Scala analysis: xen15-chalmers-triadic-reversed-diamond-19-16-tetrachord
Tetrachord 64/57 * 1083/1024 * 64/57 of triadic reversed diamond for M=19/16, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 64/57 200.531983 2: 19/16 297.513016 19th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/57 200.5320 1: 64/57 200.5320 2: 1083/1024 96.9810 3: 64/57 200.5320
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1083/1024 96.981 cents 1: 2 64/57 200.532 cents 2: 2 19/16 297.513 cents 19th harmonic 2: 1 4096/3249 401.064 cents 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 : 200.5 297.5 498.0 200.5: 97.0 297.5 498.0 297.5: 200.5 401.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 96.9810 .. 200.5320 cents 65536/61731, 103.5509 cents 1083/1024, 96.9810 cents 2: 297.5130 .. 401.0640 cents 65536/61731, 103.5509 cents 1083/1024, 96.9810 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 1083/1024, 96.9810 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/57, 200.5320 cents Average / Smallest step : 1.711830 Largest / Average step : 1.207915 Largest / Smallest step : 2.067744 Median interval of one step : 64/57, 200.5320 cents, amount: 2 Most common interval of one step : 64/57, 200.5320 cents, amount: 2 Least squares average step : 163.54950 cents, oct.: 490.64850 cents Scale is strictly proper Scale has Myhill's property chromas: 65536/61731, 103.5509 cents and 67108864/66854673, 6.5699 cents, ratio: 15.761379 generators: 1 of 200.53198 cents and 2 of 297.51302 cents ET pair of linear temperament : 144&154 Scale is distributional even Scale is a mode of a 303-tone equal temperament with octave 4/3 degrees: 122 181 303 generators: 122 and 181 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Scale is a Constant Structure, by a margin of 96.98103 cents Scale diversity : 1.052712 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.584170 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 : 1083/1024, 96.9810 cents Most common intervals : 64/57, 200.5320 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 19 Odd number limit : 3249 (O: 1083 U: 3249) Highest odd numerator or denominator: 57 Scale harmonicity : 0.012364 Average absolute harmonicity : 0.087969 Specific harmonicity : 0.064699 Fundamental : 1/912, -9.8329 octaves, 0.2869 Hz. Guide tone : 1216, 10.2479 octaves, 318136.687 Hz. Exponens Consonantiae : 1.108992E+06, 20.08082 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 81.5, average 27.16667 Mersenne's string divisions : 4235 Sum of van Prooijen's expressibility: 3.51175, average 1.17058 Sum of Tenney's harmonic distance : 7.12411, average 2.37470 Vogel's harmonic complexity : 25.33333 Wille's k value : 541 Wilson's harmonic complexity : 41 Rectangular lattice diameter : 3 Triangular lattice diameter : 3 Lattice compactness : 33.05806, average 5.50968 Lattice compactness (without 2's) : 8.06450, average 1.34408 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 6 1.33333 12 3: -1 .. 0 -0.66667 2 1 19: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 11 29| Scale is JI-epimorphic with val: <7 11 30| Scale is weakly epimorphic with val: <7 11 32| Scale is weakly epimorphic with val: <7 11 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 28.1830 c. M:-34.5170 c. 5: 2 1 2 SP M ME I SD: 1.0729 c. M: 1.3140 c. 42: 17 8 17 SP M DE I SD: 0.8636 c. M:-1.0577 c. 47: 19 9 19 SP M DE I SD: 0.6576 c. M:-0.8054 c. 52: 21 10 21 SP M DE I SD: 0.4912 c. M:-0.6016 c. 57: 23 11 23 SP M DE I SD: 0.3540 c. M:-0.4335 c. 62: 25 12 25 SP M DE I SD: 0.2389 c. M:-0.2926 c. 67: 27 13 27 SP M DE I SD: 0.1410 c. M:-0.1727 c. 72: 29 14 29 SP M DE I SD: 0.0567 c. M:-0.0695 c. 77: 31 15 31 SP M DE I SD: 0.0166 c. M:-0.0204 c. 226: 91 44 91 SP M DE I SD: 0.0067 c. M:-0.0083 c. 303: 122 59 122 SP M DE I SD: 0.0008 c. M:-0.0010 c. 986: 397 192 397 SP M DE I SD: 0.0006 c. M:-0.0007 c. 1289: 519 251 519 SP M DE I SD: 0.0002 c. M:-0.0003 c. 1592: 641 310 641 SP M DE I SD: 0.0000 c. M: 0.0000 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: 88.8007 cents 5 x 6:7 S SD: 43.1953 cents 6 x 7:8 S SD: 15.3211 cents 7:8 x 9 S SD: 35.0108 cents 8:9:10:11 H SD: 34.5366 cents 9:10:11:12 H SD: 17.6954 cents 13:15 x 17 SD: 28.9776 cents 14:16:17:19 SD: 19.3480 cents 15:17:18:20 SD: 8.0940 cents 26:29:31:35 SD: 7.1121 cents 27:30:32:36 S SD: 6.1468 cents 32:36:38:43 SD: 4.6299 cents 33:37:39:44 SD: 2.8868 cents 42:47:50:56 SD: 2.4150 cents 48:54:57:64 SD: 1.1260 cents 90:101:107:120 SD: 0.7385 cents 123:138:146:164 SD: 0.5046 cents 138:155:164:184 SD: 0.4817 cents 171:192:203:228 SD: 0.1776 cents 261:293:310:348 SD: 0.1558 cents 309:347:367:412 SD: 0.1316 cents 432:485:513:576 SD: 0.0626 cents 480:539:570:640 SD: 0.0564 cents