Scala analysis: xen18-erlich-magic-07
3L 4s MOS for Magic, L=321.92, 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: 380.800 cents 380.800000 3: 439.680 cents 439.680000 4: 761.600 cents 761.600000 5: 820.480 cents 820.480000 6: 1142.400 cents 1142.400000 7: 1201.280 cents 1201.280000
SHOW/INTERVAL
0: 58.8800 cents 58.8800 1: 58.8800 cents 58.8800 2: 321.9200 cents 321.9200 3: 58.8800 cents 58.8800 4: 321.9200 cents 321.9200 5: 58.8800 cents 58.8800 6: 321.9200 cents 321.9200 7: 58.8800 cents 58.8800
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 58.88000 cents 1: 3 321.92000 cents 2: 1 117.76000 cents 2: 6 380.80000 cents 3: 5 439.68000 cents 3: 2 702.72000 cents 4: 2 498.56000 cents 4: 5 761.60000 cents 5: 6 820.48000 cents 5: 1 1083.52000 cents 6: 3 879.36000 cents 6: 4 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 0.0 : 58.9 380.8 439.7 761.6 820.5 1142.4 1201.3 58.9 : 321.9 380.8 702.7 761.6 1083.5 1142.4 1201.3 380.8 : 58.9 380.8 439.7 761.6 820.5 879.4 1201.3 439.7 : 321.9 380.8 702.7 761.6 820.5 1142.4 1201.3 761.6 : 58.9 380.8 439.7 498.6 820.5 879.4 1201.3 820.5 : 321.9 380.8 439.7 761.6 820.5 1142.4 1201.3 1142.4: 58.9 117.8 439.7 498.6 820.5 879.4 1201.3 1201.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 58.8800 .. 321.9200 cents 263.04000 cents 58.88000 cents 2: 117.7600 .. 380.8000 cents 263.04000 cents -204.16000 cents 3: 439.6800 .. 702.7200 cents 263.04000 cents 58.88000 cents 4: 498.5600 .. 761.6000 cents 263.04000 cents -204.16000 cents 5: 820.4800 .. 1083.5200 cents 263.04000 cents 58.88000 cents 6: 879.3600 .. 1142.4000 cents 263.04000 cents -204.16000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 58.88000 cents, class 1 Average step (divided formal octave): 171.6114 cents Largest one step interval : 321.92000 cents Average / Smallest step : 2.914596 Largest / Average step : 1.875866 Largest / Smallest step : 5.467391 Median interval of one step : 58.88000 cents, amount: 4 Most common interval of one step : 58.88000 cents, amount: 4 Least squares average step : 175.36914 cents, oct.: 1227.58400 cents Scale is not proper Scale has Myhill's property chromas: 263.04000 cents and 204.16000 cents, ratio: 1.288401 generators: 2 of 380.80000 cents and 5 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: 62 401 463 802 864 1203 1265 generators: 401 and 864 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 58.88000 cents Scale diversity : 1.130680 Lumma stability : 0.196058 Lumma impropriety factor : 0.509856 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 : 58.88000 cents Most common intervals : 380.80000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 380.800 761.600 cents Most common triad is 0.0 380.800 820.480 cents, amount: 5 Number of recognisable fifths : 2, average 702.7200 cents Number of recognisable fourths : 2, average 498.5600 cents 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 1 1 1 2 0 N T3 I SD: 54.8428 c. M: 75.1543 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 49.1028 c. M: 69.6800 c. 9: 0 3 0 3 0 3 0 N M DE I SD: 39.2533 c. M: 58.8800 c. 11: 0 3 1 3 0 3 1 N T3 SD: 41.3748 c. M: 58.8800 c. 12: 1 3 0 4 0 3 1 N I SD: 32.1855 c. M: 41.2267 c. 13: 1 3 1 3 1 3 1 N M DE I SD: 22.3508 c. M: 33.5262 c. Canopus-7 16: 1 4 1 4 1 4 1 N M DE I SD: 10.8000 c. M: 16.2000 c. 19: 1 5 1 5 1 5 1 N M DE I SD: 2.8968 c. M: 4.3453 c. 22: 1 6 1 6 1 6 1 N M DE I SD: 2.8509 c. M: 4.2764 c. 41: 2 11 2 11 2 11 2 N M DE I SD: 0.1873 c. M: 0.2810 c. 183: 9 49 9 49 9 49 9 N M DE I SD: 0.1329 c. M: 0.1993 c. 224: 11 60 11 60 11 60 11 N M DE I SD: 0.0743 c. M: 0.1114 c. 265: 13 71 13 71 13 71 13 N M DE I SD: 0.0338 c. M: 0.0507 c. 306: 15 82 15 82 15 82 15 N M DE I SD: 0.0042 c. M: 0.0063 c. 959: 47 257 47 257 47 257 47 N M DE I SD: 0.0040 c. M: 0.0060 c. 1265: 62 339 62 339 62 339 62 N M DE I SD: 0.0020 c. M: 0.0030 c. 1571: 77 421 77 421 77 421 77 N M DE I SD: 0.0008 c. M: 0.0012 c. 1877: 92 503 92 503 92 503 92 N M DE I SD: 0.0000 c. M: 0.0000 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 1.2800 cents 2 x x x 3 x x 4 S SD: 29.8294 cents 3 x x 4 x 5 x 6 S SD: 28.8456 cents 4 x 5 x 6 x x 8 S SD: 19.9710 cents 5 x 6 x x 8 x 10 S SD: 21.8415 cents 6 x 7:8:9:10 x 12 S SD: 31.0006 cents 7 x x 9:11 x x 14 SD: 7.1433 cents 8:9:10 x 12:13:15:16 SD: 27.8664 cents 9:10:11:12:14 x 17:18 SD: 24.4395 cents 10:11:12:13 x 16:19:20 SD: 21.5642 cents 11:12 x 14:17:18:21:22 SD: 17.1053 cents 12:13:15 x x 19:23:24 SD: 17.0442 cents 13:14:16:17:20:21:25:26 SD: 11.3745 cents 14:15:17:18:22 x 27:28 SD: 13.0717 cents 15:16:19 x 23:24:29:30 SD: 10.6948 cents 16:17:20:21:25:26:31:32 SD: 8.6339 cents 17:18:21:22:26:27:33:34 SD: 7.7880 cents 18:19:22:23:28:29:35:36 SD: 7.3856 cents 19:20:24 x 30:31:37:38 SD: 9.3806 cents 20:21:25:26:31:32:39:40 SD: 4.8276 cents 24:25:30:31:37:39:46:48 SD: 4.5000 cents 25:26:31:32:39:40:48:50 SD: 3.4703 cents 28:29:35:36:43:45:54:56 SD: 3.0094 cents 31:32:39:40:48:50:60:62 SD: 2.7473 cents 45:47:56:58:70:72:87:90 SD: 2.6107 cents 48:50:60:62:75:77:93:96 SD: 2.5413 cents 49:51:61:63:76:79:95:98 SD: 1.9755 cents 56:58:70:72:87:90:108:112 SD: 1.3361 cents 86:89:107:111:134:138:166:172 SD: 1.1887 cents 89:92:111:115:138:143:172:178 SD: 0.7967 cents 114:118:142:147:177:183:221:228 SD: 0.5917 cents 170:176:212:219:264:273:329:340 SD: 0.3863 cents 228:236:284:294:354:366:441:456 SD: 0.2920 cents 322:333:401:415:500:517:623:644 SD: 0.2827 cents 346:358:431:446:537:556:669:693 SD: 0.2671 cents 353:365:440:455:548:567:683:707 SD: 0.2438 cents 398:412:496:513:618:639:770:797 SD: 0.2311 cents 411:425:512:530:638:660:795:823 SD: 0.2166 cents 460:476:573:593:714:739:890:921 SD: 0.1454 cents 516:534:643:665:801:829:998:1033 SD: 0.1429 cents 577:597:719:744:896:927:1116:1155 SD: 0.1072 cents 581:601:724:749:902:933:1124:1163 SD: 0.0883 cents