Scala analysis: xen15-chalmers-triadic-reversed-diamond-35-27-tetrachord
Tetrachord 36/35 * 1225/972 * 36/35 of triadic reversed diamond for M=35/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 1225/972 400.5042 3: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 1225/972 400.504 cents 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 : 48.8 449.3 498.0 48.8 : 400.5 449.3 498.0 449.3: 48.8 97.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 400.5042 cents 42875/34992, 351.7339 cents 36/35, 48.7704 cents 2: 97.5408 .. 449.2746 cents 42875/34992, 351.7339 cents 1259712/1500625,-302.9635 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1225/972, 400.5042 cents Average / Smallest step : 3.404013 Largest / Average step : 2.412458 Largest / Smallest step : 8.212038 Median interval of one step : 36/35, 48.7704 cents, amount: 2 Most common interval of one step : 36/35, 48.7704 cents, amount: 2 Least squares average step : 174.38962 cents, oct.: 523.16885 cents Scale is not proper Scale has Myhill's property chromas: 42875/34992, 351.7339 cents and 1500625/1259712, 302.9635 cents, ratio: 1.160978 generators: 1 of 48.77038 cents and 2 of 449.27462 cents ET pair of linear temperament : 20&82 Scale is distributional even Scale is a mode of a 337-tone equal temperament with octave 4/3 degrees: 33 304 337 generators: 33 and 304 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 48.77038 cents Scale diversity : 0.411921 Lumma stability : 0.195847 Lumma impropriety factor : 0.608305 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 : 36/35, 48.7704 cents Most common intervals : 36/35, 48.7704 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 : 1225 (O: 1225 U: 1225) Highest odd numerator or denominator: 35 Scale harmonicity : 0.020532 Average absolute harmonicity : 0.098809 Specific harmonicity : 0.106114 Fundamental : 1/945, -9.8842 octaves, 0.2769 Hz. Guide tone : 1260, 10.2992 octaves, 329648.212 Hz. Exponens Consonantiae : 1.190700E+06, 20.18338 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 70.0, average 23.33333 Mersenne's string divisions : 30814 Sum of van Prooijen's expressibility: 3.56526, average 1.18842 Sum of Tenney's harmonic distance : 7.15498, average 2.38499 Vogel's harmonic complexity : 20.33333 Wille's k value : 612 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 21.27664, average 3.54611 Lattice compactness (without 2's) : 18.27679, average 3.04613 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -3 .. 2 -0.66667 6 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: 10 / 3 = 3.33333 Scale is weakly epimorphic with val: <7 11 15 19| Scale is JI-epimorphic with val: <7 11 15 20| Scale is weakly epimorphic with val: <7 11 15 22| 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 JI-epimorphic with val: <7 11 17 18| Scale is weakly epimorphic with val: <7 11 17 20| = patent Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 18 19| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 18 22| Scale is weakly epimorphic with val: <7 11 19 19| Scale is weakly epimorphic with val: <7 11 19 21| Scale is weakly epimorphic with val: <7 11 19 22|
FIT/MODE
3: 0 3 0 N M DE I SD: 39.8208 c. M:-48.7704 c. 5: 0 4 1 N G T3 SD: 40.6740 c. M: 50.8386 c. 6: 0 5 1 N G T3 SD: 34.4032 c. M: 48.7704 c. 7: 1 5 1 N M DE I SD: 18.2723 c. M:-22.3789 c. 8: 1 6 1 N M DE I SD: 11.0107 c. M:-13.4852 c. 9: 1 7 1 N M DE I SD: 5.3627 c. M:-6.5680 c. 10: 1 8 1 N M DE I SD: 0.8444 c. M:-1.0341 c. 31: 3 25 3 N M DE I SD: 0.4674 c. M:-0.5725 c. 41: 4 33 4 N M DE I SD: 0.1475 c. M:-0.1806 c. 51: 5 41 5 N M DE I SD: 0.0470 c. M:-0.0576 c. 92: 9 74 9 N M DE I SD: 0.0397 c. M:-0.0486 c. 143: 14 115 14 N M DE I SD: 0.0088 c. M:-0.0107 c. 194: 19 156 19 N M DE I SD: 0.0059 c. M:-0.0072 c. 337: 33 271 33 N M DE I SD: 0.0003 c. M:-0.0004 c. 1879: 184 1511 184 N M DE I SD: 0.0003 c. M:-0.0004 c. 2216: 217 1782 217 N M DE I SD: 0.0002 c. M:-0.0003 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: 62.9609 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 91.4774 cents 8:9:10:11 H SD: 58.5666 cents 9:10 x 12 S SD: 66.8167 cents 10:11:13 x SD: 58.1694 cents 11:12:14:15 S SD: 37.8588 cents 12:13 x 16 SD: 44.9011 cents 13:14:17 x SD: 40.4793 cents 14:15:18:19 S SD: 26.1085 cents 15:16:19:20 SD: 24.8697 cents 16:17:21 x SD: 30.0802 cents 17:18:22:23 SD: 18.7549 cents 18:19:23:24 SD: 17.0961 cents 19:20 x 25 S SD: 23.0664 cents 20:21:26:27 SD: 13.9888 cents 21:22:27:28 SD: 11.5974 cents 22:23 x 29 SD: 17.2187 cents 23:24:30:31 S SD: 10.9835 cents 24:25:31:32 SD: 7.5870 cents 27:28:35:36 S SD: 4.7302 cents 30:31:39:40 SD: 3.1330 cents 63:65:82:84 SD: 2.9475 cents 64:66:83:85 SD: 2.7240 cents 67:69:87:89 SD: 2.4771 cents 68:70:88:91 SD: 2.3768 cents 71:73:92:95 SD: 2.0541 cents 75:77:97:100 SD: 1.6994 cents 101:104:131:135 SD: 1.5951 cents 102:105:132:136 SD: 1.0791 cents 105:108:136:140 SD: 0.4713 cents 108:111:140:144 SD: 0.4454 cents 138:142:179:184 SD: 0.4270 cents 213:219:276:284 SD: 0.3240 cents 243:250:315:324 SD: 0.1319 cents 351:361:455:468 SD: 0.0457 cents 594:611:770:792 SD: 0.0270 cents