Scala analysis: xen15-chalmers-triadic-reversed-diamond-17-14-tetrachord
Tetrachord 56/51 * 867/784 * 56/51 of triadic reversed diamond for M=17/14, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 56/51 161.915496 2: 17/14 336.129503 supraminor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 56/51 161.9155 1: 56/51 161.9155 2: 867/784 174.2140 3: 56/51 161.9155
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 56/51 161.915 cents 1: 1 867/784 174.214 cents 2: 1 3136/2601 323.831 cents 2: 2 17/14 336.130 cents supraminor 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 : 161.9 336.1 498.0 161.9: 174.2 336.1 498.0 336.1: 161.9 323.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 161.9155 .. 174.2140 cents 44217/43904, 12.2985 cents 56/51, 161.9155 cents 2: 323.8310 .. 336.1295 cents 44217/43904, 12.2985 cents 2458624/2255067, 149.6170 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 56/51, 161.9155 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 867/784, 174.2140 cents Average / Smallest step : 1.025319 Largest / Average step : 1.049387 Largest / Smallest step : 1.075956 Median interval of one step : 56/51, 161.9155 cents, amount: 2 Most common interval of one step : 56/51, 161.9155 cents, amount: 2 Least squares average step : 166.30782 cents, oct.: 498.92346 cents Scale is strictly proper Scale has Myhill's property chromas: 44217/43904, 12.2985 cents and 2458624/2255067, 149.6170 cents, ratio: 12.165455 generators: 1 of 161.91550 cents and 2 of 336.12950 cents ET pair of linear temperament : 80&486 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 243-tone equal temperament with octave 4/3 degrees: 79 164 243 generators: 79 and 164 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 149.61699 cents Scale diversity : 1.209908 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.950613 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 : 44217/43904, 12.2985 cents Most common intervals : 56/51, 161.9155 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 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 12.2985 cents: 1 2 Limited inverse transpositions with margin 12.2985 cents: 1 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 17 Odd number limit : 2601 (O: 867 U: 2601) Highest odd numerator or denominator: 51 Scale harmonicity : 0.011432 Average absolute harmonicity : 0.086714 Specific harmonicity : 0.059905 Fundamental : 1/714, -9.4798 octaves, 0.3664 Hz. Guide tone : 952, 9.8948 octaves, 249067.538 Hz. Exponens Consonantiae : 6.797280E+05, 19.37460 octaves Euler's gradus suavitatis : 51 Sum of Mann's harmonic distance : 72.5, average 24.16667 Mersenne's string divisions : 23219 Sum of van Prooijen's expressibility: 3.41514, average 1.13838 Sum of Tenney's harmonic distance : 6.91152, average 2.30384 Vogel's harmonic complexity : 27.33333 Wille's k value : 433 Wilson's harmonic complexity : 51 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 7: -1 .. 1 0.00000 2 17: -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 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 18 32| Scale is weakly epimorphic with val: <7 11 18 33| 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| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 33| Scale is weakly epimorphic with val: <7 11 20 28| Scale is JI-epimorphic with val: <7 11 20 29| Scale is weakly epimorphic with val: <7 11 20 31| Scale is weakly epimorphic with val: <7 11 20 32| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 29| Scale is JI-epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 32| Scale is weakly epimorphic with val: <7 11 21 33| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 11 22 30| Scale is JI-epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 11 22 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 3.3472 c. M: 4.0995 c. 22: 7 8 7 SP M ME I SD: 2.8142 c. M: 3.4466 c. 25: 8 9 8 SP M ME I SD: 2.0748 c. M: 2.5411 c. 28: 9 10 9 SP M ME I SD: 1.4939 c. M: 1.8296 c. 31: 10 11 10 SP M ME I SD: 1.0254 c. M: 1.2558 c. 34: 11 12 11 SP M ME I SD: 0.6396 c. M: 0.7833 c. 37: 12 13 12 SP M ME I SD: 0.3163 c. M: 0.3874 c. 40: 13 14 13 SP M ME I SD: 0.0415 c. M: 0.0509 c. 123: 40 43 40 SP M DE I SD: 0.0411 c. M: 0.0504 c. 163: 53 57 53 SP M DE I SD: 0.0208 c. M: 0.0255 c. 203: 66 71 66 SP M DE I SD: 0.0085 c. M: 0.0105 c. 243: 79 85 79 SP M DE I SD: 0.0003 c. M: 0.0004 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: 50.1842 cents 5 x 6:7 S SD: 43.4582 cents 6 x 7:8 S SD: 34.6293 cents 7:8 x 9 S SD: 46.7996 cents 8:9:10:11 H SD: 28.1267 cents 9:10:11:12 H SD: 7.7958 cents 28:31:34:37 SD: 7.0349 cents 29:32:35:39 SD: 6.7071 cents 32:35:39:43 SD: 5.4548 cents 33:36:40:44 S SD: 3.8979 cents 42:46:51:56 SD: 1.4740 cents 51:56:62:68 SD: 0.6652 cents 144:158:175:192 SD: 0.6377 cents 183:201:222:244 SD: 0.5818 cents 225:247:273:300 SD: 0.4732 cents 234:257:284:312 SD: 0.3189 cents 276:303:335:368 SD: 0.2703 cents 285:313:346:380 SD: 0.1611 cents 327:359:397:436 SD: 0.1404 cents 336:369:408:448 SD: 0.0920 cents 378:415:459:504 SD: 0.0818 cents