Scala analysis: 590_M98
Miscellaneous tetrachord 19/17 * 85/76 * 16/15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/17 192.557607 quasi-meantone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 19/17 192.5576 quasi-meantone 2: 85/76 193.7561 3: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 19/17 192.558 cents quasi-meantone 1: 1 85/76 193.756 cents 2: 1 304/255 304.289 cents 2: 1 68/57 305.487 cents 2: 1 5/4 386.314 cents major third 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 : 192.6 386.3 498.0 192.6: 193.8 305.5 498.0 386.3: 111.7 304.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 111.7313 .. 193.7561 cents 1275/1216, 82.0248 cents 16/15, 111.7313 cents 2: 304.2889 .. 386.3137 cents 1275/1216, 82.0248 cents 23104/21675, 110.5328 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 16/15, 111.7313 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 85/76, 193.7561 cents Average / Smallest step : 1.485842 Largest / Average step : 1.167100 Largest / Smallest step : 1.734126 Median interval of one step : 19/17, 192.5576 cents, amount: 1 Least squares average step : 175.66572 cents, oct.: 526.99715 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 419-tone equal temperament with octave 4/3 degrees: 162 325 419 Least number of segments generator : 210 of 249.617 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 256 of 304.295 cents and inv. generated superset size: 18 = 15 more = 600.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MLS Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 110.53278 cents Scale diversity : 1.151201 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.670613 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 : 1445/1444, 1.1985 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Limited inverse transpositions with margin 82.0248 cents: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 255 (O: 85 U: 255) Highest odd numerator or denominator: 19 Scale harmonicity : 0.012938 Average absolute harmonicity : 0.116301 Specific harmonicity : 0.069004 Fundamental : 1/204, -7.6724 octaves, 1.2825 Hz. Guide tone : 380, 8.5699 octaves, 99417.715 Hz. Exponens Consonantiae : 7.752000E+04, 16.24228 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 26.0, average 8.66667 Mersenne's string divisions : 252 Sum of van Prooijen's expressibility: 2.45484, average 0.81828 Sum of Tenney's harmonic distance : 4.88941, average 1.62980 Vogel's harmonic complexity : 23.33333 Wille's k value : 127 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 15.42049, average 2.57008 Lattice compactness (without 2's) : 8.29253, average 1.38209 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 4 3: -1 .. 0 -0.33333 1 1 5: 0 .. 1 0.33333 1 1 17: -1 .. 0 -0.33333 1 19: 0 .. 1 0.33333 1 1 Average exponent except 2's : 0 / 3 = 0.00000 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <6 10 15 27 28| Scale is weakly epimorphic with val: <6 10 15 27 31| Scale is weakly epimorphic with val: <6 10 15 27 34| Scale is weakly epimorphic with val: <6 10 15 28 29| Scale is weakly epimorphic with val: <6 10 15 28 32| Scale is weakly epimorphic with val: <6 10 15 29 30| Scale is weakly epimorphic with val: <6 10 15 29 33| Scale is weakly epimorphic with val: <6 10 15 30 31| Scale is weakly epimorphic with val: <6 10 15 30 34| Scale is weakly epimorphic with val: <6 10 15 31 32| Scale is weakly epimorphic with val: <6 10 15 32 33| Scale is weakly epimorphic with val: <6 10 15 33 34| Scale is weakly epimorphic with val: <6 10 16 27 30| Scale is weakly epimorphic with val: <6 10 16 28 31| Scale is weakly epimorphic with val: <6 10 16 29 32| Scale is weakly epimorphic with val: <6 10 16 30 33| Scale is weakly epimorphic with val: <6 10 16 31 34| Scale is weakly epimorphic with val: <6 10 19 27 30| Scale is weakly epimorphic with val: <6 10 19 28 31| Scale is weakly epimorphic with val: <6 10 19 29 32| Scale is weakly epimorphic with val: <6 10 19 30 33| Scale is weakly epimorphic with val: <6 10 19 31 34| Scale is weakly epimorphic with val: <6 11 15 27 29| Scale is weakly epimorphic with val: <6 11 15 27 32| Scale is weakly epimorphic with val: <6 11 15 28 30| Scale is weakly epimorphic with val: <6 11 15 28 33| Scale is weakly epimorphic with val: <6 11 15 29 31| Scale is weakly epimorphic with val: <6 11 15 29 34| Scale is weakly epimorphic with val: <6 11 15 30 32| Scale is weakly epimorphic with val: <6 11 15 31 33| Scale is weakly epimorphic with val: <6 11 15 32 34| Scale is weakly epimorphic with val: <6 11 17 27 30| Scale is weakly epimorphic with val: <6 11 17 28 31| Scale is weakly epimorphic with val: <6 11 17 29 32| Scale is weakly epimorphic with val: <6 11 17 30 33| Scale is weakly epimorphic with val: <6 11 17 31 34| Scale is weakly epimorphic with val: <7 10 16 27 30| Scale is weakly epimorphic with val: <7 10 16 28 31| Scale is weakly epimorphic with val: <7 10 16 29 32| Scale is weakly epimorphic with val: <7 10 16 30 33| Scale is weakly epimorphic with val: <7 10 16 31 34| Scale is weakly epimorphic with val: <7 10 17 27 29| Scale is weakly epimorphic with val: <7 10 17 27 32| Scale is weakly epimorphic with val: <7 10 17 28 30| Scale is weakly epimorphic with val: <7 10 17 28 33| Scale is weakly epimorphic with val: <7 10 17 29 31| Scale is weakly epimorphic with val: <7 10 17 29 34| Scale is weakly epimorphic with val: <7 10 17 30 32| Scale is weakly epimorphic with val: <7 10 17 31 33| Scale is weakly epimorphic with val: <7 10 17 32 34| Scale is weakly epimorphic with val: <7 10 19 27 30| Scale is weakly epimorphic with val: <7 10 19 28 31| Scale is weakly epimorphic with val: <7 10 19 29 32| Scale is weakly epimorphic with val: <7 10 19 30 33| Scale is weakly epimorphic with val: <7 10 19 31 34| Scale is weakly epimorphic with val: <7 11 15 27 29| Scale is weakly epimorphic with val: <7 11 15 27 32| Scale is weakly epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 29 31| Scale is weakly epimorphic with val: <7 11 15 29 34| Scale is weakly epimorphic with val: <7 11 15 30 32| Scale is weakly epimorphic with val: <7 11 15 31 33| Scale is weakly epimorphic with val: <7 11 15 32 34| Scale is JI-epimorphic with val: <7 11 16 27 28| Scale is weakly epimorphic with val: <7 11 16 27 31| Scale is weakly epimorphic with val: <7 11 16 27 34| Scale is JI-epimorphic with val: <7 11 16 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is JI-epimorphic with val: <7 11 16 29 30| Scale is weakly epimorphic with val: <7 11 16 29 33| Scale is JI-epimorphic with val: <7 11 16 30 31| Scale is weakly epimorphic with val: <7 11 16 30 34| Scale is JI-epimorphic with val: <7 11 16 31 32| Scale is JI-epimorphic with val: <7 11 16 32 33| Scale is JI-epimorphic with val: <7 11 16 33 34| Scale is weakly epimorphic with val: <7 11 18 27 29| Scale is weakly epimorphic with val: <7 11 18 27 32| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 29 31| Scale is weakly epimorphic with val: <7 11 18 29 34| Scale is weakly epimorphic with val: <7 11 18 30 32| Scale is weakly epimorphic with val: <7 11 18 31 33| Scale is weakly epimorphic with val: <7 11 18 32 34| Scale is weakly epimorphic with val: <7 11 19 27 28| Scale is weakly epimorphic with val: <7 11 19 27 31| Scale is weakly epimorphic with val: <7 11 19 27 34| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 29 30| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 19 30 31| Scale is weakly epimorphic with val: <7 11 19 30 34| Scale is weakly epimorphic with val: <7 11 19 31 32| Scale is weakly epimorphic with val: <7 11 19 32 33| Scale is weakly epimorphic with val: <7 11 19 33 34| Scale is weakly epimorphic with val: <7 12 15 27 30| Scale is weakly epimorphic with val: <7 12 15 28 31| Scale is weakly epimorphic with val: <7 12 15 29 32| Scale is weakly epimorphic with val: <7 12 15 30 33| Scale is weakly epimorphic with val: <7 12 15 31 34| Scale is weakly epimorphic with val: <7 12 17 27 28| Scale is weakly epimorphic with val: <7 12 17 27 31| Scale is weakly epimorphic with val: <7 12 17 27 34| Scale is weakly epimorphic with val: <7 12 17 28 29| Scale is weakly epimorphic with val: <7 12 17 28 32| Scale is weakly epimorphic with val: <7 12 17 29 30| Scale is weakly epimorphic with val: <7 12 17 29 33| Scale is weakly epimorphic with val: <7 12 17 30 31| Scale is weakly epimorphic with val: <7 12 17 30 34| Scale is weakly epimorphic with val: <7 12 17 31 32| Scale is weakly epimorphic with val: <7 12 17 32 33| Scale is weakly epimorphic with val: <7 12 17 33 34| Scale is weakly epimorphic with val: <7 12 18 27 30| Scale is weakly epimorphic with val: <7 12 18 28 31| Scale is weakly epimorphic with val: <7 12 18 29 32| Scale is weakly epimorphic with val: <7 12 18 30 33| Scale is weakly epimorphic with val: <7 12 18 31 34| Scale is weakly epimorphic with val: <8 11 17 27 30| Scale is weakly epimorphic with val: <8 11 17 28 31| Scale is weakly epimorphic with val: <8 11 17 29 32| Scale is weakly epimorphic with val: <8 11 17 30 33| Scale is weakly epimorphic with val: <8 11 17 31 34| Scale is weakly epimorphic with val: <8 11 19 27 28| Scale is weakly epimorphic with val: <8 11 19 27 31| Scale is weakly epimorphic with val: <8 11 19 27 34| Scale is weakly epimorphic with val: <8 11 19 28 29| Scale is weakly epimorphic with val: <8 11 19 28 32| Scale is weakly epimorphic with val: <8 11 19 29 30| Scale is weakly epimorphic with val: <8 11 19 29 33| Scale is weakly epimorphic with val: <8 11 19 30 31| Scale is weakly epimorphic with val: <8 11 19 30 34| Scale is weakly epimorphic with val: <8 11 19 31 32| Scale is weakly epimorphic with val: <8 11 19 32 33| Scale is weakly epimorphic with val: <8 11 19 33 34| Scale is weakly epimorphic with val: <8 12 15 27 30| Scale is weakly epimorphic with val: <8 12 15 28 31| Scale is weakly epimorphic with val: <8 12 15 29 32| Scale is weakly epimorphic with val: <8 12 15 30 33| Scale is weakly epimorphic with val: <8 12 15 31 34| Scale is weakly epimorphic with val: <8 12 18 27 30| Scale is weakly epimorphic with val: <8 12 18 28 31| Scale is weakly epimorphic with val: <8 12 18 29 32| Scale is weakly epimorphic with val: <8 12 18 30 33| Scale is weakly epimorphic with val: <8 12 18 31 34| Scale is weakly epimorphic with val: <8 12 19 27 29| Scale is weakly epimorphic with val: <8 12 19 27 32| Scale is weakly epimorphic with val: <8 12 19 28 30| Scale is weakly epimorphic with val: <8 12 19 28 33| Scale is weakly epimorphic with val: <8 12 19 29 31| Scale is weakly epimorphic with val: <8 12 19 29 34| Scale is weakly epimorphic with val: <8 12 19 30 32| Scale is weakly epimorphic with val: <8 12 19 31 33| Scale is weakly epimorphic with val: <8 12 19 32 34|
FIT/MODE
3: 1 1 1 SP B ME I SD: 34.8866 c. M: 54.2837 c. 5: 2 2 1 SP M ME S SD: 7.9856 c. M:-12.1223 c. 13: 5 5 3 SP M DE S SD: 1.9371 c. M: 3.2022 c. 18: 7 7 4 SP M DE S SD: 0.8909 c. M:-1.1266 c. 31: 12 12 7 SP M DE S SD: 0.4429 c. M: 0.7305 c. 49: 19 19 11 SP M DE S SD: 0.3273 c. M:-0.5619 c. 80: 31 31 18 SP M DE S SD: 0.3148 c. M:-0.4348 c. 129: 50 50 29 SP M DE S SD: 0.3095 c. M:-0.4831 c. 165: 64 64 37 SP M DE S SD: 0.3611 c. M:-0.6235 c. 178: 69 69 40 SP M DE S SD: 0.3112 c. M:-0.5048 c. 191: 74 74 43 SP M DE S SD: 0.3251 c. M:-0.4022 c. 209: 81 81 47 SP M DE S SD: 0.3100 c. M:-0.4646 c. 210: 81 82 47 SP T3 SD: 0.3035 c. M: 0.4545 c. 214: 83 83 48 SP M DE S SD: 0.3520 c. M:-0.6094 c. 218: 84 85 49 SP T3 SD: 0.3954 c. M: 0.6504 c. 223: 86 87 50 SP T3 SD: 0.2831 c. M: 0.4864 c. 228: 88 89 51 SP T3 SD: 0.2679 c. M: 0.3297 c. 236: 91 92 53 SP T3 SD: 0.3049 c. M: 0.5148 c. 241: 93 94 54 SP T3 SD: 0.2254 c. M: 0.3660 c. 254: 98 99 57 SP T3 SD: 0.2310 c. M: 0.3985 c. 259: 100 101 58 SP T3 SD: 0.1904 c. M: 0.2622 c. 272: 105 106 61 SP T3 SD: 0.1732 c. M: 0.2976 c. 277: 107 108 62 SP T3 SD: 0.1778 c. M:-0.2555 c. 285: 110 111 64 SP T3 SD: 0.2007 c. M: 0.3297 c. 290: 112 113 65 SP T3 SD: 0.1340 c. M: 0.2092 c. 303: 117 118 68 SP T3 SD: 0.1424 c. M: 0.2432 c. 308: 119 120 69 SP T3 SD: 0.1178 c. M:-0.1563 c. 321: 124 125 72 SP T3 SD: 0.0968 c. M: 0.1664 c. 339: 131 132 76 SP T3 SD: 0.0712 c. M: 0.0977 c. 352: 136 137 79 SP T3 SD: 0.0802 c. M: 0.1311 c. 357: 138 139 80 SP T3 SD: 0.0749 c. M:-0.1246 c. 370: 143 144 83 SP T3 SD: 0.0406 c. M: 0.0699 c. 388: 150 151 87 SP T3 SD: 0.0335 c. M:-0.0562 c. 401: 155 156 90 SP T3 SD: 0.0391 c. M: 0.0494 c. 419: 162 163 94 SP T3 SD: 0.0025 c. M:-0.0039 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 5 x S SD: 0.0000 cents 5 x 6:7 S SD: 55.0665 cents 6:7 x 8 S SD: 37.1566 cents 7:8:9 x S SD: 31.1038 cents 8:9:10:11 H SD: 18.1564 cents 9:10:11:12 H SD: 13.4030 cents 10:11 x 13 SD: 25.8860 cents 11:12:14:15 S SD: 21.7155 cents 12:13:15:16 SD: 17.9950 cents 15:17:19:20 SD: 11.0957 cents 16:18:20:21 S SD: 9.8444 cents 24:27:30:32 S SD: 3.7841 cents 36:40:45:48 S SD: 3.3846 cents 51:57:64:68 SD: 2.2586 cents 60:67:75:80 SD: 0.5064 cents 144:161:180:192 SD: 0.2109 cents 204:228:255:272 SD: 0.0000 cents