Scala analysis: xen15-chalmers-triadic-reversed-diamond-26-21-tetrachord
Tetrachord 14/13 * 169/147 * 14/13 of triadic reversed diamond for M=26/21, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 26/21 369.746754 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 14/13 128.2982 2/3-tone 1: 14/13 128.2982 2/3-tone 2: 169/147 241.4485 3: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 14/13 128.298 cents 2/3-tone 1: 1 169/147 241.449 cents 2: 1 196/169 256.596 cents two (2/3-tone) 2: 2 26/21 369.747 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 : 128.3 369.7 498.0 128.3: 241.4 369.7 498.0 369.7: 128.3 256.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 128.2982 .. 241.4485 cents 2197/2058, 113.1503 cents 14/13, 128.2982 cents 2: 256.5965 .. 369.7468 cents 2197/2058, 113.1503 cents 28812/28561, 15.1480 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 14/13, 128.2982 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 169/147, 241.4485 cents Average / Smallest step : 1.293977 Largest / Average step : 1.454378 Largest / Smallest step : 1.881932 Median interval of one step : 14/13, 128.2982 cents, amount: 2 Most common interval of one step : 14/13, 128.2982 cents, amount: 2 Least squares average step : 168.70905 cents, oct.: 506.12716 cents Scale is strictly proper Scale has Myhill's property chromas: 2197/2058, 113.1503 cents and 28812/28561, 15.1480 cents, ratio: 7.469660 generators: 1 of 128.29824 cents and 2 of 369.74675 cents ET pair of linear temperament : 62&132 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 427-tone equal temperament with octave 4/3 degrees: 110 317 427 generators: 110 and 317 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 15.14798 cents Scale diversity : 1.166283 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.545622 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 : 28812/28561, 15.1480 cents Most common intervals : 14/13, 128.2982 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 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: 21 Scale harmonicity : 0.014379 Average absolute harmonicity : 0.090628 Specific harmonicity : 0.075720 Fundamental : 1/273, -8.0928 octaves, 0.9583 Hz. Guide tone : 364, 8.5078 octaves, 95231.706 Hz. Exponens Consonantiae : 9.937200E+04, 16.60055 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 40.5, average 13.50000 Mersenne's string divisions : 8883 Sum of van Prooijen's expressibility: 2.91328, average 0.97109 Sum of Tenney's harmonic distance : 6.07645, average 2.02548 Vogel's harmonic complexity : 22.33333 Wille's k value : 84 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.70017, average 2.11669 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 7: -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 18 26| Scale is weakly 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 JI-epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 20 25| Scale is JI-epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 20 29| Scale is weakly epimorphic with val: <7 11 21 26| Scale is JI-epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 22 25| Scale is weakly epimorphic with val: <7 11 22 27| Scale is JI-epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 11 22 30|
FIT/MODE
3: 1 1 1 SP B ME I SD: 30.7956 c. M: 37.7168 c. 4: 1 2 1 P M ME I SD: 3.0921 c. M: 3.7870 c. 19: 5 9 5 SP M DE I SD: 2.2586 c. M: 2.7662 c. 23: 6 11 6 SP M DE I SD: 1.3281 c. M: 1.6265 c. 27: 7 13 7 SP M DE I SD: 0.6732 c. M: 0.8245 c. 31: 8 15 8 SP M DE I SD: 0.1874 c. M: 0.2295 c. 66: 17 32 17 SP M DE I SD: 0.0114 c. M: 0.0139 c. 295: 76 143 76 SP M DE I SD: 0.0095 c. M: 0.0117 c. 361: 93 175 93 SP M DE I SD: 0.0057 c. M: 0.0070 c. 427: 110 207 110 SP M DE I SD: 0.0031 c. M: 0.0037 c. 493: 127 239 127 SP M DE I SD: 0.0011 c. M: 0.0014 c. 559: 144 271 144 SP M DE I SD: 0.0003 c. M: 0.0004 c. 1052: 271 510 271 SP M DE I SD: 0.0003 c. M: 0.0004 c. 1611: 415 781 415 SP M DE I SD: 0.0001 c. M: 0.0001 c. 2170: 559 1052 559 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: 16.5670 cents 5 x 6:7 S SD: 50.1550 cents 6 x 7:8 S SD: 51.4379 cents 7:8 x 9 S SD: 60.3065 cents 8:9:10:11 H SD: 31.3220 cents 9:10:11:12 H SD: 19.5119 cents 12:13:15:16 SD: 6.4981 cents 25:27:31:33 SD: 6.0939 cents 30:32:37:40 SD: 5.9533 cents 37:40:46:49 SD: 5.0976 cents 38:41:47:51 SD: 3.9794 cents 39:42:48:52 S SD: 3.4248 cents 42:45:52:56 SD: 2.9518 cents 51:55:63:68 SD: 1.5365 cents 63:68:78:84 SD: 1.3071 cents 93:100:115:124 SD: 1.1403 cents 105:113:130:140 SD: 0.3927 cents 168:181:208:224 SD: 0.2453 cents 273:294:338:364 SD: 0.0000 cents