Scala analysis: xen15-chalmers-triadic-reversed-diamond-16-13-tetrachord
Tetrachord 13/12 * 192/169 * 13/12 of triadic reversed diamond for M=16/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/12 138.572661 tridecimal 2/3-tone 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 13/12 138.5727 tridecimal 2/3-tone 2: 192/169 220.8997 3: 13/12 138.5727 tridecimal 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 192/169 220.900 cents 2: 1 169/144 277.145 cents two (tridecimal 2/3-tone) 2: 2 16/13 359.472 cents tridecimal neutral 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 : 138.6 359.5 498.0 138.6: 220.9 359.5 498.0 359.5: 138.6 277.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 220.8997 cents 2304/2197, 82.3270 cents 13/12, 138.5727 cents 2: 277.1453 .. 359.4723 cents 2304/2197, 82.3270 cents 28561/27648, 56.2456 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 192/169, 220.8997 cents Average / Smallest step : 1.198036 Largest / Average step : 1.330601 Largest / Smallest step : 1.594107 Median interval of one step : 13/12, 138.5727 cents, amount: 2 Most common interval of one step : 13/12, 138.5727 cents, amount: 2 Least squares average step : 167.97517 cents, oct.: 503.92550 cents Scale is strictly proper Scale has Myhill's property chromas: 2304/2197, 82.3270 cents and 28561/27648, 56.2456 cents, ratio: 1.463705 generators: 1 of 138.57266 cents and 2 of 359.47234 cents ET pair of linear temperament : 36&230 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 248-tone equal temperament with octave 4/3 degrees: 69 179 248 generators: 69 and 179 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 56.24564 cents Scale diversity : 1.303203 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.669399 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 : 28561/27648, 56.2456 cents Most common intervals : 13/12, 138.5727 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle 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 : 169 (O: 169 U: 169) Highest odd numerator or denominator: 13 Scale harmonicity : 0.018877 Average absolute harmonicity : 0.096602 Specific harmonicity : 0.097805 Fundamental : 1/156, -7.2854 octaves, 1.6771 Hz. Guide tone : 208, 7.7004 octaves, 54418.118 Hz. Exponens Consonantiae : 3.244800E+04, 14.98584 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 30.5, average 10.16667 Mersenne's string divisions : 5075 Sum of van Prooijen's expressibility: 2.70501, average 0.90167 Sum of Tenney's harmonic distance : 5.59037, average 1.86346 Vogel's harmonic complexity : 17.33333 Wille's k value : 84 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 3 Triangular lattice diameter : 2 Lattice compactness : 21.78438, average 3.63073 Lattice compactness (without 2's) : 8.06450, average 1.34408 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.33333 8 3: -1 .. 0 -0.66667 2 1 13: -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 JI-epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 11 27| = patent Scale is weakly epimorphic with val: <7 11 29| Scale is weakly epimorphic with val: <7 11 30|
FIT/MODE
3: 1 1 1 SP B ME I SD: 22.4066 c. M: 27.4423 c. 4: 1 2 1 P M ME I SD: 11.4811 c. M: 14.0614 c. 7: 2 3 2 SP M ME I SD: 3.0422 c. M: 3.7259 c. 11: 3 5 3 SP M DE I SD: 2.2390 c. M: 2.7422 c. 18: 5 8 5 SP M DE I SD: 0.1852 c. M: 0.2268 c. 61: 17 27 17 SP M DE I SD: 0.1852 c. M: 0.2268 c. 79: 22 35 22 SP M DE I SD: 0.1008 c. M: 0.1234 c. 97: 27 43 27 SP M DE I SD: 0.0477 c. M: 0.0584 c. 115: 32 51 32 SP M DE I SD: 0.0112 c. M: 0.0138 c. 248: 69 110 69 SP M DE I SD: 0.0030 c. M: 0.0037 c. 363: 101 161 101 SP M DE I SD: 0.0015 c. M: 0.0018 c. 611: 170 271 170 SP M DE I SD: 0.0003 c. M: 0.0004 c. 1585: 441 703 441 SP M DE I SD: 0.0001 c. M: 0.0001 c. 2196: 611 974 611 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: 26.8414 cents 5 x 6:7 S SD: 47.5812 cents 6 x 7:8 S SD: 46.3007 cents 7:8 x 9 S SD: 55.9891 cents 8:9:10:11 H SD: 29.4909 cents 9:10:11:12 H SD: 15.1537 cents 12:13:15:16 SD: 8.9471 cents 21:23:26:28 SD: 7.1768 cents 26:28:32:35 SD: 6.4981 cents 27:29:33:36 SD: 6.3804 cents 34:37:42:45 SD: 5.4232 cents 35:38:43:47 SD: 4.4203 cents 36:39:44:48 SD: 4.0215 cents 39:42:48:52 S SD: 3.4248 cents 48:52:59:64 SD: 0.7519 cents 108:117:133:144 SD: 0.3339 cents 156:169:192:208 SD: 0.0000 cents