Scala analysis: xen15-chalmers-triadic-diamond-22-17-tetrachord
Upper tetrachord 34/33 * 968/867 * 51/44 of triadic diamond for M=22/17, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 176/153 242.452531 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 51/44 255.5925 1: 34/33 51.6825 2: 968/867 190.7701 3: 51/44 255.5925
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 34/33 51.682 cents 1: 1 968/867 190.770 cents 1: 1 51/44 255.592 cents 2: 1 176/153 242.453 cents 2: 1 289/242 307.275 cents 2: 1 22/17 446.363 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 : 51.7 242.5 498.0 51.7 : 190.8 446.4 498.0 242.5: 255.6 307.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 255.5925 cents 9/8, 203.9100 cents 34/33, 51.6825 cents 2: 242.4525 .. 446.3625 cents 9/8, 203.9100 cents 7744/7803,-13.1399 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 51/44, 255.5925 cents Average / Smallest step : 3.212211 Largest / Average step : 1.539575 Largest / Smallest step : 4.945439 Median interval of one step : 968/867, 190.7701 cents, amount: 1 Least squares average step : 145.05161 cents, oct.: 435.15483 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2274-tone equal temperament with octave 4/3 degrees: 236 1107 2274 Least number of segments generator : 1139 of 249.461 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1885 of 412.847 cents and inv. generated superset size: 129 = 126 more = 4300.000% 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 13.13994 cents Scale diversity : 0.788492 Lumma stability : 0.207541 Lumma impropriety factor : 0.026383 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 : 7803/7744, 13.1399 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 17 Odd number limit : 867 (O: 289 U: 867) Highest odd numerator or denominator: 153 Scale harmonicity : 0.009440 Average absolute harmonicity : 0.083626 Specific harmonicity : 0.050188 Fundamental : 1/1683, -10.7168 octaves, 0.1555 Hz. Guide tone : 2992, 11.5469 octaves, 782783.691 Hz. Exponens Consonantiae : 5.035536E+06, 22.26371 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 201.5, average 67.16667 Mersenne's string divisions : 22043 Sum of van Prooijen's expressibility: 4.18033, average 1.39344 Sum of Tenney's harmonic distance : 8.55938, average 2.85313 Vogel's harmonic complexity : 32.33333 Wille's k value : 433 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 17.54693, average 2.92449 Lattice compactness (without 2's) : 11.32780, average 1.88797 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 4 2.33333 7 3: -2 ..-1 -1.33333 4 1 11: -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 23 28| Scale is weakly epimorphic with val: <7 10 23 29| Scale is weakly epimorphic with val: <7 10 24 29| Scale is weakly epimorphic with val: <7 10 24 30| Scale is weakly epimorphic with val: <7 10 25 30| Scale is weakly epimorphic with val: <7 10 25 31| Scale is weakly epimorphic with val: <7 10 26 31| Scale is weakly epimorphic with val: <7 10 26 32| Scale is weakly epimorphic with val: <7 10 27 32| Scale is weakly epimorphic with val: <7 10 27 33| Scale is weakly epimorphic with val: <8 11 23 29| Scale is weakly epimorphic with val: <8 11 23 30| Scale is weakly epimorphic with val: <8 11 24 30| Scale is weakly epimorphic with val: <8 11 24 31| Scale is weakly epimorphic with val: <8 11 25 31| Scale is weakly epimorphic with val: <8 11 25 32| Scale is weakly epimorphic with val: <8 11 26 32| Scale is weakly epimorphic with val: <8 11 26 33| Scale is weakly epimorphic with val: <8 11 27 33|
FIT/MODE
3: 0 1 2 N G T3 SD: 53.2722 c. M: 76.4375 c. 4: 0 2 2 P M DE S SD: 30.0790 c. M: 51.6825 c. 6: 1 2 3 P T3 SD: 18.4790 c. M:-31.3250 c. 7: 1 2 4 N T3 SD: 20.1679 c. M: 29.0047 c. 8: 1 3 4 P T3 SD: 7.1869 c. M:-10.5732 c. 10: 1 4 5 P T3 SD: 3.9451 c. M:-6.5700 c. 18: 2 7 9 P T3 SD: 4.3409 c. M:-6.5700 c. 19: 2 7 10 N T3 SD: 3.7982 c. M: 6.5365 c. 21: 2 8 11 N T3 SD: 3.9168 c. M: 5.2882 c. 27: 3 10 14 N T3 SD: 2.6080 c. M:-3.6559 c. 29: 3 11 15 N T3 SD: 1.1682 c. M: 2.0170 c. 39: 4 15 20 N T3 SD: 0.3630 c. M: 0.6009 c. 105: 11 40 54 N T3 SD: 0.4245 c. M: 0.5450 c. 107: 11 41 55 N T3 SD: 0.3659 c. M: 0.4816 c. 115: 12 44 59 N T3 SD: 0.1713 c. M:-0.2874 c. 154: 16 59 79 N T3 SD: 0.0690 c. M:-0.1019 c. 337: 35 129 173 N T3 SD: 0.0528 c. M: 0.0805 c. 376: 39 144 193 N T3 SD: 0.0335 c. M: 0.0530 c. 491: 51 188 252 N T3 SD: 0.0315 c. M:-0.0493 c. 530: 55 203 272 N T3 SD: 0.0047 c. M: 0.0080 c. 1744: 181 668 895 N T3 SD: 0.0041 c. M:-0.0068 c. 1783: 185 683 915 N T3 SD: 0.0050 c. M: 0.0065 c. 2274: 236 871 1167 N T3 SD: 0.0032 c. M:-0.0056 c. 2313: 240 886 1187 N T3 SD: 0.0031 c. M: 0.0046 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: 55.8822 cents 6 x 7:8 S SD: 12.2092 cents 7 x 8:9 S SD: 31.9816 cents 8 x 9:11 SD: 32.8768 cents 9 x 10:12 S SD: 30.0244 cents 10 x 12:13 S SD: 42.6549 cents 11 x 13:15 SD: 30.4134 cents 12:13:14:16 S SD: 30.0854 cents 13:14:15:17 SD: 27.9445 cents 14:15:16:19 SD: 25.0724 cents 15:16:17:20 SD: 21.7811 cents 18:19:21:24 SD: 16.1713 cents 19:20:22:25 SD: 15.0276 cents 20:21:23:27 SD: 13.0708 cents 21:22:24:28 S SD: 10.3268 cents 24:25:28:32 SD: 10.3111 cents 25:26:29:33 SD: 9.2852 cents 26:27:30:35 S SD: 7.3703 cents 27:28:31:36 SD: 3.9154 cents 33:34:38:44 SD: 0.5958 cents 201:207:231:268 SD: 0.5952 cents 234:241:269:312 SD: 0.4366 cents 267:275:307:356 SD: 0.3208 cents 300:309:345:400 SD: 0.2360 cents 333:343:383:444 SD: 0.1768 cents 366:377:421:488 SD: 0.1417 cents 399:411:459:532 SD: 0.1300 cents 426:439:490:568 SD: 0.1281 cents 459:473:528:612 SD: 0.1109 cents