Scala analysis: xen15-chalmers-triadic-reversed-diamond-17-13-tetrachord
Tetrachord 52/51 * 867/676 * 52/51 of triadic reversed diamond for M=17/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 52/51 33.617251 2: 17/13 464.427748 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 52/51 33.6173 1: 52/51 33.6173 2: 867/676 430.8105 3: 52/51 33.6173
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 52/51 33.617 cents 1: 1 867/676 430.810 cents 2: 1 2704/2601 67.235 cents 2: 2 17/13 464.428 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 : 33.6 464.4 498.0 33.6 : 430.8 464.4 498.0 464.4: 33.6 67.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 430.8105 cents 44217/35152, 397.1932 cents 52/51, 33.6173 cents 2: 67.2345 .. 464.4277 cents 44217/35152, 397.1932 cents 1827904/2255067,-363.5760 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 867/676, 430.8105 cents Average / Smallest step : 4.938387 Largest / Average step : 2.595009 Largest / Smallest step : 12.815161 Median interval of one step : 52/51, 33.6173 cents, amount: 2 Most common interval of one step : 52/51, 33.6173 cents, amount: 2 Least squares average step : 175.47198 cents, oct.: 526.41595 cents Scale is not proper Scale has Myhill's property chromas: 44217/35152, 397.1932 cents and 2255067/1827904, 363.5760 cents, ratio: 1.092463 generators: 1 of 33.61725 cents and 2 of 464.42775 cents ET pair of linear temperament : 28&30 Scale is distributional even Scale is a mode of a 400-tone equal temperament with octave 4/3 degrees: 27 373 400 generators: 27 and 373 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 33.61725 cents Scale diversity : 0.186935 Lumma stability : 0.134997 Lumma impropriety factor : 0.730006 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 : 52/51, 33.6173 cents Most common intervals : 52/51, 33.6173 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 : 17 Odd number limit : 2601 (O: 867 U: 2601) Highest odd numerator or denominator: 51 Scale harmonicity : 0.009157 Average absolute harmonicity : 0.083659 Specific harmonicity : 0.048149 Fundamental : 1/663, -9.3729 octaves, 0.3946 Hz. Guide tone : 884, 9.7879 octaves, 231277.000 Hz. Exponens Consonantiae : 5.860920E+05, 19.16077 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 70.0, average 23.33333 Mersenne's string divisions : 21630 Sum of van Prooijen's expressibility: 3.41514, average 1.13838 Sum of Tenney's harmonic distance : 6.84715, average 2.28238 Vogel's harmonic complexity : 32.33333 Wille's k value : 433 Wilson's harmonic complexity : 63 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 13.96155, average 2.32692 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 13: -1 .. 1 0.00000 2 17: -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 25 27| Scale is weakly epimorphic with val: <7 11 25 29| Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 25 32| Scale is weakly epimorphic with val: <7 11 25 33| Scale is weakly epimorphic with val: <7 11 26 27| Scale is JI-epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 30| Scale is weakly epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 33| Scale is weakly epimorphic with val: <7 11 27 28| Scale is JI-epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 31| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 28 29| Scale is JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 32| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 29 30| Scale is JI-epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 11 29 33| Scale is weakly epimorphic with val: <7 11 30 31| Scale is JI-epimorphic with val: <7 11 30 32|
FIT/MODE
3: 0 3 0 N M DE I SD: 27.4484 c. M:-33.6173 c. 4: 0 4 0 N M DE I SD: 27.4484 c. M:-33.6173 c. 5: 0 5 0 N M DE I SD: 27.4484 c. M: 33.6173 c. 7: 0 6 1 N G T3 SD: 29.0905 c. M: 37.5320 c. 8: 0 7 1 N G T3 SD: 25.4969 c. M: 33.6173 c. 9: 0 8 1 N G T3 SD: 23.1079 c. M: 33.6173 c. 10: 1 8 1 N M DE I SD: 13.2168 c. M: 16.1872 c. 11: 1 9 1 N M DE I SD: 9.5200 c. M:-11.6596 c. 12: 1 10 1 N M DE I SD: 6.4393 c. M:-7.8865 c. 13: 1 11 1 N M DE I SD: 3.8326 c. M: 4.6939 c. 14: 1 12 1 N M DE I SD: 1.5982 c. M:-1.9574 c. 15: 1 13 1 N M DE I SD: 0.3382 c. M:-0.4143 c. 44: 3 38 3 N M DE I SD: 0.2779 c. M:-0.3404 c. 59: 4 51 4 N M DE I SD: 0.1213 c. M:-0.1485 c. 74: 5 64 5 N M DE I SD: 0.0281 c. M:-0.0344 c. 163: 11 141 11 N M DE I SD: 0.0056 c. M:-0.0069 c. 237: 16 205 16 N M DE I SD: 0.0049 c. M:-0.0060 c. 400: 27 346 27 N M DE I SD: 0.0006 c. M:-0.0008 c. 963: 65 833 65 N M DE I SD: 0.0004 c. M:-0.0005 c. 1363: 92 1179 92 N M DE I SD: 0.0001 c. M:-0.0001 c. 1763: 119 1525 119 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: 78.1140 cents 5 x x 7 SD: 84.4672 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 99.8621 cents 8:9:10:11 H SD: 64.9268 cents 9:10 x 12 S SD: 74.3932 cents 10:11:13 x SD: 65.8917 cents 11:12:14:15 S SD: 43.9808 cents 12:13 x 16 SD: 52.4777 cents 13:14:17 x SD: 47.3405 cents 14:15:18:19 S SD: 31.9131 cents 15:16 x 20 S SD: 39.0570 cents 16:17:21 x SD: 35.8102 cents 17:18:22:23 SD: 24.1157 cents 18:19 x 24 SD: 29.9929 cents 19:20:25 x S SD: 28.1043 cents 20:21:26:27 SD: 18.7159 cents 21:22:27:28 SD: 18.4467 cents 22:23:29 x SD: 22.7464 cents 23:24:30:31 S SD: 14.8138 cents 24:25:31:32 SD: 14.2548 cents 25:26:33 x SD: 18.9627 cents 26:27:34:35 SD: 11.9286 cents 27:28:35:36 S SD: 11.0084 cents 28:29 x 37 SD: 15.6312 cents 29:30:38:39 SD: 9.7858 cents 30:31:39:40 SD: 8.4342 cents 31:32 x 41 SD: 12.7692 cents 32:33:42:43 SD: 8.2207 cents 33:34:43:44 SD: 6.3647 cents 36:37:47:48 SD: 4.7013 cents 39:40:51:52 SD: 3.4046 cents 42:43:55:56 SD: 2.5069 cents 45:46:59:60 SD: 2.1105 cents 91:93:119:121 SD: 2.0774 cents 94:96:123:125 SD: 1.8392 cents 97:99:127:129 SD: 1.7418 cents 98:100:128:131 SD: 1.6874 cents 101:103:132:135 SD: 1.4698 cents 104:106:136:139 SD: 1.4019 cents 105:107:137:140 SD: 1.3329 cents 108:110:141:144 SD: 1.1274 cents 111:113:145:148 SD: 1.0888 cents 147:150:192:196 SD: 0.8280 cents 150:153:196:200 SD: 0.5042 cents 153:156:200:204 SD: 0.2219 cents 156:159:204:208 SD: 0.2135 cents 309:315:404:412 SD: 0.1539 cents 354:361:463:472 SD: 0.1343 cents 507:517:663:676 SD: 0.0657 cents