Scala analysis: 450_D14
Diatonic tetrachord 20/19 * 9/8 * 152/135
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 20/19 88.800698 small undevicesimal semitone 2: 45/38 292.710699 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 152/135 205.3343 1: 20/19 88.8007 small undevicesimal semitone 2: 9/8 203.9100 major whole tone 3: 152/135 205.3343
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 9/8 203.910 cents major whole tone 1: 1 152/135 205.334 cents 2: 1 45/38 292.711 cents 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 88.8 292.7 498.0 88.8 : 203.9 409.2 498.0 292.7: 205.3 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.8007 .. 205.3343 cents 722/675, 116.5336 cents 20/19, 88.8007 cents 2: 292.7107 .. 409.2443 cents 722/675, 116.5336 cents 6075/5776, 87.3764 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 20/19, 88.8007 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 152/135, 205.3343 cents Average / Smallest step : 1.869524 Largest / Average step : 1.236842 Largest / Smallest step : 2.312305 Median interval of one step : 9/8, 203.9100 cents, amount: 1 Least squares average step : 154.88265 cents, oct.: 464.64795 cents Scale is strictly 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 87.37640 cents Scale diversity : 0.996014 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.532036 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 : 1216/1215, 1.4243 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor thirds form a closed circle Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 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 with margin 115.1093 cents: 1 -- Rational properties -- Prime limit : 19 Odd number limit : 135 (O: 45 U: 135) Highest odd numerator or denominator: 45 Scale harmonicity : 0.019415 Average absolute harmonicity : 0.086387 Specific harmonicity : 0.081209 Fundamental : 1/114, -6.8329 octaves, 2.2950 Hz. Guide tone : 180, 7.4919 octaves, 47092.602 Hz. Exponens Consonantiae : 2.052000E+04, 14.32474 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 64.5, average 21.50000 Mersenne's string divisions : 22659 Sum of van Prooijen's expressibility: 3.40909, average 1.13636 Sum of Tenney's harmonic distance : 6.89196, average 2.29732 Vogel's harmonic complexity : 15.66667 Wille's k value : 67 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 17.14105, average 2.85684 Lattice compactness (without 2's) : 11.91238, average 1.98540 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -1 .. 2 0.33333 3 1 5: 0 .. 1 0.66667 2 19: -1 .. 0 -0.66667 2 2 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: <6 10 17 28| Scale is weakly epimorphic with val: <6 10 18 29| Scale is weakly epimorphic with val: <6 10 19 30| Scale is weakly epimorphic with val: <6 11 15 28| Scale is weakly epimorphic with val: <6 11 16 29| Scale is weakly epimorphic with val: <6 11 17 30| Scale is weakly epimorphic with val: <6 11 18 31| Scale is weakly epimorphic with val: <6 11 19 32| Scale is weakly epimorphic with val: <7 10 17 28| Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 19 30| Scale is JI-epimorphic with val: <7 11 15 28| Scale is weakly epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 34| Scale is JI-epimorphic with val: <7 11 16 29| Scale is weakly epimorphic with val: <7 11 16 32| Scale is JI-epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 18 28| Scale is JI-epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 19 29| Scale is JI-epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <8 11 15 28| Scale is weakly epimorphic with val: <8 11 16 29| Scale is weakly epimorphic with val: <8 11 17 30| Scale is weakly epimorphic with val: <8 11 18 31| Scale is weakly epimorphic with val: <8 11 19 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 50.0268 c. M:-77.2143 c. 4: 1 1 2 P M ME S SD: 32.5776 c. M: 43.6882 c. 5: 1 2 2 SP M ME S SD: 7.1700 c. M:-10.8083 c. 12: 2 5 5 SP M DE S SD: 3.5746 c. M: 5.7932 c. 17: 3 7 7 SP M DE S SD: 0.5462 c. M: 0.9104 c. 56: 10 23 23 SP M DE S SD: 0.4572 c. M:-0.7801 c. 73: 13 30 30 SP M DE S SD: 0.3851 c. M:-0.6583 c. 90: 16 37 37 SP M DE S SD: 0.3681 c. M:-0.5825 c. 107: 19 44 44 SP M DE S SD: 0.3712 c. M:-0.5307 c. 124: 22 51 51 SP M DE S SD: 0.3808 c. M:-0.4932 c. 129: 23 53 53 SP M DE S SD: 0.4106 c. M:-0.7112 c. 141: 25 58 58 SP M DE S SD: 0.3919 c. M: 0.4948 c. 163: 29 67 67 SP M DE S SD: 0.3727 c. M:-0.6164 c. 179: 32 73 74 SP T3 SD: 0.3514 c. M: 0.5614 c. 191: 34 78 79 SP T3 SD: 0.3919 c. M: 0.6634 c. 196: 35 80 81 SP T3 SD: 0.2938 c. M: 0.4904 c. 201: 36 82 83 SP T3 SD: 0.2986 c. M:-0.4014 c. 213: 38 87 88 SP T3 SD: 0.2505 c. M: 0.4308 c. 218: 39 89 90 SP T3 SD: 0.2368 c. M:-0.2991 c. 230: 41 94 95 SP T3 SD: 0.2196 c. M: 0.3799 c. 235: 42 96 97 SP T3 SD: 0.1855 c. M: 0.2417 c. 247: 44 101 102 SP T3 SD: 0.1995 c. M: 0.3361 c. 252: 45 103 104 SP T3 SD: 0.1435 c. M: 0.2081 c. 269: 48 110 111 SP T3 SD: 0.1108 c. M: 0.1787 c. 286: 51 117 118 SP T3 SD: 0.0885 c. M: 0.1528 c. 303: 54 124 125 SP T3 SD: 0.0785 c. M: 0.1298 c. 320: 57 131 132 SP T3 SD: 0.0804 c. M: 0.1093 c. 325: 58 133 134 SP T3 SD: 0.0475 c. M:-0.0812 c. 342: 61 140 141 SP T3 SD: 0.0184 c. M:-0.0319 c. 359: 64 147 148 SP T3 SD: 0.0102 c. M: 0.0127 c. 701: 125 287 289 SP T3 SD: 0.0063 c. M:-0.0090 c. 1060: 189 434 437 SP T3 SD: 0.0048 c. M:-0.0082 c. 1761: 314 721 726 SP T3 SD: 0.0050 c. M:-0.0074 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: 93.6030 cents 5 x 6:7 S SD: 43.7622 cents 6 x 7:8 S SD: 12.9199 cents 7 x 8:9 S SD: 44.0194 cents 8 x 9:11 SD: 51.7773 cents 9:10:11:12 H SD: 36.1376 cents 10:11:12:13 H SD: 30.2838 cents 11:12:13:15 SD: 24.3804 cents 12:13:14:16 S SD: 18.6933 cents 15:16:18:20 S SD: 10.8096 cents 16:17:19:21 SD: 10.6842 cents 17:18:20:23 SD: 9.8362 cents 18:19:21:24 SD: 8.7608 cents 21:22:25:28 SD: 4.1062 cents 38:40:45:51 SD: 3.7841 cents 39:41:46:52 SD: 2.4222 cents 54:57:64:72 SD: 1.6697 cents 60:63:71:80 SD: 1.5065 cents 75:79:89:100 SD: 1.2560 cents 93:98:110:124 SD: 0.9277 cents 114:120:135:152 SD: 0.0000 cents