Scala analysis: xen18-erlich-liese-05
2L 3s MOS for Liese, L=504.53, s=64.52
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64.520 cents 64.520000 2: 569.050 cents 569.050000 3: 633.570 cents 633.570000 4: 1138.100 cents 1138.100000 5: 1202.620 cents 1202.620000
SHOW/INTERVAL
0: 64.5200 cents 64.5200 1: 64.5200 cents 64.5200 2: 504.5300 cents 504.5300 3: 64.5200 cents 64.5200 4: 504.5300 cents 504.5300 5: 64.5200 cents 64.5200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 64.52000 cents 1: 2 504.53000 cents 2: 1 129.04000 cents 2: 4 569.05000 cents 3: 4 633.57000 cents 3: 1 1073.58000 cents 4: 2 698.09000 cents 4: 3 1138.10000 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 0.0 : 64.5 569.0 633.6 1138.1 1202.6 64.5 : 504.5 569.1 1073.6 1138.1 1202.6 569.0 : 64.5 569.1 633.6 698.1 1202.6 633.6 : 504.5 569.0 633.6 1138.1 1202.6 1138.1: 64.5 129.0 633.6 698.1 1202.6 1202.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 64.5200 .. 504.5300 cents 440.01000 cents 64.52000 cents 2: 129.0400 .. 569.0500 cents 440.01000 cents -375.49000 cents 3: 633.5700 .. 1073.5800 cents 440.01000 cents 64.52000 cents 4: 698.0900 .. 1138.1000 cents 440.01000 cents -375.49000 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 64.52000 cents, class 1 Average step (divided formal octave): 240.5240 cents Largest one step interval : 504.53000 cents Average / Smallest step : 3.727898 Largest / Average step : 2.097629 Largest / Smallest step : 7.819746 Median interval of one step : 64.52000 cents, amount: 3 Most common interval of one step : 64.52000 cents, amount: 3 Least squares average step : 248.52418 cents, oct.: 1242.62091 cents Scale is not proper Scale has Myhill's property chromas: 440.01000 cents and 375.49000 cents, ratio: 1.171829 generators: 2 of 569.05000 cents and 3 of 633.57000 cents ET pair of linear temperament : 17&19 Scale is distributional even Scale is a mode of a 727-tone equal temperament with octave 1202.620 cents degrees: 39 344 383 688 727 generators: 344 and 383 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABA Step pattern size order : SLSLS Scale is a Constant Structure, by a margin of 64.52000 cents Scale diversity : 0.954031 Lumma stability : 0.160949 Lumma impropriety factor : 0.624453 Rothenberg efficiency : 0.800000 redundancy: 0.200000 Efficiency x scale size : 4.000000 Number of different interval sizes : 8 = 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 : 64.52000 cents Most common intervals : 569.05000 cents & inv., amount: 4 Scale is a chain of 2 triads 0.0 569.050 1138.100 cents Most common triad is 0.0 569.050 633.570 cents, amount: 3 Number of recognisable fifths : 2, average 698.0900 cents Number of recognisable fourths : 2, average 504.5300 cents Formal octave complements present : 5 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 2-3 -- Rational properties --
FIT/MODE
5: 0 2 1 2 0 N T3 I SD: 69.0136 c. M: 88.0020 c. 6: 0 3 0 3 0 N M DE I SD: 45.6225 c. M: 64.5200 c. 9: 0 4 1 3 1 N SD: 47.5940 c. M: 69.1044 c. 10: 0 4 1 4 1 N T3 SD: 56.6658 c. M: 88.0020 c. 11: 1 4 1 4 1 N M DE I SD: 31.6848 c. M:-44.8091 c. 12: 1 5 0 5 1 N T3 I SD: 30.4308 c. M:-35.6983 c. 13: 1 5 1 5 1 N M DE I SD: 19.7914 c. M: 27.9892 c. 15: 1 6 1 6 1 N M DE I SD: 11.0695 c. M: 15.6547 c. 17: 1 7 1 7 1 N M DE I SD: 4.3999 c. M: 6.2224 c. 19: 1 8 1 8 1 N M DE I SD: 0.8656 c. M: 1.2242 c. 55: 3 23 3 23 3 N M DE I SD: 0.7619 c. M: 1.0775 c. 74: 4 31 4 31 4 N M DE I SD: 0.3440 c. M: 0.4865 c. 93: 5 39 5 39 5 N M DE I SD: 0.0969 c. M:-0.1370 c. 112: 6 47 6 47 6 N M DE I SD: 0.0664 c. M:-0.0939 c. 205: 11 86 11 86 11 N M DE I SD: 0.0077 c. M: 0.0108 c. 727: 39 305 39 305 39 N M DE I SD: 0.0038 c. M: 0.0053 c. 932: 50 391 50 391 50 N M DE I SD: 0.0012 c. M: 0.0018 c. 1137: 61 477 61 477 61 N M DE I SD: 0.0004 c. M: 0.0005 c.
FIT/HARMONIC
1 x x x x 2 S SD: 2.6200 cents 2 x x 3 x 4 S SD: 34.2176 cents 3 x 4 x x 6 S SD: 35.5267 cents 4 x x 6 x 8 S SD: 34.2176 cents 5:6:7 x x 10 SD: 83.8318 cents 6:7:8:9 x 12 S SD: 56.2755 cents 7:8 x 10 x 14 SD: 55.8163 cents 8:9:11:12:15:16 SD: 32.8089 cents 9:10 x 13:17:18 SD: 30.9089 cents 10:11:14 x 19:20 SD: 26.2307 cents 11:12:15:16:21:22 SD: 19.0043 cents 12:13 x 17:23:24 SD: 20.2545 cents 13:14:18:19:25:26 SD: 13.6981 cents 15:16:21:22:29:30 SD: 11.4827 cents 16:17:22:23:31:32 SD: 9.0166 cents 18:19:25:26:35:36 SD: 6.4326 cents 20:21:28:29:39:40 SD: 6.3449 cents 23:24:32:33:44:46 S SD: 3.9905 cents 25:26:35:36:48:50 SD: 3.3568 cents 29:30:40:42:56:58 S SD: 3.1752 cents 46:48:64:66:89:92 SD: 2.7692 cents 48:50:67:69:93:96 SD: 2.7553 cents 49:51:68:71:95:98 SD: 2.6030 cents 52:54:72:75:100:104 S SD: 1.7423 cents 54:56:75:78:104:108 SD: 1.1047 cents 100:104:139:144:193:200 SD: 0.9935 cents 129:134:179:186:249:258 SD: 0.7087 cents 131:136:182:189:253:262 SD: 0.6310 cents 183:190:254:264:353:367 SD: 0.5674 cents 185:192:257:267:357:371 SD: 0.5234 cents 208:216:289:300:401:417 SD: 0.4976 cents 211:219:293:304:407:423 SD: 0.4515 cents 213:221:296:307:411:427 SD: 0.3733 cents 260:270:361:375:502:521 SD: 0.3453 cents 265:275:368:382:511:531 SD: 0.3372 cents 267:277:371:385:515:535 SD: 0.2832 cents 285:296:396:411:550:571 SD: 0.2431 cents 339:352:471:489:654:679 SD: 0.2187 cents 342:355:475:493:660:685 SD: 0.1165 cents