Scala analysis: xen18-erlich-august-09
3L 6s MOS for August, L=185.37, s=107.31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 107.310 cents 107.310000 2: 292.680 cents 292.680000 3: 399.990 cents 399.990000 4: 507.300 cents 507.300000 5: 692.670 cents 692.670000 6: 799.980 cents 799.980000 7: 907.290 cents 907.290000 8: 1092.660 cents 1092.660000 9: 1199.970 cents 1199.970000
SHOW/INTERVAL
0: 107.3100 cents 107.3100 1: 107.3100 cents 107.3100 2: 185.3700 cents 185.3700 3: 107.3100 cents 107.3100 4: 107.3100 cents 107.3100 5: 185.3700 cents 185.3700 6: 107.3100 cents 107.3100 7: 107.3100 cents 107.3100 8: 185.3700 cents 185.3700 9: 107.3100 cents 107.3100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 107.31000 cents 1: 3 185.37000 cents 2: 3 214.62000 cents 2: 6 292.68000 cents 3: 9 399.99000 cents 4: 6 507.30000 cents 4: 3 585.36000 cents 5: 3 614.61000 cents 5: 6 692.67000 cents 6: 9 799.98000 cents 7: 6 907.29000 cents 7: 3 985.35000 cents 8: 3 1014.60000 cents 8: 6 1092.66000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.75000 = 7/4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 0.0 : 107.3 292.7 400.0 507.3 692.7 800.0 907.3 1092.7 1200.0 107.3 : 185.4 292.7 400.0 585.4 692.7 800.0 985.4 1092.7 1200.0 292.7 : 107.3 214.6 400.0 507.3 614.6 800.0 907.3 1014.6 1200.0 400.0 : 107.3 292.7 400.0 507.3 692.7 800.0 907.3 1092.7 1200.0 507.3 : 185.4 292.7 400.0 585.4 692.7 800.0 985.4 1092.7 1200.0 692.7 : 107.3 214.6 400.0 507.3 614.6 800.0 907.3 1014.6 1200.0 800.0 : 107.3 292.7 400.0 507.3 692.7 800.0 907.3 1092.7 1200.0 907.3 : 185.4 292.7 400.0 585.4 692.7 800.0 985.4 1092.7 1200.0 1092.7: 107.3 214.6 400.0 507.3 614.6 800.0 907.3 1014.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 107.3100 .. 185.3700 cents 78.06000 cents 107.31000 cents 2: 214.6200 .. 292.6800 cents 78.06000 cents 29.25000 cents 3: 399.9900 .. 399.9900 cents 1/1, 0.0000 cents 107.31000 cents 4: 507.3000 .. 585.3600 cents 78.06000 cents 107.31000 cents 5: 614.6100 .. 692.6700 cents 78.06000 cents 29.25000 cents 6: 799.9800 .. 799.9800 cents 1/1, 0.0000 cents 107.31000 cents 7: 907.2900 .. 985.3500 cents 78.06000 cents 107.31000 cents 8: 1014.6000 .. 1092.6600 cents 78.06000 cents 29.25000 cents
SHOW DATA
Number of notes : 9 -- Interval properties -- Smallest interval : 107.31000 cents, class 1 Average step (divided formal octave): 133.3300 cents Largest one step interval : 185.37000 cents Average / Smallest step : 1.242475 Largest / Average step : 1.390310 Largest / Smallest step : 1.727425 Median interval of one step : 107.31000 cents, amount: 6 Most common interval of one step : 107.31000 cents, amount: 6 Least squares average step : 133.60389 cents, oct.: 1202.43505 cents Scale is strictly proper Scale has 3 repeating blocks of 3 notes Blocks have Myhill's property chromas: 78.06000 cents and 29.25000 cents, ratio: 2.668718 generators: 1 of 107.31000 cents and 2 of 292.68000 cents ET pair of linear temperament : 33&45 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 123-tone equal temperament with octave 1199.970 cents degrees: 11 30 41 52 71 82 93 112 123 Least number of segments generator : 62 of 604.863 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 71 of 692.666 cents and inv. generated superset size: 85 = 76 more = 944.444% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAABAABA Step pattern size order : SLSSLSSLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 3 0 0 3 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 3 0 ] Scale is a Constant Structure, by a margin of 29.25000 cents Scale diversity : 1.177962 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.609690 Rothenberg efficiency (ambiguous key): 0.396825 redundancy: 0.603175 Efficiency x scale size : 3.571429 Number of different interval sizes : 14 = 1.75000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.75000 = 7/4 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 29.25000 cents Most common intervals : 399.99000 cents & inv., amount: 9 Most common triad is 0.0 399.990 799.980 cents, amount: 9 Number of recognisable fifths : 6, average 692.6700 cents Number of recognisable fourths : 6, average 507.3000 cents Best fifths form a closed circle Formal octave complements present : 9 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 3 6 Limited inverse transpositions : 3 6 Inversional symmetry on degrees : 0 3 6 Inversional symmetry on intervals : 1-2 4-5 7-8 -- Rational properties --
FIT/MODE
9: 1 1 1 1 1 1 1 1 1 SP B ME I SD: 21.2452 c. M: 26.0200 c. Pelog Nawanada: Sunda 12: 1 2 1 1 2 1 1 2 1 P B ME I SD: 5.9706 c. M:-7.3125 c. Genus chromaticum, Tcherepnin Nonatonic mode 1, Augmented-9 21: 2 3 2 2 3 2 2 3 2 SP B ME I SD: 5.6933 c. M:-6.9729 c. Quasi-equal Enneatonic, Deflated-9 33: 3 5 3 3 5 3 3 5 3 SP B DE I SD: 1.4519 c. M:-1.7782 c. 45: 4 7 4 4 7 4 4 7 4 SP B DE I SD: 0.5275 c. M:-0.6460 c. 78: 7 12 7 7 12 7 7 12 7 SP B DE I SD: 0.3100 c. M: 0.3796 c. 123: 11 19 11 11 19 11 11 19 11 SP B DE I SD: 0.0036 c. M: 0.0044 c.
FIT/HARMONIC
1 x x x x x x x x 2 S SD: 0.0300 cents 2 x x x x 3 x x x 4 S SD: 4.6425 cents 3 x x x 4 x x 5 x 6 S SD: 8.2428 cents 4 x x 5 x 6 x 7 x 8 S SD: 15.9294 cents 5 x 6 x 7 x 8 x 9:10 S SD: 21.9149 cents 6 x 7 x 8:9 x 10:11:12 S SD: 9.4846 cents 7 x 8:9 x 10:11:12:13:14 S SD: 15.7011 cents 8 x 9:10:11:12:13:14:15:16 S SD: 15.5829 cents 9:10 x 11:12:13:14:15:17:18 SD: 14.5006 cents 10:11:12 x 13:15:16:17:19:20 SD: 10.7679 cents 11:12:13:14:15:16:17:19:21:22 SD: 10.7668 cents 12:13:14:15:16:18:19:20:23:24 SD: 6.7410 cents 15:16:18:19:20:22:24:25:28:30 SD: 5.5060 cents 16:17:19:20:21:24:25:27:30:32 SD: 5.4493 cents 20:21:24:25:27:30:32:34:38:40 SD: 5.1313 cents 26:28:31:33:35:39:41:44:49:52 SD: 3.5935 cents 27:29:32:34:36:40:43:46:51:54 SD: 3.2166 cents 32:34:38:40:43:48:51:54:60:64 SD: 2.1923 cents 47:50:56:59:63:70:75:79:88:94 SD: 2.1091 cents 49:52:58:62:66:73:78:83:92:98 SD: 1.5882 cents 59:63:70:74:79:88:94:100:111:118 SD: 1.5540 cents 61:65:72:77:82:91:97:103:115:122 SD: 1.1561 cents 65:69:77:82:87:97:103:110:122:130 SD: 0.8309 cents 77:82:91:97:103:115:122:130:145:154 SD: 0.7972 cents 97:103:115:122:130:145:154:164:182:194 SD: 0.7831 cents 108:115:128:136:145:161:171:182:203:216 SD: 0.7733 cents 109:116:129:137:146:163:173:184:205:218 SD: 0.6837 cents 124:132:147:156:166:185:197:209:233:248 SD: 0.6176 cents 126:134:149:159:169:188:200:213:237:252 SD: 0.4811 cents 158:168:187:199:212:236:251:267:297:316 SD: 0.3817 cents 173:184:205:218:232:258:275:292:325:346 SD: 0.3663 cents 223:237:264:281:299:333:354:377:419:446 SD: 0.3505 cents 235:250:278:296:315:351:373:397:442:470 SD: 0.3197 cents 238:253:282:300:319:355:378:402:447:476 SD: 0.2989 cents 250:266:296:315:335:373:397:422:470:500 SD: 0.1498 cents 473:503:560:596:634:706:751:799:889:946 SD: 0.1473 cents 482:513:571:607:646:719:765:814:906:964 SD: 0.1457 cents 531:565:629:669:712:792:843:897:998:1062 SD: 0.1162 cents 581:618:688:732:779:867:922:981:1092:1162 SD: 0.1080 cents