Scala analysis: xen15-chalmers-triadic-diamond-23-18-tetrachord
Upper tetrachord 24/23 * 529/486 * 27/23 of triadic diamond for M=23/18, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 24/23 73.680654 vicesimotertial minor semitone 2: 92/81 220.454344 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 27/23 277.5907 vicesimotertial minor third 1: 24/23 73.6807 vicesimotertial minor semitone 2: 529/486 146.7737 3: 27/23 277.5907 vicesimotertial minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 24/23 73.681 cents vicesimotertial minor semitone 1: 1 529/486 146.774 cents 1: 1 27/23 277.591 cents vicesimotertial minor third 2: 1 92/81 220.454 cents 2: 1 648/529 351.271 cents 2: 1 23/18 424.364 cents vicesimotertial major third 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 : 73.7 220.5 498.0 73.7 : 146.8 424.4 498.0 220.5: 277.6 351.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.6807 .. 277.5907 cents 9/8, 203.9100 cents 24/23, 73.6807 cents 2: 220.4543 .. 424.3643 cents 9/8, 203.9100 cents 2116/2187,-57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 24/23, 73.6807 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 27/23, 277.5907 cents Average / Smallest step : 2.253169 Largest / Average step : 1.672082 Largest / Smallest step : 3.767484 Median interval of one step : 529/486, 146.7737 cents, amount: 1 Least squares average step : 143.48031 cents, oct.: 430.44093 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1656-tone equal temperament with octave 4/3 degrees: 245 733 1656 Least number of segments generator : 829 of 249.323 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 923 of 277.594 cents and inv. generated superset size: 42 = 39 more = 1400.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 57.13631 cents Scale diversity : 1.057624 Lumma stability : 0.295880 Lumma impropriety factor : 0.114721 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 : 2187/2116, 57.1363 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best minor thirds form a closed circle Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% -- Rational properties -- Prime limit : 23 Odd number limit : 529 (O: 529 U: 529) Highest odd numerator or denominator: 81 Scale harmonicity : 0.009950 Average absolute harmonicity : 0.084496 Specific harmonicity : 0.052599 Fundamental : 1/1863, -10.8634 octaves, 0.1404 Hz. Guide tone : 552, 9.1085 octaves, 144417.312 Hz. Exponens Consonantiae : 1.028376E+06, 19.97194 octaves Euler's gradus suavitatis : 58 Sum of Mann's harmonic distance : 113.5, average 37.83333 Mersenne's string divisions : 56917 Sum of van Prooijen's expressibility: 3.74733, average 1.24911 Sum of Tenney's harmonic distance : 7.69339, average 2.56446 Vogel's harmonic complexity : 33.33333 Wille's k value : 310 Wilson's harmonic complexity : 61 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 21.22426, average 3.53738 Lattice compactness (without 2's) : 17.32083, average 2.88680 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -4 .. 1 -1.33333 6 1 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: <8 11 31| Scale is weakly epimorphic with val: <8 11 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 52.8913 c. M: 73.6807 c. 4: 1 1 2 P M ME S SD: 33.6645 c. M:-50.8306 c. 5: 1 1 3 N M DE S SD: 19.3499 c. M:-25.9283 c. 6: 1 2 3 P T3 SD: 17.3506 c. M:-28.5682 c. 7: 1 2 4 N T3 SD: 4.3011 c. M: 7.0065 c. 20: 3 6 11 N T3 SD: 2.1979 c. M:-3.6659 c. 27: 4 8 15 N T3 SD: 0.5225 c. M:-0.8990 c. 34: 5 10 19 N T3 SD: 0.4910 c. M: 0.7286 c. 61: 9 18 34 N T3 SD: 0.1148 c. M: 0.1986 c. 149: 22 44 83 N T3 SD: 0.1226 c. M:-0.1562 c. 210: 31 62 117 N T3 SD: 0.1115 c. M: 0.1597 c. 271: 40 80 151 N T3 SD: 0.1082 c. M: 0.1685 c. 332: 49 98 185 N T3 SD: 0.1074 c. M: 0.1740 c. 359: 53 106 200 N T3 SD: 0.1153 c. M: 0.1531 c. 393: 58 116 219 N T3 SD: 0.1073 c. M: 0.1778 c. 425: 63 125 237 N T3 SD: 0.1184 c. M:-0.1472 c. 445: 66 131 248 N T3 SD: 0.1090 c. M:-0.1867 c. 452: 67 133 252 N T3 SD: 0.0955 c. M:-0.1446 c. 472: 70 139 263 N T3 SD: 0.1144 c. M:-0.1820 c. 479: 71 141 267 N T3 SD: 0.0834 c. M:-0.1423 c. 486: 72 143 271 N T3 SD: 0.0942 c. M: 0.1258 c. 506: 75 149 282 N T3 SD: 0.0822 c. M:-0.1402 c. 513: 76 151 286 N T3 SD: 0.0729 c. M:-0.1038 c. 540: 80 159 301 N T3 SD: 0.0614 c. M:-0.1038 c. 567: 84 167 316 N T3 SD: 0.0611 c. M:-0.1038 c. 574: 85 169 320 N T3 SD: 0.0559 c. M:-0.0717 c. 601: 89 177 335 N T3 SD: 0.0440 c. M:-0.0731 c. 628: 93 185 350 N T3 SD: 0.0442 c. M:-0.0744 c. 635: 94 187 354 N T3 SD: 0.0434 c. M: 0.0596 c. 662: 98 195 369 N T3 SD: 0.0302 c. M:-0.0481 c. 689: 102 203 384 N T3 SD: 0.0304 c. M:-0.0502 c. 723: 107 213 403 N T3 SD: 0.0193 c. M:-0.0273 c. 750: 111 221 418 N T3 SD: 0.0190 c. M:-0.0300 c. 784: 116 231 437 N T3 SD: 0.0121 c. M: 0.0186 c. 811: 120 239 452 N T3 SD: 0.0101 c. M:-0.0128 c. 872: 129 257 486 N T3 SD: 0.0062 c. M:-0.0105 c. 1656: 245 488 923 N T3 SD: 0.0028 c. M:-0.0035 c. 1717: 254 506 957 N T3 SD: 0.0029 c. M: 0.0036 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: 63.6303 cents 6 x 7:8 S SD: 23.2083 cents 7 x 8:9 S SD: 31.9335 cents 8 x 9:11 SD: 27.8914 cents 9 x 10:12 S SD: 19.0253 cents 10 x 11:13 SD: 35.3408 cents 11 x 13:15 SD: 39.4999 cents 12:13:14:16 S SD: 26.5946 cents 13:14:15:17 SD: 23.2326 cents 14:15:16:19 SD: 18.7024 cents 15:16:17:20 SD: 12.7456 cents 20:21:23:27 SD: 10.7569 cents 21:22:24:28 S SD: 4.2416 cents 43:45:49:57 SD: 4.2087 cents 44:46:50:59 SD: 3.4588 cents 45:47:51:60 SD: 1.3647 cents 66:69:75:88 SD: 1.1285 cents 96:100:109:128 SD: 1.0217 cents 111:116:126:148 SD: 0.9299 cents 117:122:133:156 SD: 0.6338 cents 162:169:184:216 SD: 0.1484 cents 390:407:443:520 SD: 0.0783 cents 552:576:627:736 SD: 0.0341 cents