Scala analysis: 535_M43
Miscellaneous tetrachord 240/229 * 229/218 * 109/90
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 240/229 81.224169 2: 120/109 166.447525 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 109/90 331.5975 1: 240/229 81.2242 2: 229/218 85.2234 3: 109/90 331.5975
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 240/229 81.224 cents 1: 1 229/218 85.223 cents 1: 1 109/90 331.597 cents 2: 1 120/109 166.448 cents 2: 1 872/687 412.822 cents 2: 1 229/180 416.821 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 : 81.2 166.4 498.0 81.2 : 85.2 416.8 498.0 166.4: 331.6 412.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 81.2242 .. 331.5975 cents 24961/21600, 250.3733 cents 240/229, 81.2242 cents 2: 166.4475 .. 416.8208 cents 24961/21600, 250.3733 cents 10800/11881,-165.1499 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 240/229, 81.2242 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 109/90, 331.5975 cents Average / Smallest step : 2.043911 Largest / Average step : 1.997395 Largest / Smallest step : 4.082498 Median interval of one step : 229/218, 85.2234 cents, amount: 1 Least squares average step : 136.30387 cents, oct.: 408.91162 cents Scale is not proper Scale has trivalence property 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 81.22417 cents Scale diversity : 0.910297 Lumma stability : 0.326172 Lumma impropriety factor : 0.331596 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 : 52441/52320, 3.9992 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 246.3741 cents: 2 -- Rational properties -- Prime limit : 229 Odd number limit : 687 (O: 229 U: 687) Highest odd numerator or denominator: 229 Scale harmonicity : 0.063559 Fundamental : 1/74883, -16.1924 octaves, 0.0035 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.797192E+07, 24.09924 octaves Euler's gradus suavitatis : 349 Sum of Mann's harmonic distance : 352.5, average 117.50000 Mersenne's string divisions : 107401 Sum of van Prooijen's expressibility: 4.87438, average 1.62479 Sum of Tenney's harmonic distance : 9.93584, average 3.31195 Vogel's harmonic complexity : 235.66667 Wille's k value : 12480 Wilson's harmonic complexity : 349 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 2 109: -1 .. 0 -0.33333 1 1 229: -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: 46.8955 c. M: 81.2242 c. 4: 0 1 3 N G T3 SD: 52.7763 c. M: 81.2242 c. 5: 1 1 3 N M DE S SD: 21.6941 c. M:-32.7705 c. 6: 1 1 4 N M DE S SD: 1.0595 c. M:-1.7833 c. 69: 11 12 46 N T3 SD: 1.0832 c. M: 1.8257 c. 74: 12 13 49 N T3 SD: 1.0788 c. M:-1.8109 c. 75: 12 13 50 N T3 SD: 0.9218 c. M: 1.5370 c. 81: 13 14 54 N T3 SD: 0.7861 c. M: 1.2910 c. 87: 14 15 58 N T3 SD: 0.6711 c. M: 1.0790 c. 93: 15 16 62 N T3 SD: 0.5736 c. M: 0.8943 c. 99: 16 17 66 N T3 SD: 0.4909 c. M: 0.7320 c. 105: 17 18 70 N T3 SD: 0.4216 c. M: 0.5883 c. 111: 18 19 74 N T3 SD: 0.3646 c. M: 0.4601 c. 117: 19 20 78 N T3 SD: 0.3195 c. M: 0.4325 c. 123: 20 21 82 N T3 SD: 0.2859 c. M: 0.4325 c. 129: 21 22 86 N T3 SD: 0.2638 c. M: 0.4325 c. 135: 22 23 90 N T3 SD: 0.2522 c. M: 0.4325 c. 141: 23 24 94 N T3 SD: 0.2499 c. M: 0.4325 c. 197: 32 34 131 N T3 SD: 0.3016 c. M:-0.4102 c. 203: 33 35 135 N T3 SD: 0.2687 c. M:-0.3853 c. 209: 34 36 139 N T3 SD: 0.2394 c. M:-0.3618 c. 215: 35 37 143 N T3 SD: 0.2137 c. M:-0.3396 c. 221: 36 38 147 N T3 SD: 0.1919 c. M:-0.3187 c. 227: 37 39 151 N T3 SD: 0.1745 c. M:-0.2988 c. 233: 38 40 155 N T3 SD: 0.1617 c. M:-0.2800 c. 239: 39 41 159 N T3 SD: 0.1537 c. M:-0.2621 c. 245: 40 42 163 N T3 SD: 0.1506 c. M:-0.2451 c. 251: 41 43 167 N T3 SD: 0.1519 c. M:-0.2289 c. 257: 42 44 171 N T3 SD: 0.1570 c. M:-0.2134 c. 263: 43 45 175 N T3 SD: 0.1649 c. M:-0.2052 c. 326: 53 56 217 N T3 SD: 0.1530 c. M: 0.2537 c. 332: 54 57 221 N T3 SD: 0.1311 c. M: 0.2168 c. 338: 55 58 225 N T3 SD: 0.1100 c. M: 0.1813 c. 344: 56 59 229 N T3 SD: 0.0897 c. M: 0.1471 c. 350: 57 60 233 N T3 SD: 0.0701 c. M: 0.1140 c. 356: 58 61 237 N T3 SD: 0.0512 c. M: 0.0820 c. 362: 59 62 241 N T3 SD: 0.0331 c. M: 0.0511 c. 368: 60 63 245 N T3 SD: 0.0163 c. M: 0.0212 c. 374: 61 64 249 N T3 SD: 0.0079 c. M:-0.0114 c. 1490: 243 255 992 N T3 SD: 0.0076 c. M:-0.0132 c. 1864: 304 319 1241 N T3 SD: 0.0075 c. M:-0.0128 c. 2238: 365 383 1490 N T3 SD: 0.0075 c. M:-0.0126 c. 2361: 385 404 1572 N T3 SD: 0.0083 c. M: 0.0106 c. 2367: 386 405 1576 N T3 SD: 0.0074 c. M: 0.0117 c. 2373: 387 406 1580 N T3 SD: 0.0074 c. M: 0.0128 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: 85.7226 cents 6 x 7:8 S SD: 50.2117 cents 7 x 8:9 S SD: 45.1487 cents 8 x 9:11 SD: 32.5632 cents 9 x 10:12 S SD: 7.9781 cents 10 x 11:13 SD: 21.9274 cents 11 x 12:15 S SD: 20.9978 cents 12 x 13:16 SD: 13.9374 cents 13 x 14:17 SD: 25.4238 cents 14:15 x 19 SD: 24.4929 cents 15:16:17:20 SD: 19.5921 cents 16:17:18:21 S SD: 17.3524 cents 17:18:19:23 SD: 13.4779 cents 18:19:20:24 S SD: 6.7316 cents 21:22:23:28 SD: 2.9935 cents 39:41:43:52 SD: 1.9826 cents 60:63:66:80 SD: 1.1832 cents 108:113:119:144 SD: 1.0760 cents 129:135:142:172 SD: 0.8427 cents 147:154:162:196 SD: 0.6316 cents 168:176:185:224 SD: 0.2701 cents 228:239:251:304 SD: 0.1179 cents 396:415:436:528 SD: 0.0573 cents