Scala analysis: xen18-erlich-august-06
3L 3s MOS for August, L=292.68, s=107.31
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 292.680 cents 292.680000 2: 399.990 cents 399.990000 3: 692.670 cents 692.670000 4: 799.980 cents 799.980000 5: 1092.660 cents 1092.660000 6: 1199.970 cents 1199.970000
SHOW/INTERVAL
0: 107.3100 cents 107.3100 1: 292.6800 cents 292.6800 2: 107.3100 cents 107.3100 3: 292.6800 cents 292.6800 4: 107.3100 cents 107.3100 5: 292.6800 cents 292.6800 6: 107.3100 cents 107.3100
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 107.31000 cents 1: 3 292.68000 cents 2: 6 399.99000 cents 3: 3 507.30000 cents 3: 3 692.67000 cents 4: 6 799.98000 cents 5: 3 907.29000 cents 5: 3 1092.66000 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 1.60000 = 8/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 292.7 400.0 692.7 800.0 1092.7 1200.0 292.7 : 107.3 400.0 507.3 800.0 907.3 1200.0 400.0 : 292.7 400.0 692.7 800.0 1092.7 1200.0 692.7 : 107.3 400.0 507.3 800.0 907.3 1200.0 800.0 : 292.7 400.0 692.7 800.0 1092.7 1200.0 1092.7: 107.3 400.0 507.3 800.0 907.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 107.3100 .. 292.6800 cents 185.37000 cents 107.31000 cents 2: 399.9900 .. 399.9900 cents 1/1, 0.0000 cents 107.31000 cents 3: 507.3000 .. 692.6700 cents 185.37000 cents 107.31000 cents 4: 799.9800 .. 799.9800 cents 1/1, 0.0000 cents 107.31000 cents 5: 907.2900 .. 1092.6600 cents 185.37000 cents 107.31000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 107.31000 cents, class 1 Average step (divided formal octave): 199.9950 cents Largest one step interval : 292.68000 cents Average / Smallest step : 1.863713 Largest / Average step : 1.463437 Largest / Smallest step : 2.727425 Median interval of one step : 199.99500 cents, amount: 0 Least squares average step : 209.16165 cents, oct.: 1254.96989 cents Scale is strictly proper Scale has 3 repeating blocks of 2 notes Blocks have Myhill's property chromas: 185.37000 cents and 78.06000 cents, ratio: 2.374712 generator: 107.31000 cents ET pair of linear temperament : 33&45 Scale is distributional even Scale is a mode of a 123-tone equal temperament with octave 1199.970 cents degrees: 30 41 71 82 112 123 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: 84 = 78 more = 1400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABABAB Step pattern size order : LSLSLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 107.31000 cents Scale diversity : 1.185345 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.536563 Rothenberg efficiency (ambiguous key): 1.000000 redundancy: 0.000000 Efficiency x scale size : 6.000000 Number of different interval sizes : 8 = 1.60000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 1.60000 = 8/5 Median interval variety : 2 Lowest interval variety : 1 Smallest interval difference : 107.31000 cents Most common intervals : 399.99000 cents & inv., amount: 6 Scale is a chain of 3 triads 0.0 692.670 799.980 cents Most common triad is 0.0 399.990 799.980 cents, amount: 6 Number of recognisable fifths : 3, average 692.6700 cents Number of recognisable fourths : 3, average 507.3000 cents Formal octave complements present : 3 = 50.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions : 2 4 Limited inverse transpositions : 1 3 5 Inversional symmetry on intervals : 0-1 1-2 2-3 3-4 4-5 5-6 -- Rational properties --
FIT/MODE
6: 1 1 1 1 1 1 SP B ME I SD: 65.5382 c. M: 92.6850 c. Whole-tone, Messiaen mode 1, Raga Gopriya, Anhemitonic Hexatonic 8: 2 1 2 0 2 1 P D3 SD: 41.1500 c. M:-57.3112 c. 9: 2 1 2 1 2 1 SP B ME SD: 18.3989 c. M: 26.0200 c. August-6 12: 3 1 3 1 3 1 SP B DE SD: 5.1707 c. M:-7.3125 c. Messiaen truncated mode 3 inverse, Major Augmented, Genus tertium, Raga Devamani 21: 5 2 5 2 5 2 SP B DE SD: 4.9306 c. M: 6.9729 c. August-6 33: 8 3 8 3 8 3 SP B DE SD: 1.2574 c. M: 1.7782 c. 45: 11 4 11 4 11 4 SP B DE SD: 0.4568 c. M:-0.6460 c. 78: 19 7 19 7 19 7 SP B DE SD: 0.2684 c. M: 0.3796 c. 123: 30 11 30 11 30 11 SP B DE SD: 0.0031 c. M: 0.0044 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0300 cents 2 x x 3 x x 4 S SD: 4.6425 cents 3 x 4 x 5 x 6 S SD: 43.1207 cents 4 x 5:6 x x 8 S SD: 5.5101 cents 5:6 x 7:8:9:10 S SD: 27.1915 cents 6:7:8:9:10:11:12 H SD: 23.1909 cents 7:8:9:10:11:13:14 SD: 17.8045 cents 8:9:10:12:13:15:16 SD: 16.5133 cents 9 x 11:13:14:17:18 SD: 16.9783 cents 10:12:13:15:16:19:20 SD: 10.6526 cents 12:14:15:18:19:23:24 SD: 7.6228 cents 15:18:19:22:24:28:30 SD: 7.1192 cents 16:19:20:24:25:30:32 SD: 5.4366 cents 22:26:28:33:35:41:44 SD: 4.2242 cents 26:31:33:39:41:49:52 SD: 3.8720 cents 27:32:34:40:43:51:54 SD: 2.6603 cents 39:46:49:58:62:73:78 SD: 2.1244 cents 43:51:54:64:68:81:86 SD: 1.7702 cents 49:58:62:73:78:92:98 SD: 1.5753 cents 61:72:77:91:97:115:122 SD: 1.4656 cents 65:77:82:97:103:122:130 SD: 0.7725 cents 92:109:116:137:146:173:184 SD: 0.6237 cents 124:147:156:185:197:233:248 SD: 0.5914 cents 157:186:198:234:249:295:314 SD: 0.5123 cents 158:187:199:236:251:297:316 SD: 0.4368 cents 185:219:233:276:294:348:370 SD: 0.4118 cents 189:224:238:282:300:355:378 SD: 0.3630 cents 201:238:253:300:319:378:402 SD: 0.3298 cents 223:264:281:333:354:419:446 SD: 0.2963 cents 250:296:315:373:397:470:500 SD: 0.1284 cents 315:373:397:470:500:592:630 SD: 0.1141 cents 516:611:650:770:819:970:1032 SD: 0.0834 cents 565:669:712:843:897:1062:1130 SD: 0.0816 cents