Scala analysis: xen15-chalmers-triadic-reversed-diamond-32-25-tetrachord
Tetrachord 25/24 * 768/625 * 25/24 of triadic reversed diamond for M=32/25, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/24 70.672427 classic chromatic semitone, minor chroma 2: 32/25 427.372572 classic diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 25/24 70.6724 classic chromatic semitone, minor chroma 1: 25/24 70.6724 classic chromatic semitone, minor chroma 2: 768/625 356.7001 3: 25/24 70.6724 classic chromatic semitone, minor chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 768/625 356.700 cents 2: 1 625/576 141.345 cents two (classic chromatic semitone, minor chroma) 2: 2 32/25 427.373 cents classic diminished fourth 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 : 70.7 427.4 498.0 70.7 : 356.7 427.4 498.0 427.4: 70.7 141.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.6724 .. 356.7001 cents 18432/15625, 286.0277 cents 25/24, 70.6724 cents 2: 141.3449 .. 427.3726 cents 18432/15625, 286.0277 cents 390625/442368,-215.3553 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 25/24, 70.6724 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 768/625, 356.7001 cents Average / Smallest step : 2.349077 Largest / Average step : 2.148602 Largest / Smallest step : 5.047232 Median interval of one step : 25/24, 70.6724 cents, amount: 2 Most common interval of one step : 25/24, 70.6724 cents, amount: 2 Least squares average step : 172.82518 cents, oct.: 518.47555 cents Scale is not proper Scale has Myhill's property chromas: 18432/15625, 286.0277 cents and 442368/390625, 215.3553 cents, ratio: 1.328167 generators: 1 of 70.67243 cents and 2 of 427.37257 cents ET pair of linear temperament : 296&1494 Scale is distributional even Scale is a mode of a 148-tone equal temperament with octave 4/3 degrees: 21 127 148 generators: 21 and 127 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 2 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 ] Scale is a Constant Structure, by a margin of 70.67243 cents Scale diversity : 0.739703 Lumma stability : 0.283799 Lumma impropriety factor : 0.432401 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 : 25/24, 70.6724 cents Most common intervals : 25/24, 70.6724 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 : 5 Odd number limit : 625 (O: 625 U: 625) Highest odd numerator or denominator: 25 Scale harmonicity : 0.027574 Average absolute harmonicity : 0.108205 Specific harmonicity : 0.141010 Fundamental : 1/600, -9.2288 octaves, 0.4360 Hz. Guide tone : 800, 9.6439 octaves, 209300.452 Hz. Exponens Consonantiae : 4.800000E+05, 18.87267 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 56.5, average 18.83333 Mersenne's string divisions : 2793 Sum of van Prooijen's expressibility: 3.27300, average 1.09100 Sum of Tenney's harmonic distance : 6.76042, average 2.25347 Vogel's harmonic complexity : 15.33333 Wille's k value : 312 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 29.48971, average 4.91495 Lattice compactness (without 2's) : 13.59524, average 2.26587 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.33333 10 3: -1 .. 0 -0.66667 2 1 5: -2 .. 2 0.00000 4 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 15| Scale is weakly epimorphic with val: <7 11 17| = patent Scale is weakly epimorphic with val: <7 11 18|
FIT/MODE
3: 0 3 0 N M DE I SD: 57.7038 c. M: 70.6724 c. 4: 1 2 1 P M ME I SD: 43.9592 c. M: 53.8388 c. 5: 1 3 1 N M DE I SD: 23.6266 c. M: 28.9366 c. 6: 1 4 1 N M DE I SD: 10.0715 c. M: 12.3351 c. 7: 1 5 1 N M DE I SD: 0.3894 c. M: 0.4769 c. 78: 11 56 11 N M DE I SD: 0.3554 c. M: 0.4353 c. 85: 12 61 12 N M DE I SD: 0.2941 c. M: 0.3602 c. 92: 13 66 13 N M DE I SD: 0.2421 c. M: 0.2965 c. 99: 14 71 14 N M DE I SD: 0.1974 c. M: 0.2418 c. 106: 15 76 15 N M DE I SD: 0.1587 c. M: 0.1944 c. 113: 16 81 16 N M DE I SD: 0.1247 c. M: 0.1528 c. 120: 17 86 17 N M DE I SD: 0.0948 c. M: 0.1161 c. 127: 18 91 18 N M DE I SD: 0.0681 c. M: 0.0834 c. 134: 19 96 19 N M DE I SD: 0.0442 c. M: 0.0541 c. 141: 20 101 20 N M DE I SD: 0.0227 c. M: 0.0277 c. 148: 21 106 21 N M DE I SD: 0.0032 c. M: 0.0039 c. 451: 64 323 64 N M DE I SD: 0.0029 c. M: 0.0036 c. 599: 85 429 85 N M DE I SD: 0.0014 c. M: 0.0017 c. 747: 106 535 106 N M DE I SD: 0.0005 c. M: 0.0006 c. 895: 127 641 127 N 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: 41.0589 cents 5 x 6:7 S SD: 70.0332 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 80.3434 cents 8:9:10:11 H SD: 49.7506 cents 9:10 x 12 S SD: 55.8656 cents 10:11:13 x SD: 49.0381 cents 11:12:14:15 S SD: 29.8241 cents 12:13:15:16 SD: 26.4497 cents 13:14 x 17 SD: 33.3574 cents 14:15:18:19 S SD: 19.3705 cents 15:16:19:20 SD: 14.9609 cents 17:18:22:23 SD: 14.1393 cents 18:19:23:24 SD: 7.7090 cents 21:22:27:28 SD: 4.1737 cents 46:48:59:61 SD: 3.5037 cents 47:49:60:63 SD: 3.4605 cents 50:52:64:67 SD: 3.0229 cents 51:53:65:68 SD: 2.8286 cents 54:56:69:72 SD: 2.7592 cents 68:71:87:91 SD: 2.5287 cents 69:72:88:92 SD: 2.3223 cents 71:74:91:95 SD: 2.1909 cents 72:75:92:96 SD: 1.0027 cents 75:78:96:100 SD: 0.9241 cents 93:97:119:124 SD: 0.7690 cents 96:100:123:128 SD: 0.5633 cents 168:175:215:224 SD: 0.1074 cents 432:450:553:576 SD: 0.0417 cents 600:625:768:800 SD: 0.0000 cents