Scala analysis: xen15-chalmers-triadic-diamond-17-14-tetrachord
Upper tetrachord 68/63 * 294/289 * 17/14 of triadic 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: 68/63 132.219501 supraminor second 2: 56/51 161.915496 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 68/63 132.2195 supraminor second 2: 294/289 29.6960 3: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 294/289 29.696 cents 1: 1 68/63 132.220 cents supraminor second 1: 1 17/14 336.130 cents supraminor third 2: 1 56/51 161.915 cents 2: 1 21/17 365.825 cents submajor third 2: 1 578/441 468.349 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 132.2 161.9 498.0 132.2: 29.7 365.8 498.0 161.9: 336.1 468.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.6960 .. 336.1295 cents 4913/4116, 306.4335 cents 294/289, 29.6960 cents 2: 161.9155 .. 468.3490 cents 4913/4116, 306.4335 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 294/289, 29.6960 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 5.590485 Largest / Average step : 2.024694 Largest / Smallest step : 11.319018 Median interval of one step : 68/63, 132.2195 cents, amount: 1 Least squares average step : 139.29896 cents, oct.: 417.89689 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2147-tone equal temperament with octave 4/3 degrees: 570 698 2147 Least number of segments generator : 1074 of 249.138 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 2019 of 468.353 cents and inv. generated superset size: 40 = 37 more = 1333.333% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 29.69599 cents Scale diversity : 0.642376 Lumma stability : 0.119250 Lumma impropriety factor : 0.349796 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 294/289, 29.6960 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 17 Odd number limit : 441 (O: 289 U: 441) Highest odd numerator or denominator: 63 Scale harmonicity : 0.011218 Average absolute harmonicity : 0.085646 Specific harmonicity : 0.059830 Fundamental : 1/1071, -10.0647 octaves, 0.2443 Hz. Guide tone : 952, 9.8948 octaves, 249067.538 Hz. Exponens Consonantiae : 1.019592E+06, 19.95956 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 122.5, average 40.83333 Mersenne's string divisions : 98119 Sum of van Prooijen's expressibility: 3.98403, average 1.32801 Sum of Tenney's harmonic distance : 8.16679, average 2.72226 Vogel's harmonic complexity : 28.33333 Wille's k value : 178 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.48883, average 2.58147 Lattice compactness (without 2's) : 11.32780, average 1.88797 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 ..-1 -1.33333 4 1 7: -1 .. 1 0.00000 2 17: -1 .. 1 0.00000 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 19 28| Scale is weakly epimorphic with val: <7 10 20 28| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 10 21 30| Scale is weakly epimorphic with val: <7 10 22 30| Scale is weakly epimorphic with val: <7 10 22 31| Scale is weakly epimorphic with val: <8 11 18 27| Scale is weakly epimorphic with val: <8 11 18 28| Scale is weakly epimorphic with val: <8 11 19 28| Scale is weakly epimorphic with val: <8 11 19 29| Scale is weakly epimorphic with val: <8 11 20 29| Scale is weakly epimorphic with val: <8 11 20 30| Scale is weakly epimorphic with val: <8 11 21 30| Scale is weakly epimorphic with val: <8 11 21 31| Scale is weakly epimorphic with val: <8 11 22 31| Scale is weakly epimorphic with val: <8 11 22 32|
FIT/MODE
3: 1 0 2 N G T3 SD: 19.6549 c. M:-33.7955 c. 7: 2 0 5 N G T3 SD: 12.7333 c. M: 19.6169 c. 9: 2 1 6 N T3 SD: 12.6610 c. M: 21.5428 c. 10: 3 0 7 N G T3 SD: 12.2737 c. M:-17.1940 c. 11: 3 1 7 N T3 SD: 11.2748 c. M:-19.1918 c. 12: 3 1 8 N T3 SD: 5.0406 c. M: 7.7083 c. 15: 4 1 10 N T3 SD: 2.3914 c. M:-4.0995 c. 22: 6 1 15 N T3 SD: 2.8820 c. M:-3.6110 c. 31: 8 2 21 N T3 SD: 2.2514 c. M: 3.6918 c. 34: 9 2 23 N T3 SD: 0.5037 c. M: 0.7833 c. 49: 13 3 33 N T3 SD: 0.4137 c. M:-0.7114 c. 83: 22 5 56 N T3 SD: 0.1328 c. M: 0.2076 c. 200: 53 12 135 N T3 SD: 0.1403 c. M: 0.2376 c. 237: 63 14 160 N T3 SD: 0.1160 c. M:-0.1722 c. 286: 76 17 193 N T3 SD: 0.0769 c. M:-0.1281 c. 320: 85 19 216 N T3 SD: 0.0517 c. M:-0.0737 c. 369: 98 22 249 N T3 SD: 0.0420 c. M:-0.0526 c. 403: 107 24 272 N T3 SD: 0.0147 c. M: 0.0200 c. 486: 129 29 328 N T3 SD: 0.0129 c. M: 0.0224 c. 855: 227 51 577 N T3 SD: 0.0139 c. M:-0.0219 c. 889: 236 53 600 N T3 SD: 0.0059 c. M: 0.0089 c. 1744: 463 104 1177 N T3 SD: 0.0038 c. M:-0.0062 c. 2147: 570 128 1449 N T3 SD: 0.0029 c. M:-0.0048 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 x 5 S SD: 111.7313 cents 5 x 6:7 S SD: 87.7017 cents 6 x 7:8 S SD: 52.4777 cents 7 x 8:9 S SD: 46.7996 cents 8 x 9:11 SD: 33.9173 cents 9 x 10:12 S SD: 10.2441 cents 10 x 11:13 SD: 21.9699 cents 11 x 12:15 S SD: 20.2538 cents 12:13 x 16 SD: 3.1766 cents 13:14 x 17 SD: 16.9226 cents 14:15 x 19 SD: 16.5996 cents 15:16 x 20 S SD: 10.2441 cents 19 x 21:25 SD: 12.7934 cents 20 x 22:27 SD: 10.8635 cents 21 x 23:28 SD: 2.2110 cents 22 x 24:29 SD: 11.3873 cents 23:25 x 31 SD: 11.1526 cents 24:26 x 32 SD: 3.1766 cents 25:27 x 33 SD: 8.7146 cents 27:29:30:36 SD: 7.3948 cents 30:32:33:40 SD: 6.9066 cents 32 x 35:43 SD: 7.5403 cents 33 x 36:44 SD: 5.6392 cents 34:37 x 45 SD: 9.5395 cents 35:38 x 47 SD: 7.9833 cents 36:39:40:48 S SD: 7.1502 cents 37:40:41:49 SD: 6.6253 cents 38:41:42:51 SD: 5.3562 cents 39:42:43:52 SD: 2.7093 cents 45 x 49:60 SD: 7.2437 cents 47:51:52:63 SD: 6.1505 cents 48:52:53:64 SD: 3.8468 cents 49:53:54:65 SD: 3.8193 cents 50:54:55:67 SD: 3.0756 cents 51:55:56:68 SD: 0.4994 cents 213:230:234:284 SD: 0.3760 cents 225:243:247:300 SD: 0.3661 cents 264:285:290:352 SD: 0.2532 cents 276:298:303:368 SD: 0.2158 cents 315:340:346:420 SD: 0.1963 cents 327:353:359:436 SD: 0.1225 cents 378:408:415:504 SD: 0.0818 cents