Scala analysis: xen15-chalmers-triadic-reversed-diamond-13-11-tetrachord
Tetrachord 44/39 * 507/484 * 44/39 of triadic reversed diamond for M=13/11, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 44/39 208.835280 2: 13/11 289.209719 tridecimal minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 44/39 208.8353 1: 44/39 208.8353 2: 507/484 80.3744 3: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 507/484 80.374 cents 1: 2 44/39 208.835 cents 2: 2 13/11 289.210 cents tridecimal minor third 2: 1 1936/1521 417.671 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 : 208.8 289.2 498.0 208.8: 80.4 289.2 498.0 289.2: 208.8 417.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.3744 .. 208.8353 cents 21296/19773, 128.4608 cents 507/484, 80.3744 cents 2: 289.2097 .. 417.6706 cents 21296/19773, 128.4608 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 507/484, 80.3744 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 2.065520 Largest / Average step : 1.257930 Largest / Smallest step : 2.598280 Median interval of one step : 44/39, 208.8353 cents, amount: 2 Most common interval of one step : 44/39, 208.8353 cents, amount: 2 Least squares average step : 162.95641 cents, oct.: 488.86922 cents Scale is strictly proper Scale has Myhill's property chromas: 21296/19773, 128.4608 cents and 10307264/10024911, 48.0864 cents, ratio: 2.671459 generators: 1 of 208.83528 cents and 2 of 289.20972 cents ET pair of linear temperament : 24&62 Scale is distributional even Scale is a mode of a 570-tone equal temperament with octave 4/3 degrees: 239 331 570 generators: 239 and 331 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 80.37444 cents Scale diversity : 0.918477 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.484140 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 : 507/484, 80.3744 cents Most common intervals : 44/39, 208.8353 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle Best minor 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 : 13 Odd number limit : 1521 (O: 507 U: 1521) Highest odd numerator or denominator: 39 Scale harmonicity : 0.011718 Average absolute harmonicity : 0.087099 Specific harmonicity : 0.061377 Fundamental : 1/429, -8.7448 octaves, 0.6098 Hz. Guide tone : 572, 9.1599 octaves, 149649.823 Hz. Exponens Consonantiae : 2.453880E+05, 17.90471 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 57.0, average 19.00000 Mersenne's string divisions : 13944 Sum of van Prooijen's expressibility: 3.18213, average 1.06071 Sum of Tenney's harmonic distance : 6.46903, average 2.15634 Vogel's harmonic complexity : 26.33333 Wille's k value : 253 Wilson's harmonic complexity : 51 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 11: -1 .. 1 0.00000 2 13: -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 23 25| Scale is weakly epimorphic with val: <7 11 23 27| Scale is weakly epimorphic with val: <7 11 23 28| Scale is weakly epimorphic with val: <7 11 23 30| Scale is weakly epimorphic with val: <7 11 24 25| Scale is JI-epimorphic with val: <7 11 24 26| Scale is weakly epimorphic with val: <7 11 24 28| Scale is weakly epimorphic with val: <7 11 24 29| Scale is weakly epimorphic with val: <7 11 25 26| Scale is JI-epimorphic with val: <7 11 25 27| = patent 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 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 27 28| Scale is JI-epimorphic with val: <7 11 27 29|
FIT/MODE
3: 1 1 1 SP B ME I SD: 34.9626 c. M: 42.8203 c. 4: 2 0 2 P M DE I SD: 32.8127 c. M: 40.1872 c. 5: 2 1 2 SP M ME I SD: 7.8525 c. M: 9.6173 c. 7: 3 1 3 SP M DE I SD: 3.7662 c. M: 4.6126 c. 12: 5 2 5 SP M DE I SD: 1.0749 c. M: 1.3165 c. Raga Sarvasri, Warao tritonic: South America 19: 8 3 8 SP M DE I SD: 0.7086 c. M: 0.8679 c. 31: 13 5 13 SP M DE I SD: 0.0182 c. M: 0.0223 c. 384: 161 62 161 SP M DE I SD: 0.0160 c. M: 0.0195 c. 415: 174 67 174 SP M DE I SD: 0.0134 c. M: 0.0164 c. 446: 187 72 187 SP M DE I SD: 0.0112 c. M: 0.0137 c. 477: 200 77 200 SP M DE I SD: 0.0093 c. M: 0.0114 c. 508: 213 82 213 SP M DE I SD: 0.0076 c. M: 0.0093 c. 539: 226 87 226 SP M DE I SD: 0.0061 c. M: 0.0075 c. 570: 239 92 239 SP M DE I SD: 0.0048 c. M: 0.0059 c. 601: 252 97 252 SP M DE I SD: 0.0036 c. M: 0.0044 c. 632: 265 102 265 SP M DE I SD: 0.0025 c. M: 0.0031 c. 663: 278 107 278 SP M DE I SD: 0.0016 c. M: 0.0019 c. 694: 291 112 291 SP M DE I SD: 0.0007 c. M: 0.0008 c. 725: 304 117 304 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: 97.1040 cents 5 x 6:7 S SD: 44.2531 cents 6 x 7:8 S SD: 11.1694 cents 7:8 x 9 S SD: 33.4032 cents 8:9 x 11 SD: 26.7501 cents 9:10:11:12 H SD: 21.3064 cents 12 x 14:16 S SD: 11.1694 cents 13:15 x 17 SD: 25.7088 cents 14:16:17:19 SD: 20.1092 cents 15:17:18:20 SD: 9.1910 cents 21:24:25:28 SD: 8.5551 cents 22:25:26:29 SD: 7.7966 cents 23:26:27:31 SD: 7.4310 cents 31:35:37:41 SD: 7.3823 cents 32:36:38:43 SD: 5.5249 cents 33:37:39:44 SD: 3.5881 cents 39:44:46:52 SD: 1.1393 cents 93:105:110:124 SD: 0.6376 cents 132:149:156:176 SD: 0.2980 cents 258:291:305:344 SD: 0.2299 cents 297:335:351:396 SD: 0.1325 cents 390:440:461:520 SD: 0.1138 cents 429:484:507:572 SD: 0.0000 cents