Scala analysis: xen15-chalmers-triadic-diamond-26-21-tetrachord
Upper tetrachord 14/13 * 1352/1323 * 63/52 of triadic 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: 208/189 165.836753 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 63/52 332.2082 1: 14/13 128.2982 2/3-tone 2: 1352/1323 37.5385 3: 63/52 332.2082
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1352/1323 37.539 cents 1: 1 14/13 128.298 cents 2/3-tone 1: 1 63/52 332.208 cents 2: 1 208/189 165.837 cents 2: 1 26/21 369.747 cents 2: 1 441/338 460.506 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 : 128.3 165.8 498.0 128.3: 37.5 369.7 498.0 165.8: 332.2 460.5 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.5385 .. 332.2082 cents 83349/70304, 294.6697 cents 1352/1323, 37.5385 cents 2: 165.8368 .. 460.5065 cents 83349/70304, 294.6697 cents 10816/11907,-166.3715 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 1352/1323, 37.5385 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 63/52, 332.2082 cents Average / Smallest step : 4.422525 Largest / Average step : 2.001074 Largest / Smallest step : 8.849799 Median interval of one step : 14/13, 128.2982 cents, amount: 1 Least squares average step : 139.57905 cents, oct.: 418.73716 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1844-tone equal temperament with octave 4/3 degrees: 475 614 1844 Least number of segments generator : 923 of 249.293 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1369 of 369.752 cents and inv. generated superset size: 24 = 21 more = 800.000% 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 37.53851 cents Scale diversity : 0.717313 Lumma stability : 0.150743 Lumma impropriety factor : 0.334049 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 : 1352/1323, 37.5385 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 13 Odd number limit : 1323 (O: 441 U: 1323) Highest odd numerator or denominator: 189 Scale harmonicity : 0.013007 Average absolute harmonicity : 0.088897 Specific harmonicity : 0.068287 Fundamental : 1/2457, -11.2627 octaves, 0.1065 Hz. Guide tone : 1456, 10.5078 octaves, 380926.823 Hz. Exponens Consonantiae : 3.577392E+06, 21.77048 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 215.5, average 71.83333 Mersenne's string divisions : 75033 Sum of van Prooijen's expressibility: 3.86753, average 1.28918 Sum of Tenney's harmonic distance : 7.93378, average 2.64459 Vogel's harmonic complexity : 27.33333 Wille's k value : 661 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.42557, average 3.23759 Lattice compactness (without 2's) : 14.03548, average 2.33925 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -3 .. 0 -1.33333 4 1 7: -1 .. 1 0.00000 2 13: -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 20 25| Scale is weakly epimorphic with val: <7 10 21 25| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 22 26| Scale is weakly epimorphic with val: <7 10 22 27| Scale is weakly epimorphic with val: <8 11 20 25| Scale is weakly epimorphic with val: <8 11 21 25| Scale is weakly epimorphic with val: <8 11 21 26| Scale is weakly epimorphic with val: <8 11 22 26| Scale is weakly epimorphic with val: <8 11 22 27|
FIT/MODE
3: 1 0 2 N G T3 SD: 21.7760 c. M:-37.7168 c. 5: 1 1 3 N M DE S SD: 25.4125 c. M:-33.3812 c. 6: 2 0 4 N G T3 SD: 21.7760 c. M:-37.7168 c. 7: 2 0 5 N G T3 SD: 15.8120 c. M: 23.5382 c. 8: 2 1 5 N T3 SD: 12.2802 c. M:-20.9301 c. 9: 2 1 6 N T3 SD: 10.1743 c. M: 17.6216 c. 11: 3 1 7 N T3 SD: 9.8306 c. M:-15.2705 c. 12: 3 1 8 N T3 SD: 2.1888 c. M: 3.7870 c. 27: 7 2 18 N T3 SD: 0.4870 c. M:-0.8245 c. 39: 10 3 26 N T3 SD: 0.3583 c. M: 0.5944 c. 66: 17 5 44 N T3 SD: 0.1032 c. M:-0.1782 c. 225: 58 17 150 N T3 SD: 0.1144 c. M:-0.1782 c. 291: 75 22 194 N T3 SD: 0.1093 c. M:-0.1782 c. 357: 92 27 238 N T3 SD: 0.1068 c. M:-0.1782 c. 423: 109 32 282 N T3 SD: 0.1054 c. M:-0.1782 c. 466: 120 35 311 N T3 SD: 0.1062 c. M: 0.1780 c. 478: 123 36 319 N T3 SD: 0.1268 c. M: 0.1691 c. 481: 124 36 321 N T3 SD: 0.1111 c. M: 0.1669 c. 489: 126 37 326 N T3 SD: 0.1046 c. M:-0.1782 c. 493: 127 37 329 N T3 SD: 0.0915 c. M: 0.1585 c. 505: 130 38 337 N T3 SD: 0.1008 c. M: 0.1505 c. 508: 131 38 339 N T3 SD: 0.1157 c. M: 0.1486 c. 516: 133 39 344 N T3 SD: 0.1114 c. M:-0.1782 c. 520: 134 39 347 N T3 SD: 0.0853 c. M: 0.1410 c. 532: 137 40 355 N T3 SD: 0.0810 c. M: 0.1338 c. 544: 140 41 363 N T3 SD: 0.1028 c. M: 0.1269 c. 547: 141 41 365 N T3 SD: 0.0866 c. M: 0.1253 c. 559: 144 42 373 N T3 SD: 0.0686 c. M: 0.1187 c. 571: 147 43 381 N T3 SD: 0.0797 c. M: 0.1125 c. 586: 151 44 391 N T3 SD: 0.0644 c. M: 0.1051 c. 598: 154 45 399 N T3 SD: 0.0617 c. M: 0.0994 c. 613: 158 46 409 N T3 SD: 0.0678 c. M: 0.0926 c. 625: 161 47 417 N T3 SD: 0.0505 c. M: 0.0874 c. 637: 164 48 425 N T3 SD: 0.0636 c. M: 0.0824 c. 652: 168 49 435 N T3 SD: 0.0479 c. M: 0.0764 c. 664: 171 50 443 N T3 SD: 0.0465 c. M: 0.0718 c. 679: 175 51 453 N T3 SD: 0.0531 c. M: 0.0663 c. 691: 178 52 461 N T3 SD: 0.0358 c. M: 0.0620 c. 718: 185 54 479 N T3 SD: 0.0346 c. M: 0.0530 c. 730: 188 55 487 N T3 SD: 0.0347 c. M: 0.0492 c. 757: 195 57 505 N T3 SD: 0.0238 c. M: 0.0411 c. 784: 202 59 523 N T3 SD: 0.0240 c. M: 0.0335 c. 796: 205 60 531 N T3 SD: 0.0258 c. M: 0.0329 c. 823: 212 62 549 N T3 SD: 0.0138 c. M: 0.0235 c. 850: 219 64 567 N T3 SD: 0.0159 c. M:-0.0216 c. 889: 229 67 593 N T3 SD: 0.0058 c. M: 0.0085 c. 955: 246 72 637 N T3 SD: 0.0043 c. M: 0.0060 c. 1844: 475 139 1230 N T3 SD: 0.0035 c. M: 0.0057 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: 85.9885 cents 6 x 7:8 S SD: 50.5171 cents 7 x 8:9 S SD: 45.3681 cents 8 x 9:11 SD: 32.7398 cents 9 x 10:12 S SD: 8.2835 cents 10 x 11:13 SD: 21.9195 cents 11 x 12:15 S SD: 20.8847 cents 12:13 x 16 SD: 5.1372 cents 13:14 x 17 SD: 16.8086 cents 14:15 x 19 SD: 15.9480 cents 17:18:19:23 SD: 15.6838 cents 18:19:20:24 S SD: 12.8159 cents 20 x 22:27 SD: 10.7612 cents 21 x 23:28 SD: 4.1717 cents 22 x 24:29 SD: 12.4750 cents 23:25 x 31 SD: 12.3294 cents 24:26 x 32 SD: 5.1372 cents 33 x 36:44 SD: 7.5998 cents 34:37 x 45 SD: 11.0737 cents 35:38:39:47 SD: 9.5012 cents 36:39:40:48 S SD: 6.4981 cents 37:40:41:49 SD: 5.9948 cents 38:41:42:51 SD: 4.6508 cents 39:42:43:52 SD: 1.0661 cents 90:97:99:120 SD: 0.5354 cents 129:139:142:172 SD: 0.3445 cents 249:268:274:332 SD: 0.3379 cents 288:310:317:384 SD: 0.2992 cents 339:365:373:452 SD: 0.1728 cents 378:407:416:504 SD: 0.1091 cents 468:504:515:624 SD: 0.0534 cents 507:546:558:676 SD: 0.0328 cents