Scala analysis: xen15-chalmers-triadic-diamond-23-19-tetrachord
Upper tetrachord 184/171 * 1083/1058 * 23/19 of triadic diamond for M=23/19, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184/171 126.851329 2: 76/69 167.283668 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 23/19 330.7613 1: 184/171 126.8513 2: 1083/1058 40.4323 3: 23/19 330.7613
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1083/1058 40.432 cents 1: 1 184/171 126.851 cents 1: 1 23/19 330.761 cents 2: 1 76/69 167.284 cents 2: 1 57/46 371.194 cents 2: 1 4232/3249 457.613 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 : 126.9 167.3 498.0 126.9: 40.4 371.2 498.0 167.3: 330.8 457.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 40.4323 .. 330.7613 cents 24334/20577, 290.3290 cents 1083/1058, 40.4323 cents 2: 167.2837 .. 457.6127 cents 24334/20577, 290.3290 cents 1444/1587,-163.4777 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 1083/1058, 40.4323 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 23/19, 330.7613 cents Average / Smallest step : 4.105995 Largest / Average step : 1.992358 Largest / Smallest step : 8.180613 Median interval of one step : 184/171, 126.8513 cents, amount: 1 Least squares average step : 139.68240 cents, oct.: 419.04721 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1700-tone equal temperament with octave 4/3 degrees: 433 571 1700 Least number of segments generator : 851 of 249.315 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1631 of 477.830 cents and inv. generated superset size: 44 = 41 more = 1466.667% 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 40.43234 cents Scale diversity : 0.744144 Lumma stability : 0.162364 Lumma impropriety factor : 0.328239 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 : 1083/1058, 40.4323 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 : 23 Odd number limit : 3249 (O: 1083 U: 3249) Highest odd numerator or denominator: 171 Scale harmonicity : 0.006222 Average absolute harmonicity : 0.079494 Specific harmonicity : 0.033184 Fundamental : 1/3933, -11.9414 octaves, 0.0665 Hz. Guide tone : 3496, 11.7715 octaves, 914642.976 Hz. Exponens Consonantiae : 1.374977E+07, 23.71290 octaves Euler's gradus suavitatis : 88 Sum of Mann's harmonic distance : 253.5, average 84.50000 Mersenne's string divisions : 72065 Sum of van Prooijen's expressibility: 4.54897, average 1.51632 Sum of Tenney's harmonic distance : 9.29666, average 3.09889 Vogel's harmonic complexity : 46.33333 Wille's k value : 655 Wilson's harmonic complexity : 90 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.33129, average 2.55522 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 19: -1 .. 1 0.00000 2 23: -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 28 30| Scale is weakly epimorphic with val: <7 10 29 30| Scale is weakly epimorphic with val: <7 10 29 31| Scale is weakly epimorphic with val: <7 10 30 31| Scale is weakly epimorphic with val: <7 10 30 32| Scale is weakly epimorphic with val: <7 10 31 32| Scale is weakly epimorphic with val: <7 10 31 33| Scale is weakly epimorphic with val: <7 10 32 33| Scale is weakly epimorphic with val: <7 10 32 34| Scale is weakly epimorphic with val: <7 10 33 34| Scale is weakly epimorphic with val: <7 10 33 35| Scale is weakly epimorphic with val: <7 10 34 35| Scale is weakly epimorphic with val: <7 10 34 36| Scale is weakly epimorphic with val: <8 11 28 30| Scale is weakly epimorphic with val: <8 11 29 30| Scale is weakly epimorphic with val: <8 11 29 31| Scale is weakly epimorphic with val: <8 11 30 31| Scale is weakly epimorphic with val: <8 11 30 32| Scale is weakly epimorphic with val: <8 11 31 32| Scale is weakly epimorphic with val: <8 11 31 33| Scale is weakly epimorphic with val: <8 11 32 33| Scale is weakly epimorphic with val: <8 11 32 34| Scale is weakly epimorphic with val: <8 11 33 34| Scale is weakly epimorphic with val: <8 11 33 35| Scale is weakly epimorphic with val: <8 11 34 35| Scale is weakly epimorphic with val: <8 11 34 36|
FIT/MODE
3: 1 0 2 N G T3 SD: 22.6230 c. M:-39.1637 c. 5: 1 1 3 N M DE S SD: 24.2346 c. M:-31.9343 c. 7: 2 0 5 N G T3 SD: 16.9595 c. M: 24.9851 c. 8: 2 1 5 N T3 SD: 11.3295 c. M:-19.4832 c. 9: 2 1 6 N T3 SD: 9.3671 c. M: 16.1747 c. 11: 3 1 7 N T3 SD: 9.5169 c. M:-13.8236 c. 12: 3 1 8 N T3 SD: 1.5368 c. M: 2.3401 c. 27: 7 2 18 N T3 SD: 1.5021 c. M:-2.2714 c. 39: 10 3 26 N T3 SD: 0.8825 c. M: 1.2687 c. 51: 13 4 34 N T3 SD: 0.7348 c. M: 1.2687 c. 63: 16 5 42 N T3 SD: 0.7620 c. M: 1.2687 c. 71: 18 6 47 N T3 SD: 0.7042 c. M:-1.0696 c. 74: 19 6 49 N T3 SD: 0.8167 c. M:-1.0251 c. 83: 21 7 55 N T3 SD: 0.6431 c. M: 0.8399 c. 86: 22 7 57 N T3 SD: 0.4988 c. M:-0.6617 c. 98: 25 8 65 N T3 SD: 0.2716 c. M:-0.4254 c. 110: 28 9 73 N T3 SD: 0.1457 c. M:-0.2406 c. 149: 38 12 99 N T3 SD: 0.1313 c. M:-0.1669 c. 161: 41 13 107 N T3 SD: 0.1376 c. M: 0.2375 c. 247: 63 20 164 N T3 SD: 0.1129 c. M:-0.1804 c. 259: 66 21 172 N T3 SD: 0.0375 c. M:-0.0636 c. 271: 69 22 180 N T3 SD: 0.0352 c. M: 0.0435 c. 530: 135 43 352 N T3 SD: 0.0105 c. M: 0.0157 c. 911: 232 74 605 N T3 SD: 0.0104 c. M: 0.0166 c. 1170: 298 95 777 N T3 SD: 0.0049 c. M:-0.0084 c. 1441: 367 117 957 N T3 SD: 0.0042 c. M: 0.0071 c. 1700: 433 138 1129 N T3 SD: 0.0022 c. M:-0.0037 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: 85.3591 cents 6 x 7:8 S SD: 49.7936 cents 7 x 8:9 S SD: 44.8499 cents 8 x 9:11 SD: 32.3245 cents 9 x 10:12 S SD: 7.5600 cents 10 x 11:13 SD: 21.9451 cents 11 x 12:15 S SD: 21.1587 cents 12:13 x 16 SD: 5.8607 cents 13:14 x 17 SD: 16.8242 cents 14:15 x 19 SD: 15.7625 cents 17:18:19:23 SD: 15.1135 cents 18:19:20:24 S SD: 12.1750 cents 20 x 22:27 SD: 10.8134 cents 21 x 23:28 SD: 4.8951 cents 22 x 24:29 SD: 12.9285 cents 23:25 x 31 SD: 12.8122 cents 24:26 x 32 SD: 5.8607 cents 27:29:30:36 SD: 5.1475 cents 30:32:33:40 SD: 5.0970 cents 33 x 36:44 SD: 8.3233 cents 34:37 x 45 SD: 11.6721 cents 35:38:39:47 SD: 9.3994 cents 36:39:40:48 S SD: 6.3771 cents 37:40:41:49 SD: 5.8931 cents 38:41:42:51 SD: 4.5553 cents 39:42:43:52 SD: 0.7573 cents 147:158:162:196 SD: 0.7114 cents 159:171:175:212 SD: 0.5220 cents 198:213:218:264 SD: 0.2707 cents 237:255:261:316 SD: 0.1040 cents 276:297:304:368 SD: 0.0341 cents