Scala analysis: xen18-secor-neutral-third-mos-2-tempered
Transposition of a mode of MOS generated by a neutral third, tempered
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 214.441 cents 214.441000 2: 347.923 cents 347.923000 3: 556.677 cents 556.677000 4: 707.220 cents 707.220000 5: 843.546 cents 843.546000 6: 1052.300 cents 1052.300000 7: 1200.000 cents 1200.000000
SHOW/INTERVAL
0: 147.7000 cents 147.7000 1: 214.4410 cents 214.4410 2: 133.4820 cents 133.4820 3: 208.7540 cents 208.7540 4: 150.5430 cents 150.5430 5: 136.3260 cents 136.3260 6: 208.7540 cents 208.7540 7: 147.7000 cents 147.7000
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 133.48200 cents 1: 1 136.32600 cents 1: 1 147.70000 cents 1: 1 150.54300 cents 1: 2 208.75400 cents 1: 1 214.44100 cents 2: 1 286.86900 cents 2: 1 342.23600 cents 2: 1 345.08000 cents 2: 1 347.92300 cents 2: 1 356.45400 cents 2: 1 359.29700 cents 2: 1 362.14100 cents 3: 1 492.77900 cents 3: 1 492.78000 cents 3: 3 495.62300 cents 3: 1 556.67700 cents 3: 1 570.89500 cents 4: 1 629.10500 cents 4: 1 643.32300 cents 4: 3 704.37700 cents 4: 1 707.22000 cents 4: 1 707.22100 cents 5: 1 837.85900 cents 5: 1 840.70300 cents 5: 1 843.54600 cents 5: 1 852.07700 cents 5: 1 854.92000 cents 5: 1 857.76400 cents 5: 1 913.13100 cents 6: 1 985.55900 cents 6: 2 991.24600 cents 6: 1 1049.45700 cents 6: 1 1052.30000 cents 6: 1 1063.67400 cents 6: 1 1066.51800 cents Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 6.00000 = 6
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 214.4 347.9 556.7 707.2 843.5 1052.3 1200.0 214.4 : 133.5 342.2 492.8 629.1 837.9 985.6 1200.0 347.9 : 208.8 359.3 495.6 704.4 852.1 1066.5 1200.0 556.7 : 150.5 286.9 495.6 643.3 857.8 991.2 1200.0 707.2 : 136.3 345.1 492.8 707.2 840.7 1049.5 1200.0 843.5 : 208.8 356.5 570.9 704.4 913.1 1063.7 1200.0 1052.3: 147.7 362.1 495.6 704.4 854.9 991.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.4820 .. 214.4410 cents 80.95900 cents 133.48200 cents 2: 286.8690 .. 362.1410 cents 75.27200 cents 72.42800 cents 3: 492.7790 .. 570.8950 cents 78.11600 cents 130.63800 cents 4: 629.1050 .. 707.2210 cents 78.11600 cents 58.21000 cents 5: 837.8590 .. 913.1310 cents 75.27200 cents 130.63800 cents 6: 985.5590 .. 1066.5180 cents 80.95900 cents 72.42800 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 133.48200 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 214.44100 cents Average / Smallest step : 1.284282 Largest / Average step : 1.250906 Largest / Smallest step : 1.606516 Median interval of one step : 150.54300 cents, amount: 1 Most common interval of one step : 208.75400 cents, amount: 2 Least squares average step : 173.86234 cents, oct.: 1217.03640 cents Scale is strictly proper Step pattern alph. order: ABCDECF Step pattern size order : FAEDBEC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 58.21000 cents Scale diversity : 1.345625 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.609422 Rothenberg efficiency : 0.327891 redundancy: 0.672109 Efficiency x scale size : 2.295238 Number of different interval sizes : 36 = 6.00000 / class Number of one step interval sizes : 6 Highest interval variety : 7 Mean interval variety : 6.00000 = 6 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 0.00100 cents Most common intervals : 495.62300 cents & inv., amount: 3 Most common triad is 0.0 495.623 704.377 cents, amount: 2 Number of recognisable fifths : 5, average 705.5144 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 14.2857% Limited inverse transpositions with margin 80.9590 cents: 1 -- Rational properties --
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 26.4120 c. M: 43.0124 c. Lebeng 10: 2 1 2 1 1 2 1 P M ME S SD: 22.7382 c. M:-43.3230 c. 13: 2 2 2 2 1 2 2 SP M ME S SD: 23.4631 c. M: 36.9154 c. Glacial-7, Lobonian 15: 3 1 3 2 2 2 2 SP D3 S SD: 21.0017 c. M:-36.4540 c. 17: 3 2 3 2 2 3 2 SP M ME S SD: 4.6827 c. M:-8.0289 c. 54: 10 6 9 7 6 9 7 SP SD: 5.3147 c. M: 7.8556 c. 56: 10 6 10 7 6 10 7 SP T3 SD: 3.6358 c. M: 7.8317 c. 58: 10 7 10 7 7 10 7 SP M DE S SD: 4.1403 c. M: 7.5444 c. 63: 11 7 11 8 7 11 8 SP T3 SD: 4.2420 c. M: 5.4508 c. 71: 13 8 12 9 8 12 9 SP SD: 3.9069 c. M:-7.0066 c. 73: 13 8 13 9 8 13 9 SP T3 SD: 2.3913 c. M: 5.1898 c. 80: 14 9 14 10 9 14 10 SP T3 SD: 2.7741 c. M: 4.4410 c. 90: 16 10 16 11 10 16 11 SP T3 SD: 1.9927 c. M: 3.5460 c. 114: 20 13 20 14 13 20 14 SP T3 SD: 1.8178 c. M: 3.9147 c. 127: 23 14 22 16 14 22 16 SP SD: 2.1628 c. M: 3.4811 c. 129: 23 14 23 16 15 22 16 SP SD: 1.9453 c. M: 3.7370 c. 131: 23 15 23 16 15 23 16 SP T3 SD: 1.8510 c. M: 3.7540 c. 138: 25 15 24 17 16 24 17 SP SD: 1.5587 c. M:-2.9503 c. 144: 26 16 25 18 16 25 18 SP SD: 1.7757 c. M: 2.3000 c. 145: 26 16 25 18 17 25 18 SP SD: 1.7583 c. M: 3.7717 c. 151: 27 17 26 19 17 26 19 SP SD: 1.4839 c. M: 3.2934 c. 155: 28 17 27 19 18 27 19 SP SD: 1.4137 c. M: 2.7039 c. 168: 30 19 29 21 19 29 21 SP SD: 1.2145 c. M: 2.3000 c. 185: 33 21 32 23 21 32 23 SP SD: 1.1559 c. M:-2.3473 c. 196: 35 22 34 25 22 34 24 SP SD: 1.3453 c. M:-2.9841 c. 202: 36 23 35 25 23 35 25 SP SD: 1.2377 c. M:-2.5720 c. 203: 36 23 35 26 23 35 25 SP SD: 1.3168 c. M:-2.1396 c. 211: 38 23 37 26 24 37 26 SP SD: 1.2924 c. M: 2.0067 c. 212: 38 23 37 27 24 37 26 SP SD: 1.2900 c. M: 2.6400 c. 213: 38 24 37 27 24 37 26 SP SD: 1.4110 c. M:-2.6392 c. 218: 39 24 38 27 25 38 27 SP SD: 1.2786 c. M: 2.6328 c. 220: 39 25 38 28 25 38 27 SP SD: 1.2942 c. M:-1.9085 c. 222: 40 24 39 28 25 39 27 SP SD: 1.2549 c. M: 1.9771 c. 228: 41 25 40 28 26 40 28 SP SD: 1.1725 c. M: 1.9568 c. 229: 41 25 40 29 26 40 28 SP SD: 0.9963 c. M: 2.0715 c. 235: 42 26 41 29 27 41 29 SP SD: 1.0733 c. M: 2.5391 c. 246: 44 27 43 31 28 43 30 SP SD: 0.8329 c. M: 1.5815 c. 263: 47 29 46 33 30 46 32 SP SD: 0.8029 c. M:-1.6924 c. 270: 48 30 47 34 31 47 33 SP SD: 0.9445 c. M: 1.2563 c. 276: 49 31 48 35 31 48 34 SP SD: 0.7732 c. M:-1.4757 c. 293: 52 33 51 37 33 51 36 SP SD: 0.7670 c. M: 1.4717 c. 300: 54 33 52 38 34 52 37 SP SD: 0.7367 c. M:-1.5590 c. 317: 57 35 55 40 36 55 39 SP SD: 0.6285 c. M:-1.3319 c. 324: 58 36 56 41 37 56 40 SP SD: 0.5966 c. M: 1.1214 c. 334: 60 37 58 42 38 58 41 SP SD: 0.6225 c. M:-1.1279 c. 341: 61 38 59 43 39 59 42 SP SD: 0.5054 c. M:-1.0288 c. 351: 63 39 61 44 40 61 43 SP SD: 0.6945 c. M:-0.9436 c. 358: 64 40 62 45 41 62 44 SP SD: 0.5205 c. M:-1.1467 c. 380: 68 42 66 48 43 66 47 SP SD: 0.5176 c. M: 0.8875 c. 390: 70 43 68 49 44 68 48 SP SD: 0.4547 c. M:-0.9436 c. 397: 71 44 69 50 45 69 49 SP SD: 0.2949 c. M: 0.5057 c. 414: 74 46 72 52 47 72 51 SP SD: 0.0905 c. M: 0.1553 c. 845: 151 94 147 106 96 147 104 SP SD: 0.0055 c. M:-0.0094 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 2.6325 cents 3 x x 4 x 5 x 6 S SD: 23.8127 cents 4 x 5 x 6 x 7:8 S SD: 23.0075 cents 5 x 6:7 x 8:9:10 S SD: 12.3378 cents 6:7 x 8:9:10:11:12 S SD: 14.8030 cents 7:8:9:10 x 11:13:14 SD: 20.8693 cents 8:9:10:11:12:13:15:16 SD: 7.7513 cents 14:16:17:19:21:23:26:28 SD: 6.1604 cents 18:20:22:25:27:29:33:36 SD: 5.5835 cents 22:25:27:30:33:36:40:44 SD: 4.2598 cents 24:27:29:33:36:39:44:48 SD: 3.4911 cents 30:34:37:41:45:49:55:60 SD: 3.3726 cents 32:36:39:44:48:52:59:64 SD: 2.2735 cents 45:51:55:62:68:73:83:90 SD: 1.7933 cents 53:60:65:73:80:86:97:106 SD: 1.6407 cents 67:76:82:92:101:109:123:134 SD: 1.3511 cents 68:77:83:94:102:111:125:136 SD: 1.2549 cents 81:92:99:112:122:132:149:162 SD: 1.1996 cents 85:96:104:117:128:138:156:170 SD: 1.0369 cents 99:112:121:137:149:161:182:198 SD: 0.9068 cents 105:119:128:145:158:171:193:210 SD: 0.8782 cents 113:128:138:156:170:184:208:226 SD: 0.7053 cents 121:137:148:167:182:197:222:242 SD: 0.3265 cents 234:265:286:323:352:381:430:468 SD: 0.3013 cents 256:290:313:353:385:417:470:512 SD: 0.3003 cents 274:310:335:378:412:446:503:548 SD: 0.2128 cents 311:352:380:429:468:506:571:622 SD: 0.2075 cents 319:361:390:440:480:519:586:638 SD: 0.1601 cents 440:498:538:607:662:716:808:880 SD: 0.1046 cents 575:651:703:793:865:936:1056:1150 SD: 0.0812 cents