Scala analysis: xen18-erlich-miracle-04
1L 3s MOS for Miracle, L=850.47, s=116.72
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 116.720 cents 116.720000 2: 967.190 cents 967.190000 3: 1083.910 cents 1083.910000 4: 1200.630 cents 1200.630000
SHOW/INTERVAL
0: 116.7200 cents 116.7200 1: 116.7200 cents 116.7200 2: 850.4700 cents 850.4700 3: 116.7200 cents 116.7200 4: 116.7200 cents 116.7200
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 116.72000 cents 1: 1 850.47000 cents 2: 2 233.44000 cents 2: 2 967.19000 cents 3: 1 350.16000 cents 3: 3 1083.91000 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 0.0 : 116.7 967.2 1083.9 1200.6 116.7 : 850.5 967.2 1083.9 1200.6 967.2 : 116.7 233.4 350.2 1200.6 1083.9: 116.7 233.4 1083.9 1200.6 1200.6
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 116.7200 .. 850.4700 cents 733.75000 cents 116.72000 cents 2: 233.4400 .. 967.1900 cents 733.75000 cents -617.03000 cents 3: 350.1600 .. 1083.9100 cents 733.75000 cents -617.03000 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 116.72000 cents, class 1 Average step (divided formal octave): 300.1575 cents Largest one step interval : 850.47000 cents Average / Smallest step : 2.571603 Largest / Average step : 2.833412 Largest / Smallest step : 7.286412 Median interval of one step : 116.72000 cents, amount: 3 Most common interval of one step : 116.72000 cents, amount: 3 Least squares average step : 336.84500 cents, oct.: 1347.38000 cents Scale is not proper Scale has Myhill's property chromas: 733.75000 cents and 617.03000 cents, ratio: 1.189164 generators: 1 of 116.72000 cents and 3 of 1083.91000 cents ET pair of linear temperament : 10&31 Scale is distributional even Scale is a mode of a 1543-tone equal temperament with octave 1200.630 cents degrees: 150 1243 1393 1543 generators: 150 and 1393 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABAA Step pattern size order : SLSS Scale is a Constant Structure, by a margin of 116.72000 cents Scale diversity : 1.058732 Lumma stability : 0.194431 Lumma impropriety factor : 0.611137 Rothenberg efficiency : 0.833333 redundancy: 0.166667 Efficiency x scale size : 3.333333 Number of different interval sizes : 6 = 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 : 116.72000 cents Most common intervals : 116.72000 cents & inv., amount: 3 Scale is a chain of 2 triads 0.0 116.720 1083.910 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 3 = 75.0000% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 3-4 -- Rational properties --
FIT/MODE
4: 0 3 0 1 N D3 SD: 113.7147 c. M: 183.4375 c. 5: 0 4 0 1 N D3 SD: 84.9960 c. M: 123.4060 c. 6: 1 4 0 1 N G SD: 61.2726 c. M: 83.3850 c. 8: 1 5 1 1 N M DE SD: 40.8560 c. M: 66.7175 c. 9: 1 6 1 1 N M DE SD: 20.4328 c. M: 33.3667 c. 10: 1 7 1 1 N M DE SD: 4.0943 c. M: 6.6860 c. 21: 2 15 2 2 N M DE SD: 2.9079 c. M:-4.7486 c. 31: 3 22 3 3 N M DE SD: 0.6491 c. M:-1.0600 c. 41: 4 29 4 4 N M DE SD: 0.5078 c. M: 0.8293 c. 72: 7 51 7 7 N M DE SD: 0.0097 c. M: 0.0158 c. 1111: 108 787 108 108 N M DE SD: 0.0087 c. M:-0.0142 c. 1183: 115 838 115 115 N M DE SD: 0.0076 c. M:-0.0124 c. 1255: 122 889 122 122 N M DE SD: 0.0066 c. M:-0.0107 c. 1327: 129 940 129 129 N M DE SD: 0.0057 c. M:-0.0093 c. 1399: 136 991 136 136 N M DE SD: 0.0049 c. M:-0.0080 c. 1471: 143 1042 143 143 N M DE SD: 0.0042 c. M:-0.0068 c. 1543: 150 1093 150 150 N M DE SD: 0.0035 c. M:-0.0058 c. 1615: 157 1144 157 157 N M DE SD: 0.0030 c. M:-0.0048 c. 1687: 164 1195 164 164 N M DE SD: 0.0024 c. M:-0.0039 c. 1759: 171 1246 171 171 N M DE SD: 0.0019 c. M:-0.0031 c. 1831: 178 1297 178 178 N M DE SD: 0.0015 c. M:-0.0024 c. 1903: 185 1348 185 185 N M DE SD: 0.0010 c. M:-0.0017 c. 1975: 192 1399 192 192 N M DE SD: 0.0006 c. M:-0.0011 c. 2047: 199 1450 199 199 N M DE SD: 0.0003 c. M:-0.0005 c. 2119: 206 1501 206 206 N M DE SD: 0.0001 c. M: 0.0001 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.6300 cents 2 x x x 4 S SD: 0.6300 cents 3:4:5 x 6 S SD: 130.0727 cents 4:5:7 x 8 SD: 89.8665 cents 5:6:9 x 10 S SD: 68.4031 cents 6:7 x 11:12 SD: 51.3584 cents 7:8:12:13:14 S SD: 30.0097 cents 8:9:14:15:16 SD: 21.8291 cents 9:10:16:17:18 SD: 18.4452 cents 10:11:17:19:20 SD: 18.4279 cents 11:12:19:21:22 SD: 13.3594 cents 12:13:21:22:24 SD: 10.2290 cents 13:14:23:24:26 SD: 8.1490 cents 15:16:26:28:30 SD: 4.0270 cents 16:17:28:30:32 SD: 3.1670 cents 28:30:49:52:56 SD: 3.1576 cents 31:33:54:58:62 SD: 2.6600 cents 40:43:70:75:80 SD: 2.4245 cents 44:47:77:82:88 SD: 1.7229 cents 55:59:96:103:110 SD: 1.5197 cents 56:60:98:105:112 SD: 1.3575 cents 71:76:124:133:142 SD: 0.8836 cents 84:90:147:157:168 SD: 0.8588 cents 99:106:173:185:198 SD: 0.5999 cents 100:107:175:187:200 SD: 0.4551 cents 115:123:201:215:230 SD: 0.2730 cents 215:230:376:402:430 SD: 0.2323 cents 286:306:500:535:572 SD: 0.1932 cents 401:429:701:750:802 SD: 0.1699 cents 501:536:876:937:1002 SD: 0.1689 cents