Scala analysis: xen15-chalmers-triadic-diamond-17-13-tetrachord
Upper tetrachord 52/51 * 578/507 * 39/34 of triadic 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: 136/117 260.517746 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/34 237.5273 1: 52/51 33.6173 2: 578/507 226.9005 3: 39/34 237.5273
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 52/51 33.617 cents 1: 1 578/507 226.900 cents 1: 1 39/34 237.527 cents 2: 1 136/117 260.518 cents 2: 1 338/289 271.145 cents 2: 1 17/13 464.428 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 : 33.6 260.5 498.0 33.6 : 226.9 464.4 498.0 260.5: 237.5 271.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 237.5273 cents 9/8, 203.9100 cents 52/51, 33.6173 cents 2: 260.5177 .. 464.4277 cents 9/8, 203.9100 cents 4624/4563, 22.9905 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 : 39/34, 237.5273 cents Average / Smallest step : 4.938387 Largest / Average step : 1.430758 Largest / Smallest step : 7.065636 Median interval of one step : 578/507, 226.9005 cents, amount: 1 Least squares average step : 146.34198 cents, oct.: 439.02594 cents Scale is strictly proper Scale has trivalence property Scale is a mode of a 1126-tone equal temperament with octave 4/3 degrees: 76 589 1126 Least number of segments generator : 565 of 249.907 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1107 of 489.641 cents and inv. generated superset size: 32 = 29 more = 1066.667% 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 22.99049 cents Scale diversity : 0.501208 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.181158 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 : 19773/19652, 10.6268 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% Limited inverse transpositions with margin 193.2832 cents: 1 -- Rational properties -- Prime limit : 17 Odd number limit : 507 (O: 289 U: 507) Highest odd numerator or denominator: 117 Scale harmonicity : 0.008859 Average absolute harmonicity : 0.082783 Specific harmonicity : 0.047249 Fundamental : 1/1989, -10.9578 octaves, 0.1315 Hz. Guide tone : 1768, 10.7879 octaves, 462553.999 Hz. Exponens Consonantiae : 3.516552E+06, 21.74573 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 181.5, average 60.50000 Mersenne's string divisions : 182413 Sum of van Prooijen's expressibility: 4.25288, average 1.41763 Sum of Tenney's harmonic distance : 8.70448, average 2.90149 Vogel's harmonic complexity : 34.33333 Wille's k value : 331 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 15.33129, average 2.55522 Lattice compactness (without 2's) : 11.32780, average 1.88797 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 3 2.33333 7 3: -2 ..-1 -1.33333 4 1 13: -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 25 27| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 26 28| Scale is weakly epimorphic with val: <7 10 27 28| Scale is weakly epimorphic with val: <7 10 27 29| Scale is weakly epimorphic with val: <7 10 28 29| Scale is weakly epimorphic with val: <7 10 28 30| Scale is weakly epimorphic with val: <7 10 29 30| Scale is weakly epimorphic with val: <7 10 29 31| Scale is weakly epimorphic with val: <7 10 30 31| Scale is weakly epimorphic with val: <7 10 30 32| Scale is weakly epimorphic with val: <8 11 25 27| Scale is weakly epimorphic with val: <8 11 26 27| Scale is weakly epimorphic with val: <8 11 26 28| Scale is weakly epimorphic with val: <8 11 27 28| Scale is weakly epimorphic with val: <8 11 27 29| Scale is weakly epimorphic with val: <8 11 28 29| Scale is weakly epimorphic with val: <8 11 28 30| Scale is weakly epimorphic with val: <8 11 29 30| Scale is weakly epimorphic with val: <8 11 29 31| Scale is weakly epimorphic with val: <8 11 30 31| Scale is weakly epimorphic with val: <8 11 30 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 57.9105 c. M: 94.5027 c. 4: 0 2 2 P M DE S SD: 20.5123 c. M: 33.6173 c. 6: 0 3 3 P M DE S SD: 20.5123 c. M: 33.6173 c. 9: 1 4 4 SP M DE S SD: 15.6354 c. M:-21.7211 c. 10: 1 4 5 P T3 SD: 11.4625 c. M:-16.1872 c. 11: 1 5 5 SP M DE S SD: 9.3116 c. M:-11.6596 c. 12: 1 5 6 P T3 SD: 8.0486 c. M: 11.4952 c. 13: 1 6 6 SP M DE S SD: 5.1870 c. M:-7.6603 c. 15: 1 7 7 SP M DE S SD: 2.9578 c. M:-5.1063 c. 17: 1 8 8 SP M DE S SD: 3.0881 c. M: 4.3205 c. 27: 2 12 13 SP T3 SD: 2.3013 c. M:-3.2750 c. 29: 2 13 14 SP T3 SD: 1.7313 c. M: 2.9083 c. 42: 3 19 20 SP T3 SD: 1.1494 c. M:-1.9574 c. 44: 3 20 21 SP T3 SD: 0.2212 c. M:-0.3404 c. 134: 9 61 64 SP T3 SD: 0.2212 c. M: 0.3450 c. 149: 10 68 71 SP T3 SD: 0.1614 c. M:-0.2038 c. 178: 12 81 85 SP T3 SD: 0.1767 c. M: 0.3032 c. 193: 13 88 92 SP T3 SD: 0.0789 c. M:-0.1172 c. 237: 16 108 113 SP T3 SD: 0.0364 c. M:-0.0628 c. 281: 19 128 134 SP T3 SD: 0.0368 c. M:-0.0584 c. 518: 35 236 247 SP T3 SD: 0.0316 c. M:-0.0425 c. 608: 41 277 290 SP T3 SD: 0.0242 c. M: 0.0320 c. 652: 44 297 311 SP T3 SD: 0.0218 c. M: 0.0372 c. 845: 57 385 403 SP T3 SD: 0.0124 c. M: 0.0213 c. 889: 60 405 424 SP T3 SD: 0.0064 c. M: 0.0105 c. 1126: 76 513 537 SP T3 SD: 0.0029 c. M:-0.0049 c. 2015: 136 918 961 SP T3 SD: 0.0017 c. M: 0.0023 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: 50.4314 cents 6 x 7:8 S SD: 3.1766 cents 7 x 8:9 S SD: 34.7316 cents 8 x 9:11 SD: 38.8666 cents 9 x 10:12 S SD: 39.0570 cents 10 x 12:13 S SD: 35.2128 cents 11 x 13:15 SD: 24.1707 cents 18:19:21:24 SD: 20.1071 cents 19:20:22:25 SD: 20.0446 cents 20:21:23:27 SD: 19.4154 cents 21:22:24:28 S SD: 18.4467 cents 23:24:27:31 SD: 15.8003 cents 24:25:28:32 SD: 12.5320 cents 27:28:31:36 SD: 12.0957 cents 29:30:34:39 SD: 10.9056 cents 30:31:35:40 SD: 8.0019 cents 35:36:41:47 SD: 7.8962 cents 36:37:42:48 SD: 5.0691 cents 42:43:49:56 SD: 3.1807 cents 48:49:56:64 S SD: 2.2283 cents 54:55:63:72 SD: 2.2057 cents 87:89:101:116 SD: 2.0457 cents 92:94:107:123 SD: 2.0022 cents 93:95:108:124 SD: 1.2047 cents 99:101:115:132 SD: 0.5118 cents 105:107:122:140 SD: 0.3993 cents 204:208:237:272 SD: 0.3121 cents 252:257:293:336 SD: 0.2010 cents 351:358:408:468 SD: 0.1897 cents 357:364:415:476 SD: 0.0357 cents