Scala analysis: xen15-chalmers-triadic-reversed-diamond-23-19-tetrachord
Tetrachord 76/69 * 1587/1444 * 76/69 of triadic reversed diamond for M=23/19, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76/69 167.283668 2: 23/19 330.761331 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 76/69 167.2837 1: 76/69 167.2837 2: 1587/1444 163.4777 3: 76/69 167.2837
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1587/1444 163.478 cents 1: 2 76/69 167.284 cents 2: 2 23/19 330.761 cents 2: 1 5776/4761 334.567 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 : 167.3 330.8 498.0 167.3: 163.5 330.8 498.0 330.8: 167.3 334.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 163.4777 .. 167.2837 cents 109744/109503, 3.8060 cents 1587/1444, 163.4777 cents 2: 330.7613 .. 334.5673 cents 109744/109503, 3.8060 cents 1587/1444, 163.4777 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 1587/1444, 163.4777 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 76/69, 167.2837 cents Average / Smallest step : 1.015521 Largest / Average step : 1.007642 Largest / Smallest step : 1.023281 Median interval of one step : 76/69, 167.2837 cents, amount: 2 Most common interval of one step : 76/69, 167.2837 cents, amount: 2 Least squares average step : 165.92438 cents, oct.: 497.77314 cents Scale is strictly proper Scale has Myhill's property chromas: 109744/109503, 3.8060 cents and 173781261/158470336, 159.6717 cents, ratio: 41.952563 generators: 1 of 167.28367 cents and 2 of 330.76133 cents Scale is maximally even in 131-tone equal temperament ET pair of linear temperament : 256&262 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 131-tone equal temperament with octave 4/3 degrees: 44 87 131 generators: 44 and 87 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 163.47766 cents Scale diversity : 1.153823 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.984716 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 : 109744/109503, 3.8060 cents Most common intervals : 76/69, 167.2837 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 Formal octave complements present : 3 = 100.0000% 2/1 octave complements present : 0 = 0.0000% Limited transpositions with margin 3.8060 cents: 1 2 Limited inverse transpositions with margin 3.8060 cents: 1 2 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 1-2 -- Rational properties -- Prime limit : 23 Odd number limit : 4761 (O: 1587 U: 4761) Highest odd numerator or denominator: 69 Scale harmonicity : 0.006367 Average absolute harmonicity : 0.079925 Specific harmonicity : 0.033626 Fundamental : 1/1311, -10.3565 octaves, 0.1996 Hz. Guide tone : 1748, 10.7715 octaves, 457321.488 Hz. Exponens Consonantiae : 2.291628E+06, 21.12794 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 97.0, average 32.33333 Mersenne's string divisions : 6090 Sum of van Prooijen's expressibility: 3.67770, average 1.22590 Sum of Tenney's harmonic distance : 7.43933, average 2.47978 Vogel's harmonic complexity : 44.33333 Wille's k value : 793 Wilson's harmonic complexity : 87 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 19: -1 .. 1 0.00000 2 23: -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 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 28 35| Scale is weakly epimorphic with val: <7 11 28 36| 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 29 34| Scale is weakly epimorphic with val: <7 11 29 36| Scale is weakly epimorphic with val: <7 11 30 31| Scale is JI-epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <7 11 30 34| Scale is weakly epimorphic with val: <7 11 30 35| Scale is weakly epimorphic with val: <7 11 31 32| Scale is JI-epimorphic with val: <7 11 31 33| = patent Scale is weakly epimorphic with val: <7 11 31 35| Scale is weakly epimorphic with val: <7 11 31 36| Scale is weakly epimorphic with val: <7 11 32 33| Scale is JI-epimorphic with val: <7 11 32 34| Scale is weakly epimorphic with val: <7 11 32 36| Scale is weakly epimorphic with val: <7 11 33 34| Scale is JI-epimorphic with val: <7 11 33 35| Scale is weakly epimorphic with val: <7 11 34 35| Scale is JI-epimorphic with val: <7 11 34 36|
FIT/MODE
3: 1 1 1 SP B ME I SD: 1.0359 c. M: 1.2687 c. 68: 23 22 23 SP M ME I SD: 0.9575 c. M: 1.1727 c. 71: 24 23 24 SP M ME I SD: 0.8733 c. M: 1.0696 c. 74: 25 24 25 SP M ME I SD: 0.7959 c. M:-0.9748 c. 77: 26 25 26 SP M ME I SD: 0.7245 c. M: 0.8874 c. 80: 27 26 27 SP M ME I SD: 0.6585 c. M: 0.8065 c. 83: 28 27 28 SP M ME I SD: 0.5973 c. M: 0.7315 c. 86: 29 28 29 SP M ME I SD: 0.5403 c. M: 0.6617 c. 89: 30 29 30 SP M ME I SD: 0.4872 c. M: 0.5967 c. 92: 31 30 31 SP M ME I SD: 0.4375 c. M: 0.5358 c. 95: 32 31 32 SP M ME I SD: 0.3910 c. M: 0.4789 c. 98: 33 32 33 SP M ME I SD: 0.3473 c. M: 0.4254 c. 101: 34 33 34 SP M ME I SD: 0.3062 c. M:-0.3750 c. 104: 35 34 35 SP M ME I SD: 0.2675 c. M: 0.3276 c. 107: 36 35 36 SP M ME I SD: 0.2310 c. M: 0.2829 c. 110: 37 36 37 SP M ME I SD: 0.1964 c. M: 0.2406 c. 113: 38 37 38 SP M ME I SD: 0.1637 c. M: 0.2005 c. 116: 39 38 39 SP M ME I SD: 0.1327 c. M: 0.1625 c. 119: 40 39 40 SP M ME I SD: 0.1032 c. M: 0.1264 c. 122: 41 40 41 SP M ME I SD: 0.0752 c. M: 0.0921 c. 125: 42 41 42 SP M ME I SD: 0.0485 c. M: 0.0595 c. 128: 43 42 43 SP M ME I SD: 0.0231 c. M: 0.0283 c. 131: 44 43 44 SP M ME I SD: 0.0011 c. M: 0.0014 c. 1438: 483 472 483 SP M DE I SD: 0.0010 c. M: 0.0013 c. 1569: 527 515 527 SP M DE I SD: 0.0009 c. M: 0.0010 c. 1700: 571 558 571 SP M DE I SD: 0.0007 c. M:-0.0009 c. 1831: 615 601 615 SP M DE I SD: 0.0006 c. M:-0.0007 c. 1962: 659 644 659 SP M DE I SD: 0.0005 c. M:-0.0006 c. 2093: 703 687 703 SP M DE I SD: 0.0004 c. M:-0.0004 c. 2224: 747 730 747 SP M DE I SD: 0.0003 c. M: 0.0003 c. 2355: 791 773 791 SP M DE I SD: 0.0002 c. M: 0.0002 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: 55.5524 cents 5 x 6:7 S SD: 42.9049 cents 6 x 7:8 S SD: 31.9452 cents 7:8 x 9 S SD: 44.8499 cents 8:9:10:11 H SD: 28.4128 cents 9:10:11:12 H SD: 7.4961 cents 28:31:34:37 SD: 6.2323 cents 29:32:35:39 SD: 5.3512 cents 30:33:36:40 S SD: 5.0970 cents 38:42:46:51 SD: 4.2777 cents 39:43:47:52 SD: 2.6444 cents 48:53:58:64 SD: 1.7655 cents 81:89:98:108 SD: 1.4415 cents 90:99:109:120 SD: 0.8093 cents 99:109:120:132 SD: 0.7939 cents 129:142:156:172 SD: 0.6824 cents 138:152:167:184 SD: 0.1818 cents 285:314:345:380 SD: 0.1598 cents 375:413:454:500 SD: 0.0904 cents 513:565:621:684 SD: 0.0444 cents