Scala analysis: xen15-chalmers-triadic-reversed-diamond-39-32-tetrachord
Tetrachord 128/117 * 4563/4096 * 128/117 of triadic reversed diamond for M=39/32, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128/117 155.562336 2: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 128/117 155.5623 1: 128/117 155.5623 2: 4563/4096 186.9203 3: 128/117 155.5623
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 128/117 155.562 cents 1: 1 4563/4096 186.920 cents 2: 1 16384/13689 311.125 cents 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 155.6 342.5 498.0 155.6: 186.9 342.5 498.0 342.5: 155.6 311.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 155.5623 .. 186.9203 cents 533871/524288, 31.3580 cents 128/117, 155.5623 cents 2: 311.1247 .. 342.4827 cents 533871/524288, 31.3580 cents 67108864/62462907, 124.2043 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 128/117, 155.5623 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 4563/4096, 186.9203 cents Average / Smallest step : 1.067193 Largest / Average step : 1.125924 Largest / Smallest step : 1.201578 Median interval of one step : 128/117, 155.5623 cents, amount: 2 Most common interval of one step : 128/117, 155.5623 cents, amount: 2 Least squares average step : 166.76162 cents, oct.: 500.28486 cents Scale is strictly proper Scale has Myhill's property chromas: 533871/524288, 31.3580 cents and 67108864/62462907, 124.2043 cents, ratio: 3.960852 generators: 1 of 155.56234 cents and 2 of 342.48266 cents ET pair of linear temperament : 26&32 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 381-tone equal temperament with octave 4/3 degrees: 119 262 381 generators: 119 and 262 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 124.20435 cents Scale diversity : 1.291461 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.874076 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 533871/524288, 31.3580 cents Most common intervals : 128/117, 155.5623 cents & inv., amount: 2 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 : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 13 Odd number limit : 13689 (O: 4563 U: 13689) Highest odd numerator or denominator: 117 Scale harmonicity : 0.015550 Average absolute harmonicity : 0.092272 Specific harmonicity : 0.080975 Fundamental : 1/3744, -11.8704 octaves, 0.0699 Hz. Guide tone : 4992, 12.2854 octaves, 1306034.822 Hz. Exponens Consonantiae : 1.869005E+07, 24.15577 octaves Euler's gradus suavitatis : 43 Sum of Mann's harmonic distance : 161.5, average 53.83333 Mersenne's string divisions : 17395 Sum of van Prooijen's expressibility: 4.13637, average 1.37879 Sum of Tenney's harmonic distance : 8.35079, average 2.78360 Vogel's harmonic complexity : 23.33333 Wille's k value : 2281 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 39.85528, average 6.64255 Lattice compactness (without 2's) : 11.90611, average 1.98435 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 7 1.33333 14 3: -2 .. 1 -0.66667 4 1 13: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is weakly epimorphic with val: <7 11 25| Scale is JI-epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 11 28| Scale is weakly epimorphic with val: <7 11 29|
FIT/MODE
3: 1 1 1 SP B ME I SD: 8.5346 c. M: 10.4527 c. 10: 3 4 3 SP M ME I SD: 5.0205 c. M: 6.1488 c. 13: 4 5 4 SP M ME I SD: 1.8924 c. M: 2.3177 c. 16: 5 6 5 SP M ME I SD: 0.0626 c. M: 0.0767 c. 205: 64 77 64 SP M DE I SD: 0.0613 c. M: 0.0751 c. 221: 69 83 69 SP M DE I SD: 0.0524 c. M: 0.0641 c. 237: 74 89 74 SP M DE I SD: 0.0446 c. M: 0.0546 c. 253: 79 95 79 SP M DE I SD: 0.0378 c. M: 0.0463 c. 269: 84 101 84 SP M DE I SD: 0.0318 c. M: 0.0390 c. 285: 89 107 89 SP M DE I SD: 0.0265 c. M: 0.0325 c. 301: 94 113 94 SP M DE I SD: 0.0218 c. M: 0.0267 c. 317: 99 119 99 SP M DE I SD: 0.0175 c. M: 0.0215 c. 333: 104 125 104 SP M DE I SD: 0.0137 c. M: 0.0168 c. 349: 109 131 109 SP M DE I SD: 0.0102 c. M: 0.0125 c. 365: 114 137 114 SP M DE I SD: 0.0070 c. M: 0.0086 c. 381: 119 143 119 SP M DE I SD: 0.0041 c. M: 0.0050 c. 397: 124 149 124 SP M DE I SD: 0.0014 c. M: 0.0017 c. 413: 129 155 129 SP M DE I SD: 0.0011 c. M: 0.0014 c. 810: 253 304 253 SP M DE I SD: 0.0001 c. M: 0.0001 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: 43.8311 cents 5 x 6:7 S SD: 44.3147 cents 6 x 7:8 S SD: 37.8059 cents 7:8 x 9 S SD: 49.1966 cents 8:9:10:11 H SD: 28.0806 cents 9:10:11:12 H SD: 9.0965 cents 22:24:27:29 SD: 7.8971 cents 23:25:28:31 SD: 7.3005 cents 31:34:38:41 SD: 5.9198 cents 32:35:39:43 SD: 4.4931 cents 33:36:40:44 S SD: 3.5498 cents 42:46:51:56 SD: 2.2134 cents 54:59:66:72 SD: 1.8057 cents 63:69:77:84 SD: 1.7634 cents 87:95:106:116 SD: 1.1025 cents 96:105:117:128 SD: 0.1409 cents 393:430:479:524 SD: 0.0785 cents 489:535:596:652 SD: 0.0410 cents 585:640:713:780 SD: 0.0253 cents