Scala analysis: 493_M1
Miscellaneous tetrachord 176/175 * 175/174 * 29/22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 176/175 9.864608 valinorsma 2: 88/87 19.785747 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 29/22 478.2593 1: 176/175 9.8646 valinorsma 2: 175/174 9.9211 3: 29/22 478.2593
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 176/175 9.865 cents valinorsma 1: 1 175/174 9.921 cents 1: 1 29/22 478.259 cents 2: 1 88/87 19.786 cents 2: 1 232/175 488.124 cents 2: 1 175/132 488.180 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 : 9.9 19.8 498.0 9.9 : 9.9 488.2 498.0 19.8 : 478.3 488.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 9.8646 .. 478.2593 cents 5075/3872, 468.3946 cents 176/175, 9.8646 cents 2: 19.7857 .. 488.1804 cents 5075/3872, 468.3946 cents 1936/2523,-458.4735 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 176/175, 9.8646 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 29/22, 478.2593 cents Average / Smallest step : 16.829356 Largest / Average step : 2.880820 Largest / Smallest step : 48.482336 Median interval of one step : 175/174, 9.9211 cents, amount: 1 Least squares average step : 110.25508 cents, oct.: 330.76524 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 9.86461 cents Scale diversity :-0.141341 Lumma stability : 0.039613 Lumma impropriety factor : 0.920546 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 : 30625/30624, 0.0565 cents Number of recognisable fifths : 0 Number of recognisable fourths : 2, average 488.1521 cents Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions : 2 Inversional symmetry on degrees : 1 Inversional symmetry on intervals : 2-3 -- Rational properties -- Prime limit : 29 Odd number limit : 175 (O: 175 U: 175) Highest odd numerator or denominator: 175 Scale harmonicity : 0.009804 Average absolute harmonicity : 0.083070 Specific harmonicity : 0.048801 Fundamental : 1/15225, -13.8942 octaves, 0.0172 Hz. Guide tone : 176, 7.4594 octaves, 46046.099 Hz. Exponens Consonantiae : 2.679600E+06, 21.35359 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 266.5, average 88.83333 Mersenne's string divisions : 61425 Sum of van Prooijen's expressibility: 4.65968, average 1.55323 Sum of Tenney's harmonic distance : 9.45173, average 3.15058 Vogel's harmonic complexity : 42.00000 Wille's k value : 2537 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 18.26769, average 3.04461 Lattice compactness (without 2's) : 11.88726, average 1.98121 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.00000 9 3: -1 .. 0 -0.66667 2 1 5: -2 .. 0 -0.66667 2 7: -1 .. 0 -0.33333 1 11: 0 .. 1 0.66667 2 1 29: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 16 19 24 35| Scale is weakly epimorphic with val: <7 11 16 19 25 34| Scale is weakly epimorphic with val: <7 11 16 19 25 37| Scale is JI-epimorphic with val: <7 11 16 20 25 33| Scale is weakly epimorphic with val: <7 11 16 20 25 36| Scale is weakly epimorphic with val: <7 11 16 20 26 35| Scale is weakly epimorphic with val: <7 11 16 21 24 33| Scale is weakly epimorphic with val: <7 11 16 21 24 36| Scale is JI-epimorphic with val: <7 11 16 21 26 34| Scale is weakly epimorphic with val: <7 11 16 21 26 37| Scale is weakly epimorphic with val: <7 11 17 19 24 33| Scale is weakly epimorphic with val: <7 11 17 19 24 36| Scale is JI-epimorphic with val: <7 11 17 19 26 34| Scale is weakly epimorphic with val: <7 11 17 19 26 37| Scale is weakly epimorphic with val: <7 11 17 20 24 35| Scale is weakly epimorphic with val: <7 11 17 20 25 34| Scale is weakly epimorphic with val: <7 11 17 20 25 37| Scale is weakly epimorphic with val: <7 11 17 21 25 33| Scale is weakly epimorphic with val: <7 11 17 21 25 36| Scale is weakly epimorphic with val: <7 11 17 21 26 35| Scale is weakly epimorphic with val: <7 11 18 19 25 33| Scale is weakly epimorphic with val: <7 11 18 19 25 36| Scale is weakly epimorphic with val: <7 11 18 19 26 35| Scale is weakly epimorphic with val: <7 11 18 20 24 33| Scale is weakly epimorphic with val: <7 11 18 20 24 36| Scale is weakly epimorphic with val: <7 11 18 20 26 34| Scale is weakly epimorphic with val: <7 11 18 20 26 37| Scale is weakly epimorphic with val: <7 11 18 21 24 35| Scale is weakly epimorphic with val: <7 11 18 21 25 34| Scale is weakly epimorphic with val: <7 11 18 21 25 37| Scale is weakly epimorphic with val: <7 12 16 19 26 34| Scale is weakly epimorphic with val: <7 12 16 19 26 37|
FIT/MODE
3: 0 0 3 N M DE S SD: 12.7644 c. M: 19.7857 c. 17: 0 1 16 N G T3 SD: 7.9114 c. M: 9.8646 c. 18: 0 1 17 N G T3 SD: 7.2906 c. M: 9.8646 c. 19: 0 1 18 N G T3 SD: 6.7975 c. M: 9.8646 c. 20: 0 1 19 N G T3 SD: 6.4158 c. M: 9.8646 c. 21: 0 1 20 N G T3 SD: 6.1308 c. M: 9.8646 c. 22: 0 1 21 N G T3 SD: 5.9287 c. M: 9.8646 c. 23: 0 1 22 N G T3 SD: 5.7966 c. M: 9.8646 c. 24: 0 1 23 N G T3 SD: 5.7226 c. M: 9.8646 c. 25: 0 1 24 N G T3 SD: 5.6959 c. M: 9.8646 c. 26: 0 1 25 N G T3 SD: 5.7069 c. M: 9.8646 c. 27: 0 1 26 N G T3 SD: 5.7476 c. M: 9.8646 c. 28: 0 1 27 N G T3 SD: 5.8110 c. M: 9.8646 c. 29: 0 1 28 N G T3 SD: 5.8916 c. M: 9.8646 c. 30: 0 1 29 N G T3 SD: 5.9847 c. M: 9.8646 c. 31: 0 1 30 N G T3 SD: 6.0868 c. M: 9.8646 c. 32: 0 1 31 N G T3 SD: 6.1950 c. M: 9.8646 c. 33: 0 1 32 N G T3 SD: 6.3071 c. M: 9.8646 c. 34: 1 0 33 N G T3 SD: 4.0529 c. M: 5.1374 c. 37: 1 1 35 N M DE S SD: 4.6133 c. M:-7.1356 c. 39: 1 1 37 N M DE S SD: 3.7222 c. M:-5.7550 c. 40: 1 1 38 N M DE S SD: 3.3100 c. M:-5.1165 c. 41: 1 1 39 N M DE S SD: 2.9180 c. M:-4.5091 c. 42: 1 1 40 N M DE S SD: 2.5446 c. M:-3.9307 c. 43: 1 1 41 N M DE S SD: 2.1886 c. M:-3.3791 c. 44: 1 1 42 N M DE S SD: 1.8487 c. M:-2.8527 c. 45: 1 1 43 N M DE S SD: 1.5240 c. M:-2.3496 c. 46: 1 1 44 N M DE S SD: 1.2134 c. M:-1.8684 c. 47: 1 1 45 N M DE S SD: 0.9161 c. M:-1.4077 c. 48: 1 1 46 N M DE S SD: 0.6311 c. M:-0.9661 c. 49: 1 1 47 N M DE S SD: 0.3579 c. M:-0.5426 c. 50: 1 1 48 N M DE S SD: 0.0962 c. M:-0.1361 c. 101: 2 2 97 N M DE S SD: 0.0354 c. M: 0.0612 c. 151: 3 3 145 N M DE S SD: 0.0177 c. M:-0.0303 c. 252: 5 5 242 N M DE S SD: 0.0162 c. M: 0.0221 c. 403: 8 8 387 N M DE S SD: 0.0146 c. M:-0.0221 c. 655: 13 13 629 N M DE S SD: 0.0149 c. M:-0.0203 c. 856: 17 17 822 N M DE S SD: 0.0154 c. M:-0.0265 c. 907: 18 18 871 N M DE S SD: 0.0152 c. M:-0.0194 c. 957: 19 19 919 N M DE S SD: 0.0146 c. M:-0.0234 c. 1007: 20 20 967 N M DE S SD: 0.0157 c. M:-0.0271 c. 1058: 21 21 1016 N M DE S SD: 0.0147 c. M:-0.0210 c. 1158: 23 23 1112 N M DE S SD: 0.0159 c. M:-0.0275 c. 1159: 23 23 1113 N M DE S SD: 0.0153 c. M:-0.0189 c. 1259: 25 25 1209 N M DE S SD: 0.0149 c. M:-0.0251 c. 1309: 26 26 1257 N M DE S SD: 0.0161 c. M:-0.0278 c. 1360: 27 27 1306 N M DE S SD: 0.0146 c. M:-0.0230 c. 1460: 29 29 1402 N M DE S SD: 0.0162 c. M:-0.0281 c. 1461: 29 29 1403 N M DE S SD: 0.0147 c. M:-0.0213 c. 1511: 30 30 1451 N M DE S SD: 0.0147 c. M:-0.0238 c. 1611: 32 32 1547 N M DE S SD: 0.0163 c. M:-0.0283 c. 1663: 33 33 1597 N M DE S SD: 0.0156 c. M: 0.0197 c. 1713: 34 34 1645 N M DE S SD: 0.0148 c. M:-0.0207 c. 1763: 35 35 1693 N M DE S SD: 0.0146 c. M:-0.0228 c. 2166: 43 43 2080 N M DE S SD: 0.0146 c. M:-0.0227 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 x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7 x 8:9 S SD: 110.2827 cents 8 x 9:11 SD: 95.8381 cents 9 x 10:12 S SD: 81.3090 cents 10 x 11:13 SD: 75.8445 cents 11 x 12:15 S SD: 68.2564 cents 12 x 13:16 SD: 59.3935 cents 13 x 14:17 SD: 56.8003 cents 14 x 15:19 SD: 52.1308 cents 15 x 16:20 S SD: 45.9728 cents 16 x 17:21 SD: 44.7135 cents 17 x 18:23 SD: 41.5526 cents 18 x 19:24 SD: 36.9086 cents 19 x 20:25 S SD: 36.3623 cents 20 x 21:27 SD: 34.0816 cents 21 x 22:28 SD: 30.3756 cents 22 x 23:29 SD: 30.2488 cents 23 x 24:31 SD: 28.5261 cents 24 x 25:32 SD: 25.4433 cents 25 x 26:33 SD: 25.5820 cents 26 x 27:35 SD: 24.2354 cents 27 x 28:36 SD: 21.5876 cents 28 x 29:37 SD: 21.9047 cents 29 x 30:39 SD: 20.8236 cents 30 x 31:40 SD: 18.4906 cents 31 x 32:41 SD: 18.9344 cents 32 x 33:43 SD: 18.0479 cents 33 x 34:44 SD: 15.9484 cents 34 x 35:45 SD: 16.4872 cents 35 x 36:47 SD: 15.7475 cents 36 x 37:48 SD: 13.8241 cents 37 x 38:49 SD: 14.4381 cents 38 x 39:51 SD: 13.8122 cents 39 x 40:52 SD: 12.0227 cents 40 x 41:53 SD: 12.6995 cents 41 x 42:55 SD: 12.1635 cents 42 x 43:56 SD: 10.4755 cents 43 x 44:57 SD: 11.2081 cents 44 x 45:59 SD: 10.7446 cents 45 x 46:60 SD: 9.1324 cents 46 x 47:61 SD: 9.9171 cents 47 x 48:63 SD: 9.5131 cents 48 x 49:64 SD: 7.9555 cents 49 x 50:65 SD: 8.7913 cents 50 x 51:67 SD: 8.4369 cents 51 x 52:68 SD: 6.9158 cents 52 x 53:69 SD: 7.8041 cents 53 x 54:71 SD: 7.4916 cents 54 x 55:72 SD: 5.9905 cents 55 x 56:73 SD: 6.9347 cents 56 x 57:75 SD: 6.6582 cents 57 x 58:76 SD: 5.1617 cents 58 x 59:77 SD: 6.1672 cents 59 x 60:79 SD: 5.9221 cents 60 x 61:80 SD: 4.4152 cents 61 x 62:81 SD: 5.4891 cents 62 x 63:83 SD: 5.2720 cents 63 x 64:84 SD: 3.7392 cents 64 x 65:85 SD: 4.8912 cents 65 x 66:87 SD: 4.6993 cents 66 x 67:88 SD: 3.1242 cents 67 x 68:89 SD: 4.3662 cents 68 x 69:91 SD: 4.1977 cents 69 x 70:92 SD: 2.5623 cents 70 x 71:93 SD: 3.9093 cents 71 x 72:95 SD: 3.7628 cents 72 x 73:96 SD: 2.0469 cents 73 x 74:97 SD: 3.5170 cents 74 x 75:99 SD: 3.3917 cents 75 x 76:100 SD: 1.5724 cents 76 x 77:101 SD: 3.1872 cents 77 x 78:103 SD: 3.0826 cents 78 x 79:104 SD: 1.1342 cents 79 x 80:105 SD: 2.9187 cents 80 x 81:107 SD: 2.8345 cents 81 x 82:108 SD: 0.7283 cents 82 x 83:109 SD: 2.7103 cents 83 x 84:111 SD: 2.6461 cents 84 x 85:112 SD: 0.3512 cents 85 x 86:113 SD: 2.5602 cents 86 x 87:115 SD: 2.5153 cents 87 x 88:116 SD: 0.0000 cents 88 x 89:117 SD: 2.4652 cents 89 x 90:119 SD: 2.4381 cents 90 x 91:120 SD: 0.3279 cents 91 x 92:121 SD: 2.4203 cents 92 x 93:123 SD: 2.4091 cents 93 x 94:124 SD: 0.6348 cents 94 x 95:125 SD: 2.4189 cents 95 x 96:127 SD: 2.4212 cents 96 x 97:128 SD: 0.9227 cents 97 x 98:129 SD: 2.4535 cents 98 x 99:131 SD: 2.4667 cents 99 x 100:132 SD: 1.1931 cents 100 x 101:133 SD: 2.5164 cents 101 x 102:135 SD: 2.5380 cents 102 x 103:136 SD: 1.4478 cents 103 x 104:137 SD: 2.6008 cents 104 x 105:139 SD: 2.6286 cents 105 x 106:140 SD: 1.6879 cents 106 x 107:141 SD: 2.7005 cents 107 x 108:143 SD: 2.7329 cents 108 x 109:144 SD: 1.9148 cents 109 x 110:145 SD: 2.8109 cents 110 x 111:147 SD: 2.8464 cents 111 x 112:148 SD: 2.1294 cents 112 x 113:149 SD: 2.9283 cents 113 x 114:151 SD: 2.9657 cents 114 x 115:152 SD: 2.3329 cents 115 x 116:153 SD: 3.0497 cents 116 x 117:155 SD: 3.0883 cents 117:118 x 156 SD: 2.4347 cents 118:119 x 157 SD: 2.9999 cents 119:120 x 159 SD: 2.9398 cents 120:121 x 160 SD: 2.2513 cents 121:122 x 161 SD: 2.8303 cents 122:123 x 163 SD: 2.7738 cents 123:124 x 164 SD: 2.0768 cents 124:125 x 165 SD: 2.6710 cents 125:126 x 167 SD: 2.6178 cents 126:127 x 168 SD: 1.9106 cents 127:128 x 169 SD: 2.5214 cents 128:129 x 171 SD: 2.4713 cents 129:130 x 172 SD: 1.7520 cents 130:131 x 173 SD: 2.3810 cents 132:133:134:176 SD: 2.3402 cents 135:136:137:180 SD: 2.1259 cents 138:139:140:184 SD: 1.9208 cents 141:142:143:188 SD: 1.7244 cents 144:145:146:192 SD: 1.5361 cents 147:148:149:196 SD: 1.3555 cents 150:151:152:200 SD: 1.1821 cents 153:154:155:204 SD: 1.0154 cents 156:157:158:208 SD: 0.8551 cents 159:160:161:212 SD: 0.7008 cents 162:163:164:216 SD: 0.5522 cents 165:166:167:220 SD: 0.4091 cents 168:169:170:224 SD: 0.2711 cents 171:172:173:228 SD: 0.1383 cents 174:175:176:232 SD: 0.0188 cents