 1 3 1 N SD: 22.8222 c. M: 40.8320 c. 16: 1 3 1 1 1 3 1 1 3 1 N M DE SD: 15.7436 c. M:-27.0000 c. 19: 1 4 1 1 1 4 1 1 4 1 N M DE SD: 4.2228 c. M:-7.2421 c. 22: 1 5 1 1 1 5 1 1 5 1 N M DE SD: 4.1559 c. M: 7.1273 c. 41: 2 9 2 2 2 9 2 2 9 2 N M DE SD: 0.2731 c. M: 0.4683 c. 183: 9 40 9 9 9 40 9 9 40 9 N M DE SD: 0.1937 c. M:-0.3322 c. 224: 11 49 11 11 11 49 11 11 49 11 N M DE SD: 0.1083 c. M:-0.1857 c. 265: 13 58 13 13 13 58 13 13 58 13 N M DE SD: 0.0493 c. M:-0.0845 c. 306: 15 67 15 15 15 67 15 15 67 15 N M DE SD: 0.0061 c. M:-0.0105 c. 959: 47 210 47 47 47 210 47 47 210 47 N M DE SD: 0.0058 c. M: 0.0100 c. 1265: 62 277 62 62 62 277 62 62 277 62 N M DE SD: 0.0030 c. M: 0.0051 c. 1571: 77 344 77 77 77 344 77 77 344 77 N M DE SD: 0.0012 c. M: 0.0020 c. 1877: 92 411 92 92 92 411 92 92 411 92 N M DE SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x x x x 2 S SD: 1.2800 cents 2 x x x x x 3 x x x 4 S SD: 29.8294 cents 3 x x x x 4 x x 5 x 6 S SD: 1.7285 cents 4 x x 5 x x 6 x 7 x 8 S SD: 26.9185 cents 5 x 6 x x 7 x 8 x x 10 S SD: 21.1175 cents 6 x 7 x x 8:9 x 10 x 12 S SD: 16.2663 cents 7 x 8 x 9 x 11 x 12 x 14 SD: 21.5269 cents 8 x x 10 x 11:12:13 x 15:16 SD: 16.4191 cents 9:10:11 x x 12:14 x 15:17:18 SD: 18.9822 cents 10:11:12 x 13 x x 16:17:19:20 SD: 16.9497 cents 11:12:13 x 14:15:17 x 18:21:22 SD: 14.1214 cents 12:13:14:15 x 16 x 19:20:23:24 SD: 12.6974 cents 13:14 x 16:17 x 20:21:22:25:26 SD: 10.7000 cents 14:15:17 x 18:19:22 x 23:27:28 SD: 9.4057 cents 15:16:18:19 x 20:23:24:25:29:30 SD: 7.1856 cents 16:17:19:20 x 21:25:26:27:31:32 SD: 7.6621 cents 17:18:20:21:22:23:26:27:28:33:34 SD: 7.3960 cents 18:19:22 x 23:24:28:29:30:35:36 SD: 5.2501 cents 19:20:23:24 x 25:30:31:32:37:38 SD: 7.3119 cents 20:21:24:25:26:27:31:32:33:39:40 SD: 4.2141 cents 22:23 x 27:28:29:34:35:37:43:44 SD: 6.0920 cents 23:24:28:29:30:31:36:37:38:44:46 SD: 4.9122 cents 24:25:29:30:31:32:37:39:40:46:48 SD: 3.2404 cents 29:30:35:36:37:39:45:47:48:56:58 SD: 2.9694 cents 33:34:40:41:43:44:51:53:55:64:66 SD: 2.5579 cents 45:47:54:56:58:60:70:72:75:87:90 SD: 1.9966 cents 48:50:58:60:62:64:75:77:80:93:96 SD: 1.9345 cents 49:51:59:61:63:65:76:79:81:95:98 SD: 1.9071 cents 53:55:64:66:68:71:82:85:88:103:106 SD: 1.6904 cents 56:58:67:70:72:75:87:90:93:108:112 SD: 1.6478 cents 58:60:70:72:75:77:90:93:96:112:116 SD: 1.4765 cents 60:62:72:75:77:80:93:96:100:116:120 SD: 1.4756 cents 65:67:78:81:84:87:101:104:108:126:130 SD: 1.4087 cents 69:71:83:86:89:92:107:111:115:133:138 SD: 1.3101 cents 78:81:94:97:101:104:121:125:130:151:156 SD: 1.2655 cents 82:85:99:102:106:109:127:132:136:159:164 SD: 1.2477 cents 83:86:100:103:107:111:129:133:138:161:166 SD: 1.1120 cents 87:90:105:108:112:116:135:140:145:168:174 SD: 1.0408 cents 89:92:107:111:115:119:138:143:148:172:178 SD: 0.7772 cents 114:118:137:142:147:152:177:183:189:221:228 SD: 0.6971 cents 117:121:141:146:151:156:182:188:194:226:234 SD: 0.6886 cents 138:143:166:172:178:184:214:222:229:267:276 SD: 0.5700 cents 166:172:200:207:214:221:258:267:276:321:332 SD: 0.5496 cents 170:176:205:212:219:227:264:273:283:329:340 SD: 0.4998 cents 180:186:217:224:232:240:279:289:299:348:360 SD: 0.4997 cents 183:189:220:228:236:244:284:294:304:354:366 SD: 0.4737 cents 195:202:235:243:251:260:303:313:324:377:390 SD: 0.4433 cents 201:208:242:250:259:268:312:323:334:389:402 SD: 0.3724 cents 228:236:275:284:294:304:354:366:379:441:456 SD: 0.3343 cents 231:239:278:288:298:308:359:371:384:447:462 SD: 0.3087 cents 260:269:313:324:335:347:404:418:432:503:520 SD: 0.2956 cents 264:273:318:329:340:352:410:424:439:511:528 SD: 0.2814 cents 284:294:342:354:366:379:441:456:472:549:568 SD: 0.2592 cents 342:354:412:426:441:456:531:549:568:662:685 SD: 0.2582 cents 353:365:425:440:455:471:548:567:587:683:707 SD: 0.2210 cents 378:391:455:471:487:504:587:607:628:731:757 SD: 0.2097 cents 402:416:484:501:518:536:624:646:668:778:805 SD: 0.1833 cents 411:425:495:512:530:548:638:660:683:795:823 SD: 0.1603 cents 488:505:588:608:629:651:758:784:811:944:977 SD: 0.1411 cents 577:597:695:719:744:770:896:927:959:1116:1155 SD: 0.1270 cents 581:601:700:724:749:775:902:933:966:1124:1163 SD: 0.1243 cents