Scala analysis: xen15-chalmers-triadic-reversed-diamond-40-33-tetrachord
Tetrachord 11/10 * 400/363 * 11/10 of triadic reversed diamond for M=40/33, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 40/33 333.040771 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 11/10 165.0042 Ptolemy's second, 4/5-tone 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 400/363 168.0365 3: 11/10 165.0042 Ptolemy's second, 4/5-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 400/363 168.037 cents 2: 1 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 2: 2 40/33 333.041 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 : 165.0 333.0 498.0 165.0: 168.0 333.0 498.0 333.0: 165.0 330.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 168.0365 cents 4000/3993, 3.0323 cents 11/10, 165.0042 cents 2: 330.0085 .. 333.0408 cents 4000/3993, 3.0323 cents 43923/40000, 161.9719 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 400/363, 168.0365 cents Average / Smallest step : 1.006126 Largest / Average step : 1.012177 Largest / Smallest step : 1.018377 Median interval of one step : 11/10, 165.0042 cents, amount: 2 Most common interval of one step : 11/10, 165.0042 cents, amount: 2 Least squares average step : 166.08720 cents, oct.: 498.26159 cents Scale is strictly proper Scale has Myhill's property chromas: 4000/3993, 3.0323 cents and 43923/40000, 161.9719 cents, ratio: 53.415291 generators: 1 of 165.00423 cents and 2 of 333.04077 cents ET pair of linear temperament : 326&658 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 329-tone equal temperament with octave 4/3 degrees: 109 220 329 generators: 109 and 220 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 161.97191 cents Scale diversity : 1.158885 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.987823 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 : 4000/3993, 3.0323 cents Most common intervals : 11/10, 165.0042 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle 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 Limited transpositions with margin 3.0323 cents: 1 2 Limited inverse transpositions with margin 3.0323 cents: 1 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 11 Odd number limit : 363 (O: 121 U: 363) Highest odd numerator or denominator: 33 Scale harmonicity : 0.017911 Average absolute harmonicity : 0.095478 Specific harmonicity : 0.092938 Fundamental : 1/330, -8.3663 octaves, 0.7928 Hz. Guide tone : 440, 8.7814 octaves, 115115.249 Hz. Exponens Consonantiae : 1.452000E+05, 17.14768 octaves Euler's gradus suavitatis : 35 Sum of Mann's harmonic distance : 50.5, average 16.83333 Mersenne's string divisions : 1533 Sum of van Prooijen's expressibility: 3.03703, average 1.01234 Sum of Tenney's harmonic distance : 6.24115, average 2.08038 Vogel's harmonic complexity : 19.33333 Wille's k value : 181 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 17.62837, average 2.93806 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -1 .. 0 -0.66667 2 1 5: -1 .. 1 0.00000 2 11: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 15 23| Scale is weakly epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 15 26| Scale is weakly epimorphic with val: <7 11 15 27| Scale is JI-epimorphic with val: <7 11 16 24| Scale is weakly epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 16 27| Scale is weakly epimorphic with val: <7 11 17 23| Scale is JI-epimorphic with val: <7 11 17 25| = patent Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 24| Scale is JI-epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 25| Scale is JI-epimorphic with val: <7 11 19 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 0.8253 c. M: 1.0108 c. 85: 28 29 28 SP M ME I SD: 0.7694 c. M: 0.9423 c. 88: 29 30 29 SP M ME I SD: 0.7151 c. M: 0.8758 c. 91: 30 31 30 SP M ME I SD: 0.6643 c. M: 0.8136 c. 94: 31 32 31 SP M ME I SD: 0.6167 c. M: 0.7553 c. 97: 32 33 32 SP M ME I SD: 0.5721 c. M: 0.7007 c. 100: 33 34 33 SP M ME I SD: 0.5302 c. M: 0.6494 c. 103: 34 35 34 SP M ME I SD: 0.4907 c. M: 0.6010 c. 106: 35 36 35 SP M ME I SD: 0.4535 c. M: 0.5554 c. 109: 36 37 36 SP M ME I SD: 0.4183 c. M: 0.5123 c. 112: 37 38 37 SP M ME I SD: 0.3850 c. M: 0.4715 c. 115: 38 39 38 SP M ME I SD: 0.3534 c. M: 0.4328 c. 118: 39 40 39 SP M ME I SD: 0.3234 c. M: 0.3961 c. 121: 40 41 40 SP M ME I SD: 0.2950 c. M: 0.3613 c. 124: 41 42 41 SP M ME I SD: 0.2679 c. M: 0.3281 c. 127: 42 43 42 SP M ME I SD: 0.2420 c. M: 0.2964 c. 130: 43 44 43 SP M ME I SD: 0.2174 c. M: 0.2663 c. 133: 44 45 44 SP M ME I SD: 0.1939 c. M: 0.2375 c. 136: 45 46 45 SP M ME I SD: 0.1714 c. M: 0.2099 c. 139: 46 47 46 SP M ME I SD: 0.1499 c. M: 0.1836 c. 142: 47 48 47 SP M ME I SD: 0.1293 c. M: 0.1583 c. 145: 48 49 48 SP M ME I SD: 0.1095 c. M: 0.1342 c. 148: 49 50 49 SP M ME I SD: 0.0906 c. M: 0.1110 c. 151: 50 51 50 SP M ME I SD: 0.0724 c. M: 0.0887 c. 154: 51 52 51 SP M ME I SD: 0.0549 c. M: 0.0672 c. 157: 52 53 52 SP M ME I SD: 0.0381 c. M: 0.0466 c. 160: 53 54 53 SP M ME I SD: 0.0219 c. M: 0.0268 c. 163: 54 55 54 SP M ME I SD: 0.0063 c. M: 0.0077 c. 329: 109 111 109 SP M DE I SD: 0.0013 c. M: 0.0016 c. 492: 163 166 163 SP M DE I SD: 0.0012 c. M: 0.0015 c. 821: 272 277 272 SP M DE I SD: 0.0002 c. M: 0.0003 c. 1150: 381 388 381 SP M DE I SD: 0.0002 c. M: 0.0002 c. 1971: 653 665 653 SP M DE I SD: 0.0000 c. M: 0.0000 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: 53.2729 cents 5 x 6:7 S SD: 43.1203 cents 6 x 7:8 S SD: 33.0849 cents 7:8 x 9 S SD: 45.6687 cents 8:9:10:11 H SD: 28.2640 cents 9:10:11:12 H SD: 7.5215 cents 28:31:34:37 SD: 6.4652 cents 29:32:35:39 SD: 5.8321 cents 30:33:36:40 S SD: 5.7998 cents 33:36:40:44 S SD: 4.7891 cents 38:42:46:51 SD: 4.7418 cents 39:43:47:52 SD: 3.5991 cents 42:46:51:56 SD: 2.7070 cents 51:56:62:68 SD: 1.9830 cents 80:88:97:107 SD: 1.8096 cents 81:89:98:108 SD: 1.2506 cents 90:99:109:120 SD: 0.4811 cents 189:208:229:252 SD: 0.3598 cents 231:254:280:308 SD: 0.2272 cents 240:264:291:320 SD: 0.1803 cents 330:363:400:440 SD: 0.0000 cents