Scala analysis: nomar3a
Non-octave marvel
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 115.587 cents 115.587050 2: 231.174 cents 231.174090 3: 268.799 cents 268.798790 4: 384.386 cents 384.385830 5: 499.973 cents 499.972880
SHOW/INTERVAL
0: 115.5871 cents 115.5871 1: 115.5871 cents 115.5871 2: 115.5870 cents 115.5870 3: 37.6247 cents 37.6247 4: 115.5870 cents 115.5870 5: 115.5871 cents 115.5871
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 37.62470 cents 1: 4 115.58705 cents 2: 2 153.21174 cents 2: 3 231.17409 cents 3: 3 268.79879 cents 3: 2 346.76114 cents 4: 4 384.38583 cents 4: 1 462.34818 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 : 115.6 231.2 268.8 384.4 500.0 115.6: 115.6 153.2 268.8 384.4 500.0 231.2: 37.6 153.2 268.8 384.4 500.0 268.8: 115.6 231.2 346.8 462.3 500.0 384.4: 115.6 231.2 346.8 384.4 500.0 500.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.6247 .. 115.5871 cents 77.96235 cents 37.62470 cents 2: 153.2117 .. 231.1741 cents 77.96235 cents 37.62469 cents 3: 268.7988 .. 346.7611 cents 77.96235 cents 37.62470 cents 4: 384.3858 .. 462.3482 cents 77.96235 cents 37.62469 cents
SHOW DATA
Number of notes : 5 -- Interval properties -- Smallest interval : 37.62470 cents, class 1 Average step (divided formal octave): 99.9946 cents Largest one step interval : 115.58705 cents Average / Smallest step : 2.657684 Largest / Average step : 1.155933 Largest / Smallest step : 3.072106 Median interval of one step : 115.58705 cents, amount: 4 Most common interval of one step : 115.58705 cents, amount: 4 Least squares average step : 98.57708 cents, oct.: 492.88539 cents Scale is strictly proper Scale has Myhill's property chromas: 77.96235 cents and 40.33765 cents, ratio: 1.932744 generators: 1 of 115.58705 cents and 4 of 384.38583 cents ET pair of linear temperament : 26&346 Scale is distributional even Scale is a mode of a 186-tone equal temperament with octave 499.973 cents degrees: 43 86 100 143 186 generators: 43 and 143 Number of contiguous 1-step segments: 0 Step pattern alph. order: AABAA Step pattern size order : LLSLL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 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 ] Scale is a Constant Structure, by a margin of 37.62469 cents Scale diversity : 0.604339 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.376267 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 : 37.62469 cents Most common intervals : 115.58705 cents & inv., amount: 4 Scale is a chain of 2 triads 0.0 231.174 384.386 cents Most common triad is 0.0 115.587 384.386 cents, amount: 3 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best minor thirds form a closed circle 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: 1 1 1 1 1 SP B ME I SD: 22.0511 c. M: 31.1849 c. 7: 2 1 1 1 2 N D3 I SD: 20.2864 c. M: 27.2623 c. 8: 2 2 0 2 2 P M DE I SD: 13.3023 c. M: 18.8124 c. 9: 2 2 1 2 2 SP M ME I SD: 6.3385 c. M: 8.9639 c. 13: 3 3 1 3 3 SP M DE I SD: 0.2951 c. M: 0.4174 c. 95: 22 22 7 22 22 SP M DE I SD: 0.2774 c. M: 0.3923 c. 108: 25 25 8 25 25 SP M DE I SD: 0.2085 c. M: 0.2948 c. 121: 28 28 9 28 28 SP M DE I SD: 0.1544 c. M: 0.2183 c. 134: 31 31 10 31 31 SP M DE I SD: 0.1108 c. M: 0.1566 c. 147: 34 34 11 34 34 SP M DE I SD: 0.0749 c. M: 0.1059 c. 160: 37 37 12 37 37 SP M DE I SD: 0.0448 c. M: 0.0634 c. 173: 40 40 13 40 40 SP M DE I SD: 0.0193 c. M: 0.0272 c. 186: 43 43 14 43 43 SP M DE I SD: 0.0027 c. M: 0.0038 c. 731: 169 169 55 169 169 SP M DE I SD: 0.0025 c. M: 0.0035 c. 917: 212 212 69 212 212 SP M DE I SD: 0.0014 c. M: 0.0020 c. 1103: 255 255 83 255 255 SP M DE I SD: 0.0007 c. M: 0.0010 c. 1289: 298 298 97 298 298 SP M DE I SD: 0.0002 c. M: 0.0003 c. 1475: 341 341 111 341 341 SP M DE I SD: 0.0001 c. M: 0.0002 c.
FIT/HARMONIC
1 x x x x 2 S SD: 700.0271 cents 2 x x x x 3 S SD: 201.9821 cents 3 x x x x 4 S SD: 1.9279 cents 4 x x x 5 x S SD: 1.9279 cents 5 x x 6 x 7 S SD: 47.4525 cents 6 x x 7 x 8 S SD: 1.3632 cents 7 x 8 x 9 x S SD: 25.3491 cents 8 x 9 x 10:11 S SD: 19.3889 cents 9 x 10 x 11:12 S SD: 20.4114 cents 10:11 x 12 x 13 S SD: 27.3458 cents 11:12 x 13:14:15 S SD: 16.0264 cents 12:13 x 14:15:16 S SD: 5.8067 cents 13:14:15 x 16:17 S SD: 12.0421 cents 14:15:16 x 17:19 SD: 14.0714 cents 15:16:17:18:19:20 H SD: 11.0284 cents 16:17:18:19:20:21 H SD: 10.0732 cents 18:19 x 21:22:24 SD: 10.7764 cents 19:20 x 22:24:25 S SD: 11.0751 cents 20:21:23 x 25:27 SD: 9.5911 cents 23:25:26:27:29:31 SD: 8.5576 cents 24:26:27:28:30:32 S SD: 7.1633 cents 25:27 x 29:31:33 SD: 7.7820 cents 26:28:30 x 32:35 SD: 8.9129 cents 27:29:31:32:34:36 SD: 6.2987 cents 28:30:32:33:35:37 SD: 4.7671 cents 29:31:33:34:36:39 SD: 3.8343 cents 32:34 x 37:40:43 SD: 5.8880 cents 33:35:38:39:41:44 SD: 5.8419 cents 35:37:40:41:44:47 SD: 5.0953 cents 36:38:41:42:45:48 SD: 4.6074 cents 40:43:46:47:50:53 SD: 4.3999 cents 41:44:47:48:51:55 SD: 2.8681 cents 48:51:55:56:60:64 SD: 2.4038 cents 60:64:69:70:75:80 SD: 2.3863 cents 69:74:79:81:86:92 SD: 2.2889 cents 71:76:81:83:89:95 SD: 1.7908 cents 72:77:82:84:90:96 SD: 1.3832 cents 84:90:96:98:105:112 S SD: 1.0201 cents 113:121:129:132:141:151 SD: 0.8166 cents 132:141:151:154:165:176 SD: 0.7948 cents 161:172:184:188:201:215 SD: 0.2931 cents 245:262:280:286:306:327 SD: 0.2402 cents 406:434:464:474:507:542 SD: 0.1563 cents 595:636:680:695:743:794 SD: 0.1147 cents