Scala analysis: 546_M54
Miscellaneous tetrachord 240/227 * 227/214 * 107/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 240/227 96.410530 2: 120/107 198.508331 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 107/90 299.5367 1: 240/227 96.4105 2: 227/214 102.0978 3: 107/90 299.5367
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 240/227 96.411 cents 1: 1 227/214 102.098 cents 1: 1 107/90 299.537 cents 2: 1 120/107 198.508 cents 2: 1 856/681 395.947 cents 2: 1 227/180 401.634 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 96.4 198.5 498.0 96.4 : 102.1 401.6 498.0 198.5: 299.5 395.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.4105 .. 299.5367 cents 24289/21600, 203.1261 cents 240/227, 96.4105 cents 2: 198.5083 .. 401.6345 cents 24289/21600, 203.1261 cents 10800/11449,-101.0283 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 240/227, 96.4105 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 107/90, 299.5367 cents Average / Smallest step : 1.721959 Largest / Average step : 1.804275 Largest / Smallest step : 3.106887 Median interval of one step : 227/214, 102.0978 cents, amount: 1 Least squares average step : 141.96873 cents, oct.: 425.90618 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1400-tone equal temperament with octave 4/3 degrees: 271 558 1400 Least number of segments generator : 701 of 249.378 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 759 of 270.012 cents and inv. generated superset size: 39 = 36 more = 1300.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 96.41053 cents Scale diversity : 1.074885 Lumma stability : 0.387156 Lumma impropriety factor : 0.202850 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 51529/51360, 5.6873 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Steps are strictly increasing Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 197.4389 cents: 2 -- Rational properties -- Prime limit : 227 Odd number limit : 681 (O: 227 U: 681) Highest odd numerator or denominator: 227 Scale harmonicity : 0.063559 Fundamental : 1/72867, -16.1530 octaves, 0.0036 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.748808E+07, 24.05987 octaves Euler's gradus suavitatis : 345 Sum of Mann's harmonic distance : 350.5, average 116.83333 Mersenne's string divisions : 742063 Sum of van Prooijen's expressibility: 4.86253, average 1.62084 Sum of Tenney's harmonic distance : 9.92398, average 3.30799 Vogel's harmonic complexity : 233.00000 Wille's k value : 12144 Wilson's harmonic complexity : 345 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 16.24482, average 2.70747 Lattice compactness (without 2's) : 8.30056, average 1.38343 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 1 0.33333 3 1 5: 0 .. 1 0.66667 2 107: -1 .. 0 -0.33333 1 1 227: -1 .. 0 -0.33333 1 1 Average exponent except 2's : 1 / 3 = 0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <7 11 15 48 56| Scale is weakly epimorphic with val: <7 11 15 49 58| Scale is weakly epimorphic with val: <7 11 16 49 57| Scale is weakly epimorphic with val: <7 11 16 50 56| Scale is weakly epimorphic with val: <7 11 17 48 57| Scale is weakly epimorphic with val: <7 11 17 50 58| Scale is JI-epimorphic with val: <7 11 18 48 56| Scale is weakly epimorphic with val: <7 11 18 49 58| Scale is JI-epimorphic with val: <7 11 19 49 57| Scale is weakly epimorphic with val: <7 11 19 50 56| Scale is weakly epimorphic with val: <7 12 18 48 57| Scale is weakly epimorphic with val: <7 12 19 48 56| Scale is weakly epimorphic with val: <7 12 19 49 58| Scale is weakly epimorphic with val: <8 11 16 48 58| Scale is weakly epimorphic with val: <8 11 16 50 56| Scale is weakly epimorphic with val: <8 11 17 48 57| Scale is weakly epimorphic with val: <8 11 17 49 56| Scale is weakly epimorphic with val: <8 11 18 49 58| Scale is weakly epimorphic with val: <8 11 18 50 57| Scale is weakly epimorphic with val: <8 12 15 48 57| Scale is weakly epimorphic with val: <8 12 15 49 56| Scale is weakly epimorphic with val: <8 12 16 49 58| Scale is weakly epimorphic with val: <8 12 16 50 57| Scale is weakly epimorphic with val: <8 12 17 48 58| Scale is weakly epimorphic with val: <8 12 17 50 56|
FIT/MODE
3: 0 1 2 N G T3 SD: 58.7390 c. M: 96.4105 c. 4: 1 1 2 P M ME S SD: 33.3733 c. M:-50.5142 c. 5: 1 1 3 N M DE S SD: 1.8915 c. M:-3.1985 c. 42: 8 9 25 N T3 SD: 1.9901 c. M:-3.0813 c. 47: 9 10 28 N T3 SD: 1.7402 c. M:-2.8290 c. 48: 9 10 29 N T3 SD: 1.9173 c. M: 3.0271 c. 52: 10 11 31 N T3 SD: 1.5591 c. M:-2.6252 c. 53: 10 11 32 N T3 SD: 1.5621 c. M: 2.4398 c. 57: 11 12 34 N T3 SD: 1.4290 c. M:-2.4572 c. 58: 11 12 35 N T3 SD: 1.2692 c. M: 1.9537 c. 63: 12 13 38 N T3 SD: 1.0240 c. M: 1.5448 c. 68: 13 14 41 N T3 SD: 0.8167 c. M: 1.1960 c. 73: 14 15 44 N T3 SD: 0.6403 c. M: 0.8951 c. 78: 15 16 47 N T3 SD: 0.4906 c. M: 0.6326 c. 83: 16 17 50 N T3 SD: 0.3661 c. M: 0.4904 c. 88: 17 18 53 N T3 SD: 0.2691 c. M: 0.4223 c. 93: 18 19 56 N T3 SD: 0.2088 c. M: 0.3614 c. 98: 19 20 59 N T3 SD: 0.1969 c. M: 0.3067 c. 103: 20 21 62 N T3 SD: 0.2270 c. M:-0.2972 c. 181: 35 37 109 N T3 SD: 0.2335 c. M: 0.3910 c. 191: 37 39 115 N T3 SD: 0.1966 c. M: 0.3334 c. 201: 39 41 121 N T3 SD: 0.2081 c. M: 0.2815 c. 233: 45 48 140 N T3 SD: 0.2071 c. M:-0.2822 c. 238: 46 49 143 N T3 SD: 0.1890 c. M:-0.2911 c. 243: 47 50 146 N T3 SD: 0.1792 c. M:-0.2998 c. 248: 48 51 149 N T3 SD: 0.1780 c. M:-0.3080 c. 253: 49 52 152 N T3 SD: 0.1846 c. M:-0.3160 c. 258: 50 53 155 N T3 SD: 0.1973 c. M:-0.3236 c. 289: 56 59 174 N T3 SD: 0.1954 c. M: 0.3243 c. 304: 59 62 183 N T3 SD: 0.2137 c. M: 0.2733 c. 311: 60 64 187 N T3 SD: 0.1917 c. M: 0.3247 c. 316: 61 65 190 N T3 SD: 0.1619 c. M: 0.2689 c. 321: 62 66 193 N T3 SD: 0.1343 c. M: 0.2149 c. 326: 63 67 196 N T3 SD: 0.1098 c. M: 0.1626 c. 331: 64 68 199 N T3 SD: 0.0897 c. M: 0.1118 c. 336: 65 69 202 N T3 SD: 0.0765 c. M:-0.1168 c. 341: 66 70 205 N T3 SD: 0.0729 c. M:-0.1255 c. 346: 67 71 208 N T3 SD: 0.0794 c. M:-0.1339 c. 419: 81 86 252 N T3 SD: 0.0749 c. M: 0.1298 c. 424: 82 87 255 N T3 SD: 0.0523 c. M: 0.0905 c. 429: 83 88 258 N T3 SD: 0.0311 c. M: 0.0522 c. 434: 84 89 261 N T3 SD: 0.0149 c. M:-0.0211 c. 873: 169 179 525 N T3 SD: 0.0146 c. M:-0.0251 c. 961: 186 197 578 N T3 SD: 0.0125 c. M: 0.0159 c. 966: 187 198 581 N T3 SD: 0.0071 c. M: 0.0121 c. 1400: 271 287 842 N T3 SD: 0.0022 c. M: 0.0032 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 72.2060 cents 6 x 7:8 S SD: 34.1813 cents 7 x 8:9 S SD: 35.4652 cents 8 x 9:11 SD: 26.7730 cents 9 x 10:12 S SD: 8.0523 cents 10 x 11:13 SD: 27.5848 cents 11 x 12:15 S SD: 30.8436 cents 12:13 x 16 SD: 21.0811 cents 14:15:16:19 SD: 16.7878 cents 15:16:17:20 SD: 7.9245 cents 18:19:20:24 S SD: 5.4492 cents 33:35:37:44 SD: 1.8245 cents 84:89:94:112 SD: 1.7611 cents 90:95:101:120 SD: 1.0078 cents 123:130:138:164 SD: 0.3053 cents 156:165:175:208 SD: 0.2778 cents 279:295:313:372 SD: 0.1944 cents 297:314:333:396 SD: 0.1466 cents 420:444:471:560 SD: 0.0768 cents 576:609:646:768 SD: 0.0209 cents