Scala analysis: xen15-chalmers-triadic-reversed-diamond-33-28-tetrachord
Tetrachord 112/99 * 3267/3136 * 112/99 of triadic reversed diamond for M=33/28, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 112/99 213.597962 2: 33/28 284.447037 undecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 112/99 213.5980 1: 112/99 213.5980 2: 3267/3136 70.8491 3: 112/99 213.5980
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 3267/3136 70.849 cents 1: 2 112/99 213.598 cents 2: 2 33/28 284.447 cents undecimal minor third 2: 1 12544/9801 427.196 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 : 213.6 284.4 498.0 213.6: 70.8 284.4 498.0 284.4: 213.6 427.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.8491 .. 213.5980 cents 351232/323433, 142.7489 cents 3267/3136, 70.8491 cents 2: 284.4470 .. 427.1959 cents 351232/323433, 142.7489 cents 3267/3136, 70.8491 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 3267/3136, 70.8491 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 112/99, 213.5980 cents Average / Smallest step : 2.343220 Largest / Average step : 1.286618 Largest / Smallest step : 3.014831 Median interval of one step : 112/99, 213.5980 cents, amount: 2 Most common interval of one step : 112/99, 213.5980 cents, amount: 2 Least squares average step : 162.61622 cents, oct.: 487.84865 cents Scale is strictly proper Scale has Myhill's property chromas: 351232/323433, 142.7489 cents and 1101463552/1056655611, 71.8998 cents, ratio: 1.985386 generators: 1 of 213.59796 cents and 2 of 284.44704 cents ET pair of linear temperament : 942&1898 Scale is distributional even Scale is a mode of a 457-tone equal temperament with octave 4/3 degrees: 196 261 457 generators: 196 and 261 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Scale is a Constant Structure, by a margin of 70.84907 cents Scale diversity : 0.832308 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.426763 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 : 3267/3136, 70.8491 cents Most common intervals : 112/99, 213.5980 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 11 Odd number limit : 9801 (O: 3267 U: 9801) Highest odd numerator or denominator: 99 Scale harmonicity : 0.014097 Average absolute harmonicity : 0.090306 Specific harmonicity : 0.073572 Fundamental : 1/2772, -11.4367 octaves, 0.0944 Hz. Guide tone : 3696, 11.8517 octaves, 966968.089 Hz. Exponens Consonantiae : 1.024531E+07, 23.28846 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 139.5, average 46.50000 Mersenne's string divisions : 90097 Sum of van Prooijen's expressibility: 3.99127, average 1.33042 Sum of Tenney's harmonic distance : 8.08971, average 2.69657 Vogel's harmonic complexity : 25.33333 Wille's k value : 1633 Wilson's harmonic complexity : 45 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 24.18851, average 4.03142 Lattice compactness (without 2's) : 13.48619, average 2.24770 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 4 1.33333 8 3: -2 .. 1 -0.66667 4 1 7: -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: 8 / 3 = 2.66667 Scale is JI-epimorphic with val: <7 11 18 23| Scale is weakly epimorphic with val: <7 11 18 25| Scale is weakly epimorphic with val: <7 11 18 26| Scale is weakly epimorphic with val: <7 11 19 23| Scale is JI-epimorphic with val: <7 11 19 24| Scale is weakly epimorphic with val: <7 11 19 26| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 20 24| Scale is JI-epimorphic with val: <7 11 20 25| = patent Scale is weakly epimorphic with val: <7 11 20 27| Scale is weakly epimorphic with val: <7 11 21 23| Scale is weakly epimorphic with val: <7 11 21 25| Scale is JI-epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 22 23| Scale is weakly epimorphic with val: <7 11 22 24| Scale is weakly epimorphic with val: <7 11 22 26| Scale is JI-epimorphic with val: <7 11 22 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 38.8513 c. M: 47.5830 c. 4: 2 0 2 P M DE I SD: 28.9240 c. M: 35.4245 c. 5: 2 1 2 SP M ME I SD: 11.7412 c. M: 14.3800 c. 7: 3 1 3 SP M DE I SD: 0.1226 c. M: 0.1501 c. 240: 103 34 103 SP M DE I SD: 0.1195 c. M: 0.1463 c. 247: 106 35 106 SP M DE I SD: 0.1126 c. M: 0.1379 c. 254: 109 36 109 SP M DE I SD: 0.1062 c. M: 0.1300 c. 261: 112 37 112 SP M DE I SD: 0.1000 c. M: 0.1225 c. 268: 115 38 115 SP M DE I SD: 0.0942 c. M: 0.1154 c. 275: 118 39 118 SP M DE I SD: 0.0887 c. M: 0.1086 c. 282: 121 40 121 SP M DE I SD: 0.0834 c. M: 0.1022 c. 289: 124 41 124 SP M DE I SD: 0.0785 c. M: 0.0961 c. 296: 127 42 127 SP M DE I SD: 0.0737 c. M: 0.0903 c. 303: 130 43 130 SP M DE I SD: 0.0692 c. M: 0.0847 c. 310: 133 44 133 SP M DE I SD: 0.0648 c. M: 0.0794 c. 317: 136 45 136 SP M DE I SD: 0.0607 c. M: 0.0743 c. 324: 139 46 139 SP M DE I SD: 0.0567 c. M: 0.0695 c. 331: 142 47 142 SP M DE I SD: 0.0529 c. M: 0.0648 c. 338: 145 48 145 SP M DE I SD: 0.0493 c. M: 0.0604 c. 345: 148 49 148 SP M DE I SD: 0.0458 c. M: 0.0561 c. 352: 151 50 151 SP M DE I SD: 0.0425 c. M: 0.0520 c. 359: 154 51 154 SP M DE I SD: 0.0393 c. M: 0.0481 c. 366: 157 52 157 SP M DE I SD: 0.0362 c. M: 0.0443 c. 373: 160 53 160 SP M DE I SD: 0.0332 c. M: 0.0406 c. 380: 163 54 163 SP M DE I SD: 0.0303 c. M: 0.0371 c. 387: 166 55 166 SP M DE I SD: 0.0276 c. M: 0.0337 c. 394: 169 56 169 SP M DE I SD: 0.0249 c. M: 0.0305 c. 401: 172 57 172 SP M DE I SD: 0.0223 c. M: 0.0273 c. 408: 175 58 175 SP M DE I SD: 0.0198 c. M: 0.0243 c. 415: 178 59 178 SP M DE I SD: 0.0174 c. M: 0.0213 c. 422: 181 60 181 SP M DE I SD: 0.0151 c. M: 0.0185 c. 429: 184 61 184 SP M DE I SD: 0.0129 c. M: 0.0157 c. 436: 187 62 187 SP M DE I SD: 0.0107 c. M: 0.0131 c. 443: 190 63 190 SP M DE I SD: 0.0086 c. M: 0.0105 c. 450: 193 64 193 SP M DE I SD: 0.0065 c. M: 0.0080 c. 457: 196 65 196 SP M DE I SD: 0.0046 c. M: 0.0056 c. 464: 199 66 199 SP M DE I SD: 0.0026 c. M: 0.0032 c. 471: 202 67 202 SP M DE I SD: 0.0008 c. M: 0.0010 c. 949: 407 135 407 SP M DE I SD: 0.0001 c. M: 0.0002 c. 2369: 1016 337 1016 SP 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: 101.8667 cents 5 x 6:7 S SD: 45.0216 cents 6 x 7:8 S SD: 8.7881 cents 7:8 x 9 S SD: 32.6841 cents 8:9 x 11 SD: 27.0733 cents 9:10:11:12 H SD: 23.4216 cents 12 x 14:16 S SD: 8.7881 cents 13:15 x 17 SD: 23.9576 cents 14:16:17:19 SD: 20.8671 cents 15:17:18:20 SD: 10.4489 cents 19 x 22:25 SD: 19.1360 cents 20:23:24:27 SD: 15.7764 cents 21:24:25:28 SD: 8.2439 cents 22:25:26:29 SD: 7.2543 cents 23:26:27:31 SD: 6.6593 cents 30:34:35:40 SD: 5.9485 cents 33:37:39:44 SD: 5.4136 cents 38:43:45:51 SD: 4.6825 cents 39:44:46:52 SD: 1.6496 cents 45:51:53:60 SD: 1.1005 cents 84:95:99:112 SD: 0.1840 cents 213:241:251:284 SD: 0.1096 cents 297:336:350:396 SD: 0.0589 cents