Scala analysis: xen15-chalmers-triadic-reversed-diamond-13-10-tetrachord
Tetrachord 40/39 * 507/400 * 40/39 of triadic reversed diamond for M=13/10, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 13/10 454.213948 tridecimal semi-diminished fourth 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 40/39 43.8311 tridecimal minor diesis 2: 507/400 410.3829 3: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 40/39 43.831 cents tridecimal minor diesis 1: 1 507/400 410.383 cents 2: 1 1600/1521 87.662 cents two (tridecimal minor diesis) 2: 2 13/10 454.214 cents tridecimal semi-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 : 43.8 454.2 498.0 43.8 : 410.4 454.2 498.0 454.2: 43.8 87.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 410.3829 cents 19773/16000, 366.5518 cents 40/39, 43.8311 cents 2: 87.6621 .. 454.2139 cents 19773/16000, 366.5518 cents 640000/771147,-322.7208 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 507/400, 410.3829 cents Average / Smallest step : 3.787612 Largest / Average step : 2.471963 Largest / Smallest step : 9.362835 Median interval of one step : 40/39, 43.8311 cents, amount: 2 Most common interval of one step : 40/39, 43.8311 cents, amount: 2 Least squares average step : 174.74242 cents, oct.: 524.22727 cents Scale is not proper Scale has Myhill's property chromas: 19773/16000, 366.5518 cents and 771147/640000, 322.7208 cents, ratio: 1.135817 generators: 1 of 43.83105 cents and 2 of 454.21395 cents ET pair of linear temperament : 22&46 Scale is distributional even Scale is a mode of a 125-tone equal temperament with octave 4/3 degrees: 11 114 125 generators: 11 and 114 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 2 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 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 0.337661 Lumma stability : 0.176012 Lumma impropriety factor : 0.647975 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 : 40/39, 43.8311 cents Most common intervals : 40/39, 43.8311 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 : 13 Odd number limit : 1521 (O: 507 U: 1521) Highest odd numerator or denominator: 39 Scale harmonicity : 0.015680 Average absolute harmonicity : 0.092448 Specific harmonicity : 0.081636 Fundamental : 1/390, -8.6073 octaves, 0.6708 Hz. Guide tone : 520, 9.0224 octaves, 136045.294 Hz. Exponens Consonantiae : 2.028000E+05, 17.62970 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 54.5, average 18.16667 Mersenne's string divisions : 12719 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.38625, average 2.12875 Vogel's harmonic complexity : 21.33333 Wille's k value : 253 Wilson's harmonic complexity : 39 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.62837, average 2.93806 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 .. 0 -0.66667 2 1 5: -1 .. 1 0.00000 2 13: -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 15 26| Scale is weakly epimorphic with val: <7 11 15 27| Scale is weakly epimorphic with val: <7 11 15 29| Scale is weakly epimorphic with val: <7 11 15 30| Scale is JI-epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 16 28| Scale is weakly epimorphic with val: <7 11 16 30| Scale is weakly epimorphic with val: <7 11 17 25| Scale is JI-epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 17 28| Scale is weakly epimorphic with val: <7 11 17 29| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 29| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 27| Scale is JI-epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 30|
FIT/MODE
3: 0 3 0 N M DE I SD: 35.7879 c. M:-43.8311 c. 5: 0 5 0 N M DE I SD: 35.7879 c. M: 43.8311 c. 6: 0 5 1 N G T3 SD: 33.9409 c. M: 43.8311 c. 7: 0 6 1 N G T3 SD: 29.8186 c. M: 43.8311 c. 8: 1 6 1 N M DE I SD: 15.0436 c. M:-18.4246 c. 9: 1 7 1 N M DE I SD: 9.3957 c. M:-11.5073 c. 10: 1 8 1 N M DE I SD: 4.8773 c. M:-5.9734 c. 11: 1 9 1 N M DE I SD: 1.1805 c. M:-1.4458 c. 23: 2 19 2 N M DE I SD: 0.4269 c. M:-0.5228 c. 34: 3 28 3 N M DE I SD: 0.0932 c. M:-0.1141 c. 91: 8 75 8 N M DE I SD: 0.0383 c. M:-0.0469 c. 125: 11 103 11 N M DE I SD: 0.0025 c. M:-0.0031 c. 659: 58 543 58 N M DE I SD: 0.0024 c. M:-0.0030 c. 784: 69 646 69 N M DE I SD: 0.0016 c. M:-0.0020 c. 909: 80 749 80 N M DE I SD: 0.0011 c. M:-0.0013 c. 1034: 91 852 91 N M DE I SD: 0.0006 c. M:-0.0008 c. 1159: 102 955 102 N M DE I SD: 0.0003 c. M:-0.0003 c. 1284: 113 1058 113 N 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: 67.9002 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 94.1586 cents 8:9:10:11 H SD: 60.6206 cents 9:10 x 12 S SD: 69.2863 cents 10:11:13 x SD: 60.5866 cents 11:12:14:15 S SD: 39.8170 cents 12:13 x 16 SD: 47.3708 cents 13:14:17 x SD: 42.5412 cents 14:15:18:19 S SD: 27.9325 cents 15:16 x 20 S SD: 33.9501 cents 16:17:21 x SD: 31.6649 cents 17:18:22:23 SD: 20.3825 cents 18:19:23:24 SD: 19.3455 cents 19:20:25 x S SD: 24.7946 cents 20:21:26:27 SD: 15.3254 cents 21:22:27:28 SD: 13.7973 cents 22:23 x 29 SD: 19.2923 cents 23:24:30:31 S SD: 11.9010 cents 24:25:31:32 SD: 9.6863 cents 25:26 x 33 SD: 14.8498 cents 26:27:34:35 SD: 9.6684 cents 27:28:35:36 S SD: 6.5857 cents 30:31:39:40 SD: 4.3119 cents 33:34:43:44 SD: 2.9419 cents 36:37:47:48 SD: 2.7383 cents 69:71:90:92 SD: 2.6911 cents 70:72:91:93 SD: 2.6408 cents 73:75:95:97 SD: 2.2942 cents 76:78:99:101 SD: 2.2630 cents 77:79:100:103 SD: 1.9664 cents 80:82:104:107 SD: 1.8363 cents 81:83:105:108 SD: 1.7311 cents 84:86:109:112 SD: 1.4775 cents 111:114:144:148 SD: 1.4317 cents 113:116:147:151 SD: 1.4287 cents 114:117:148:152 SD: 0.8668 cents 117:120:152:156 SD: 0.3795 cents 120:123:156:160 SD: 0.3608 cents 237:243:308:316 SD: 0.2616 cents 270:277:351:360 SD: 0.1603 cents 387:397:503:516 SD: 0.1602 cents 390:400:507:520 SD: 0.0000 cents