Scala analysis: xen15-chalmers-triadic-reversed-diamond-56-45-tetrachord
Tetrachord 15/14 * 784/675 * 15/14 of triadic reversed diamond for M=56/45, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 15/14 119.442808 major diatonic semitone 2: 56/45 378.602191 septimal narrow major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 15/14 119.4428 major diatonic semitone 1: 15/14 119.4428 major diatonic semitone 2: 784/675 259.1594 3: 15/14 119.4428 major diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 784/675 259.159 cents 2: 1 225/196 238.886 cents two (major diatonic semitone) 2: 2 56/45 378.602 cents septimal narrow 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 : 119.4 378.6 498.0 119.4: 259.2 378.6 498.0 378.6: 119.4 238.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 119.4428 .. 259.1594 cents 10976/10125, 139.7166 cents 15/14, 119.4428 cents 2: 238.8856 .. 378.6022 cents 10976/10125, 139.7166 cents 151875/153664,-20.2738 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 15/14, 119.4428 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 784/675, 259.1594 cents Average / Smallest step : 1.389912 Largest / Average step : 1.561060 Largest / Smallest step : 2.169736 Median interval of one step : 15/14, 119.4428 cents, amount: 2 Most common interval of one step : 15/14, 119.4428 cents, amount: 2 Least squares average step : 169.34158 cents, oct.: 508.02475 cents Scale is not proper Scale has Myhill's property chromas: 10976/10125, 139.7166 cents and 153664/151875, 20.2738 cents, ratio: 6.891496 generators: 1 of 119.44281 cents and 2 of 378.60219 cents ET pair of linear temperament : 42&50 Scale is distributional even Scale is a mode of a 221-tone equal temperament with octave 4/3 degrees: 53 168 221 generators: 53 and 168 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 20.27377 cents Scale diversity : 1.116389 Lumma stability : 0.479647 Lumma impropriety factor : 0.040707 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 : 153664/151875, 20.2738 cents Most common intervals : 15/14, 119.4428 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 : 7 Odd number limit : 675 (O: 225 U: 675) Highest odd numerator or denominator: 45 Scale harmonicity : 0.022040 Average absolute harmonicity : 0.101129 Specific harmonicity : 0.113651 Fundamental : 1/630, -9.2992 octaves, 0.4153 Hz. Guide tone : 840, 9.7142 octaves, 219765.475 Hz. Exponens Consonantiae : 5.292000E+05, 19.01345 octaves Euler's gradus suavitatis : 31 Sum of Mann's harmonic distance : 68.5, average 22.83333 Mersenne's string divisions : 20503 Sum of van Prooijen's expressibility: 3.30643, average 1.10214 Sum of Tenney's harmonic distance : 6.80280, average 2.26760 Vogel's harmonic complexity : 18.33333 Wille's k value : 337 Wilson's harmonic complexity : 33 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.72660, average 3.28777 Lattice compactness (without 2's) : 13.48619, average 2.24770 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -2 .. 1 -0.66667 4 1 5: -1 .. 1 0.00000 2 7: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 15 18| Scale is weakly epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 15 21| Scale is weakly epimorphic with val: <7 11 16 18| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 16 21| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 19| Scale is JI-epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 18| Scale is weakly epimorphic with val: <7 11 18 20| Scale is JI-epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 21| Scale is JI-epimorphic with val: <7 11 19 22|
FIT/MODE
3: 1 1 1 SP B ME I SD: 38.0260 c. M:-46.5722 c. 4: 1 2 1 P M ME I SD: 4.1384 c. M:-5.0684 c. 13: 3 7 3 N M DE I SD: 3.6819 c. M: 4.5093 c. 17: 4 9 4 N M DE I SD: 1.8418 c. M: 2.2557 c. 21: 5 11 5 N M DE I SD: 0.7027 c. M: 0.8607 c. 25: 6 13 6 N M DE I SD: 0.0718 c. M: 0.0880 c. 121: 29 63 29 N M DE I SD: 0.0626 c. M: 0.0767 c. 146: 35 76 35 N M DE I SD: 0.0396 c. M: 0.0485 c. 171: 41 89 41 N M DE I SD: 0.0233 c. M: 0.0285 c. 196: 47 102 47 N M DE I SD: 0.0111 c. M: 0.0137 c. 221: 53 115 53 N M DE I SD: 0.0018 c. M: 0.0022 c. 688: 165 358 165 N M DE I SD: 0.0009 c. M: 0.0011 c. 909: 218 473 218 N M DE I SD: 0.0003 c. M:-0.0003 c. 1130: 271 588 271 N M DE I SD: 0.0001 c. M:-0.0002 c. 2039: 489 1061 489 N M DE I SD: 0.0000 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: 7.7115 cents 5 x 6:7 S SD: 52.6754 cents 6 x 7:8 S SD: 55.8656 cents 7:8:9 x S SD: 62.5981 cents 8:9:10:11 H SD: 33.3869 cents 9:10:11:12 H SD: 23.4216 cents 11:12:14:15 S SD: 21.0829 cents 12:13:15:16 SD: 6.8752 cents 28:30:35:37 SD: 5.7788 cents 29:31:36:39 SD: 5.3222 cents 40:43:50:53 SD: 4.8359 cents 41:44:51:55 SD: 3.6399 cents 42:45:52:56 SD: 2.9518 cents 45:48:56:60 S SD: 2.5705 cents 54:58:67:72 SD: 2.2325 cents 57:61:71:76 SD: 0.8660 cents 111:119:138:148 SD: 0.6562 cents 156:167:194:208 SD: 0.6330 cents 168:180:209:224 SD: 0.1840 cents 225:241:280:300 SD: 0.1710 cents 393:421:489:524 SD: 0.1256 cents 405:434:504:540 SD: 0.0950 cents 462:495:575:616 SD: 0.0669 cents