Scala analysis: xen15-chalmers-triadic-reversed-diamond-23-18-tetrachord
Tetrachord 24/23 * 529/432 * 24/23 of triadic reversed diamond for M=23/18, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 23/18 424.364346 vicesimotertial major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 24/23 73.6807 vicesimotertial minor semitone 1: 24/23 73.6807 vicesimotertial minor semitone 2: 529/432 350.6837 3: 24/23 73.6807 vicesimotertial minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 24/23 73.681 cents vicesimotertial minor semitone 1: 1 529/432 350.684 cents 2: 1 576/529 147.361 cents two (vicesimotertial minor semitone) 2: 2 23/18 424.364 cents vicesimotertial major third 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 : 73.7 424.4 498.0 73.7 : 350.7 424.4 498.0 424.4: 73.7 147.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 350.6837 cents 12167/10368, 277.0030 cents 24/23, 73.6807 cents 2: 147.3613 .. 424.3643 cents 12167/10368, 277.0030 cents 248832/279841,-203.3224 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 529/432, 350.6837 cents Average / Smallest step : 2.253169 Largest / Average step : 2.112361 Largest / Smallest step : 4.759508 Median interval of one step : 24/23, 73.6807 cents, amount: 2 Most common interval of one step : 24/23, 73.6807 cents, amount: 2 Least squares average step : 172.61031 cents, oct.: 517.83093 cents Scale is not proper Scale has Myhill's property chromas: 12167/10368, 277.0030 cents and 279841/248832, 203.3224 cents, ratio: 1.362383 generators: 1 of 73.68065 cents and 2 of 424.36435 cents ET pair of linear temperament : 54&338 Scale is distributional even Scale is a mode of a 169-tone equal temperament with octave 4/3 degrees: 25 144 169 generators: 25 and 144 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 73.68065 cents Scale diversity : 0.782492 Lumma stability : 0.295880 Lumma impropriety factor : 0.408241 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 : 24/23, 73.6807 cents Most common intervals : 24/23, 73.6807 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 23 Odd number limit : 529 (O: 529 U: 529) Highest odd numerator or denominator: 23 Scale harmonicity : 0.010398 Average absolute harmonicity : 0.085293 Specific harmonicity : 0.054572 Fundamental : 1/414, -8.6935 octaves, 0.6319 Hz. Guide tone : 552, 9.1085 octaves, 144417.312 Hz. Exponens Consonantiae : 2.285280E+05, 17.80201 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 47.5, average 15.83333 Mersenne's string divisions : 13489 Sum of van Prooijen's expressibility: 3.20058, average 1.06686 Sum of Tenney's harmonic distance : 6.43812, average 2.14604 Vogel's harmonic complexity : 29.33333 Wille's k value : 264 Wilson's harmonic complexity : 55 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 19.15346, average 3.19224 Lattice compactness (without 2's) : 11.90611, average 1.98435 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -2 .. 1 -0.66667 4 1 23: -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 30| Scale is JI-epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 11 33| = patent Scale is weakly epimorphic with val: <7 11 34| Scale is weakly epimorphic with val: <7 11 36|
FIT/MODE
3: 0 2 1 N G T3 SD: 68.2018 c. M: 92.3343 c. 4: 0 3 1 N G T3 SD: 51.6804 c. M: 73.6807 c. 5: 1 3 1 N M DE I SD: 21.1704 c. M:-25.9283 c. 6: 1 4 1 N M DE I SD: 7.6153 c. M:-9.3268 c. 7: 1 5 1 N M DE I SD: 2.0669 c. M:-2.5314 c. 20: 3 14 3 N M DE I SD: 0.8378 c. M:-1.0261 c. 27: 4 19 4 N M DE I SD: 0.0847 c. M:-0.1038 c. 115: 17 81 17 N M DE I SD: 0.0462 c. M:-0.0566 c. 142: 21 100 21 N M DE I SD: 0.0213 c. M:-0.0261 c. 169: 25 119 25 N M DE I SD: 0.0044 c. M:-0.0054 c. 365: 54 257 54 N M DE I SD: 0.0022 c. M:-0.0027 c. 534: 79 376 79 N M DE I SD: 0.0001 c. M:-0.0002 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: 38.0506 cents 5 x 6:7 S SD: 68.8393 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 78.9289 cents 8:9:10:11 H SD: 48.5862 cents 9:10 x 12 S SD: 54.3615 cents 10:11:13 x SD: 48.0390 cents 11:12:14:15 S SD: 28.8347 cents 12:13:15:16 SD: 25.0750 cents 13:14 x 17 SD: 32.0671 cents 14:15:18:19 S SD: 18.7024 cents 15:16:19:20 SD: 13.6482 cents 18:19:23:24 SD: 6.6408 cents 21:22:27:28 SD: 4.2416 cents 43:45:55:57 SD: 3.8038 cents 47:49:60:63 SD: 3.1495 cents 51:53:65:68 SD: 2.7863 cents 65:68:83:87 SD: 2.6908 cents 66:69:84:88 SD: 2.5329 cents 68:71:87:91 SD: 2.2701 cents 69:72:88:92 SD: 1.0919 cents 72:75:92:96 SD: 1.0027 cents 90:94:115:120 SD: 0.5341 cents 162:169:207:216 SD: 0.1484 cents 252:263:322:336 SD: 0.0954 cents 414:432:529:552 SD: 0.0000 cents