Scala analysis: xen15-chalmers-triadic-reversed-diamond-30-23-tetrachord
Tetrachord 46/45 * 675/529 * 46/45 of triadic reversed diamond for M=30/23, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 46/45 38.050632 23rd-partial chroma 2: 30/23 459.994367 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 46/45 38.0506 23rd-partial chroma 1: 46/45 38.0506 23rd-partial chroma 2: 675/529 421.9437 3: 46/45 38.0506 23rd-partial chroma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 46/45 38.051 cents 23rd-partial chroma 1: 1 675/529 421.944 cents 2: 1 2116/2025 76.101 cents two (23rd-partial chroma) 2: 2 30/23 459.994 cents Highest number of different intervals for one interval class: 2 Average number of different intervals per interval class: 2.00000 = 2
SHOW/LINE/CENTS INTERVALS
1 2 3 0.0 : 38.1 460.0 498.0 38.1 : 421.9 460.0 498.0 460.0: 38.1 76.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 38.0506 .. 421.9437 cents 30375/24334, 383.8931 cents 46/45, 38.0506 cents 2: 76.1013 .. 459.9944 cents 30375/24334, 383.8931 cents 1119364/1366875,-345.8425 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 46/45, 38.0506 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 675/529, 421.9437 cents Average / Smallest step : 4.363002 Largest / Average step : 2.541600 Largest / Smallest step : 11.089007 Median interval of one step : 46/45, 38.0506 cents, amount: 2 Most common interval of one step : 46/45, 38.0506 cents, amount: 2 Least squares average step : 175.15531 cents, oct.: 525.46594 cents Scale is not proper Scale has Myhill's property chromas: 30375/24334, 383.8931 cents and 1366875/1119364, 345.8425 cents, ratio: 1.110023 generators: 1 of 38.05063 cents and 2 of 459.99437 cents ET pair of linear temperament : 26&288 Scale is distributional even Scale is a mode of a 144-tone equal temperament with octave 4/3 degrees: 11 133 144 generators: 11 and 133 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 38.05063 cents Scale diversity : 0.251796 Lumma stability : 0.152800 Lumma impropriety factor : 0.694400 Rothenberg efficiency : 0.888889 redundancy: 0.111111 Efficiency x scale size : 2.666667 Number of different interval sizes : 4 = 2.00000 / class Number of one step interval sizes : 2 Highest interval variety : 2 Mean interval variety : 2.00000 = 2 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 46/45, 38.0506 cents Most common intervals : 46/45, 38.0506 cents & inv., amount: 2 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 : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 23 Odd number limit : 2025 (O: 675 U: 2025) Highest odd numerator or denominator: 45 Scale harmonicity : 0.009348 Average absolute harmonicity : 0.083900 Specific harmonicity : 0.049445 Fundamental : 1/1035, -10.0154 octaves, 0.2528 Hz. Guide tone : 1380, 10.4305 octaves, 361043.280 Hz. Exponens Consonantiae : 1.428300E+06, 20.44587 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 75.5, average 25.16667 Mersenne's string divisions : 4823 Sum of van Prooijen's expressibility: 3.49206, average 1.16402 Sum of Tenney's harmonic distance : 7.23400, average 2.41133 Vogel's harmonic complexity : 33.33333 Wille's k value : 337 Wilson's harmonic complexity : 65 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 15.65068, average 2.60845 Lattice compactness (without 2's) : 13.48619, average 2.24770 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -2 .. 1 -0.66667 4 1 5: -1 .. 1 0.00000 2 23: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 32| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 15 35| Scale is weakly epimorphic with val: <7 11 16 30| Scale is JI-epimorphic with val: <7 11 16 32| Scale is weakly epimorphic with val: <7 11 16 33| Scale is weakly epimorphic with val: <7 11 16 35| Scale is weakly epimorphic with val: <7 11 16 36| Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 31| Scale is JI-epimorphic with val: <7 11 17 33| = patent Scale is weakly epimorphic with val: <7 11 17 34| Scale is weakly epimorphic with val: <7 11 17 36| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 32| Scale is JI-epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 11 18 35| Scale is weakly epimorphic with val: <7 11 19 30| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 19 33| Scale is JI-epimorphic with val: <7 11 19 35| Scale is weakly epimorphic with val: <7 11 19 36|
FIT/MODE
3: 0 3 0 N M DE I SD: 31.0682 c. M:-38.0506 c. 4: 0 4 0 N M DE I SD: 31.0682 c. M:-38.0506 c. 5: 0 5 0 N M DE I SD: 31.0682 c. M: 38.0506 c. 6: 0 5 1 N G T3 SD: 34.0048 c. M: 44.9569 c. 7: 0 6 1 N G T3 SD: 29.1168 c. M: 38.0506 c. 8: 1 6 1 N M DE I SD: 19.7633 c. M: 24.2050 c. 9: 1 7 1 N M DE I SD: 14.1153 c. M:-17.2877 c. 10: 1 8 1 N M DE I SD: 9.5970 c. M: 11.7539 c. 11: 1 9 1 N M DE I SD: 5.9002 c. M:-7.2262 c. 12: 1 10 1 N M DE I SD: 2.8195 c. M:-3.4531 c. 13: 1 11 1 N M DE I SD: 0.2127 c. M: 0.2605 c. 79: 6 67 6 N M DE I SD: 0.1832 c. M:-0.2244 c. 92: 7 78 7 N M DE I SD: 0.1273 c. M:-0.1559 c. 105: 8 89 8 N M DE I SD: 0.0852 c. M:-0.1043 c. 118: 9 100 9 N M DE I SD: 0.0524 c. M: 0.0641 c. 131: 10 111 10 N M DE I SD: 0.0261 c. M:-0.0319 c. 144: 11 122 11 N M DE I SD: 0.0045 c. M:-0.0055 c. 445: 34 377 34 N M DE I SD: 0.0018 c. M:-0.0022 c. 589: 45 499 45 N M DE I SD: 0.0003 c. M:-0.0003 c. 1322: 101 1120 101 N M DE I SD: 0.0002 c. M:-0.0003 c. 1911: 146 1619 146 N M DE I SD: 0.0001 c. M:-0.0001 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 5 x S SD: 73.6807 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 97.3617 cents 8:9:10:11 H SD: 63.0486 cents 9:10 x 12 S SD: 72.1765 cents 10:11:13 x SD: 63.5426 cents 11:12:14:15 S SD: 42.1564 cents 12:13 x 16 SD: 50.2610 cents 13:14:17 x SD: 45.1782 cents 14:15:18:19 S SD: 30.1554 cents 15:16 x 20 S SD: 36.8403 cents 16:17:21 x SD: 33.8844 cents 17:18:22:23 SD: 22.4447 cents 18:19:23:24 SD: 21.9989 cents 19:20:25 x S SD: 26.4773 cents 20:21:26:27 SD: 17.1608 cents 21:22:27:28 SD: 16.4168 cents 22:23:29 x SD: 21.4899 cents 23:24:30:31 S SD: 13.4156 cents 24:25:31:32 SD: 12.2486 cents 25:26 x 33 SD: 17.2753 cents 26:27:34:35 SD: 10.7429 cents 27:28:35:36 S SD: 9.0396 cents 28:29 x 37 SD: 13.7514 cents 29:30:38:39 SD: 8.8816 cents 30:31:39:40 SD: 6.5295 cents 33:34:43:44 SD: 4.5812 cents 36:37:47:48 SD: 3.1731 cents 39:40:51:52 SD: 2.4283 cents 81:83:106:108 SD: 2.3528 cents 82:84:107:109 SD: 2.1575 cents 85:87:111:113 SD: 1.9732 cents 89:91:116:119 SD: 1.6814 cents 92:94:120:123 SD: 1.5896 cents 93:95:121:124 SD: 1.5051 cents 96:98:125:128 SD: 1.2732 cents 129:132:168:172 SD: 1.0686 cents 132:135:172:176 SD: 0.6491 cents 135:138:176:180 SD: 0.2850 cents 138:141:180:184 SD: 0.2728 cents 273:279:356:364 SD: 0.1972 cents 312:319:407:416 SD: 0.1355 cents 447:457:583:596 SD: 0.0946 cents 450:460:587:600 SD: 0.0427 cents 585:598:763:780 SD: 0.0329 cents