Scala analysis: 465_D15
Diatonic tetrachord 56/51 * 9/8 * 68/63
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/51 161.915496 2: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 68/63 132.2195 supraminor second 1: 56/51 161.9155 2: 9/8 203.9100 major whole tone 3: 68/63 132.2195 supraminor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 68/63 132.220 cents supraminor second 1: 1 56/51 161.915 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 1 17/14 336.130 cents supraminor third 2: 1 21/17 365.825 cents submajor 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 : 161.9 365.8 498.0 161.9: 203.9 336.1 498.0 365.8: 132.2 294.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.2195 .. 203.9100 cents 567/544, 71.6905 cents 68/63, 132.2195 cents 2: 294.1350 .. 365.8255 cents 567/544, 71.6905 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/63, 132.2195 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.255601 Largest / Average step : 1.228263 Largest / Smallest step : 1.542208 Median interval of one step : 56/51, 161.9155 cents, amount: 1 Least squares average step : 170.55011 cents, oct.: 511.65032 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 2147-tone equal temperament with octave 4/3 degrees: 698 1577 2147 Least number of segments generator : 1074 of 249.138 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1838 of 426.365 cents and inv. generated superset size: 38 = 35 more = 1266.667% 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 90.22500 cents Scale diversity : 1.350923 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.712112 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 : 294/289, 29.6960 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% -- Rational properties -- Prime limit : 17 Odd number limit : 63 (O: 21 U: 63) Highest odd numerator or denominator: 51 Scale harmonicity : 0.020518 Average absolute harmonicity : 0.086403 Specific harmonicity : 0.083647 Fundamental : 1/51, -5.6724 octaves, 5.1299 Hz. Guide tone : 168, 7.3923 octaves, 43953.095 Hz. Exponens Consonantiae : 8.568000E+03, 13.06474 octaves Euler's gradus suavitatis : 30 Sum of Mann's harmonic distance : 76.0, average 25.33333 Mersenne's string divisions : 28462 Sum of van Prooijen's expressibility: 3.50691, average 1.16897 Sum of Tenney's harmonic distance : 7.08761, average 2.36254 Vogel's harmonic complexity : 14.00000 Wille's k value : 31 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 15.93210, average 2.65535 Lattice compactness (without 2's) : 10.32780, average 1.72130 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 3 1.66667 5 3: -1 .. 1 -0.33333 3 1 7: 0 .. 1 0.66667 2 17: -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 20 27| Scale is weakly epimorphic with val: <6 10 21 28| Scale is weakly epimorphic with val: <6 10 22 29| Scale is weakly epimorphic with val: <6 11 19 27| Scale is weakly epimorphic with val: <6 11 20 28| Scale is weakly epimorphic with val: <6 11 21 29| Scale is weakly epimorphic with val: <6 11 22 30| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 20 28| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 10 22 30| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 33| Scale is JI-epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 31| Scale is JI-epimorphic with val: <7 11 20 29| Scale is weakly epimorphic with val: <7 11 20 32| Scale is weakly epimorphic with val: <7 11 21 27| Scale is JI-epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 33| Scale is weakly epimorphic with val: <7 11 22 28| Scale is JI-epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 19 29| Scale is weakly epimorphic with val: <8 11 20 30| Scale is weakly epimorphic with val: <8 11 21 31| Scale is weakly epimorphic with val: <8 11 22 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 19.6549 c. M: 33.7955 c. 7: 2 3 2 SP M ME I SD: 12.7333 c. M: 19.6169 c. 9: 3 4 2 SP T3 SD: 12.6610 c. M:-21.5428 c. 10: 3 4 3 SP M ME I SD: 12.2737 c. M: 17.1940 c. 11: 4 4 3 SP M ME S SD: 11.2748 c. M:-19.1918 c. 12: 4 5 3 SP T3 SD: 5.0406 c. M:-7.7083 c. Raga Bilwadala 15: 5 6 4 SP T3 SD: 2.3914 c. M:-4.0995 c. 22: 7 9 6 SP T3 SD: 2.8820 c. M: 3.6110 c. 31: 10 13 8 SP T3 SD: 2.2514 c. M:-3.6918 c. 34: 11 14 9 SP T3 SD: 0.5037 c. M: 0.7833 c. 49: 16 20 13 SP T3 SD: 0.4137 c. M:-0.7114 c. 83: 27 34 22 SP T3 SD: 0.1328 c. M:-0.2076 c. 237: 77 97 63 SP T3 SD: 0.1160 c. M: 0.1722 c. 286: 93 117 76 SP T3 SD: 0.0769 c. M: 0.1281 c. 320: 104 131 85 SP T3 SD: 0.0517 c. M: 0.0737 c. 369: 120 151 98 SP T3 SD: 0.0420 c. M: 0.0526 c. 403: 131 165 107 SP T3 SD: 0.0147 c. M: 0.0200 c. 486: 158 199 129 SP T3 SD: 0.0129 c. M:-0.0224 c. 889: 289 364 236 SP T3 SD: 0.0059 c. M: 0.0089 c. 1744: 567 714 463 SP T3 SD: 0.0038 c. M:-0.0062 c. 2147: 698 879 570 SP T3 SD: 0.0029 c. M: 0.0048 c. 2230: 725 913 592 SP T3 SD: 0.0034 c. M:-0.0050 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: 20.4882 cents 5 x 6:7 S SD: 49.1253 cents 6 x 7:8 S SD: 49.4773 cents 7:8 x 9 S SD: 46.7996 cents 8:9:10:11 H SD: 23.6204 cents 9:10:11:12 H SD: 9.1832 cents 21:23:26:28 SD: 1.9701 cents 30:33:37:40 SD: 1.3786 cents 51:56:63:68 SD: 0.0000 cents