Scala analysis: xen15-chalmers-triadic-reversed-diamond-39-34-tetrachord
Tetrachord 39/34 * 4624/4563 * 39/34 of triadic reversed diamond for M=39/34, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/34 237.527253 2: 136/117 260.517746 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 39/34 237.5273 1: 39/34 237.5273 2: 4624/4563 22.9905 3: 39/34 237.5273
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 4624/4563 22.990 cents 1: 2 39/34 237.527 cents 2: 2 136/117 260.518 cents 2: 1 1521/1156 475.055 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 : 237.5 260.5 498.0 237.5: 23.0 260.5 498.0 260.5: 237.5 475.1 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.9905 .. 237.5273 cents 177957/157216, 214.5368 cents 4624/4563, 22.9905 cents 2: 260.5177 .. 475.0545 cents 177957/157216, 214.5368 cents 4624/4563, 22.9905 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 4624/4563, 22.9905 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 39/34, 237.5273 cents Average / Smallest step : 7.221028 Largest / Average step : 1.430758 Largest / Smallest step : 10.331542 Median interval of one step : 39/34, 237.5273 cents, amount: 2 Most common interval of one step : 39/34, 237.5273 cents, amount: 2 Least squares average step : 160.90698 cents, oct.: 482.72094 cents Scale is strictly proper Scale has Myhill's property chromas: 177957/157216, 214.5368 cents and 812017791/726966784, 191.5463 cents, ratio: 1.120026 generators: 1 of 237.52725 cents and 2 of 260.51775 cents ET pair of linear temperament : 42&130 Scale is distributional even Scale is a mode of a 65-tone equal temperament with octave 4/3 degrees: 31 34 65 generators: 31 and 34 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : LSL Interval vector is [ 0 0 1 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 2 0 ] Scale is a Constant Structure, by a margin of 22.99049 cents Scale diversity : 0.370428 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.138484 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 : 4624/4563, 22.9905 cents Most common intervals : 39/34, 237.5273 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 17 Odd number limit : 4563 (O: 1521 U: 4563) Highest odd numerator or denominator: 117 Scale harmonicity : 0.008581 Average absolute harmonicity : 0.082887 Specific harmonicity : 0.045160 Fundamental : 1/3978, -11.9578 octaves, 0.0658 Hz. Guide tone : 5304, 12.3729 octaves, 1387661.998 Hz. Exponens Consonantiae : 2.109931E+07, 24.33069 octaves Euler's gradus suavitatis : 67 Sum of Mann's harmonic distance : 166.5, average 55.50000 Mersenne's string divisions : 129283 Sum of van Prooijen's expressibility: 4.13637, average 1.37879 Sum of Tenney's harmonic distance : 8.40345, average 2.80115 Vogel's harmonic complexity : 36.33333 Wille's k value : 2281 Wilson's harmonic complexity : 69 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.72660, average 3.28777 Lattice compactness (without 2's) : 13.48619, average 2.24770 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -2 .. 1 -0.66667 4 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: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <7 11 25 27| Scale is JI-epimorphic with val: <7 11 25 28| Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 25 31| Scale is weakly epimorphic with val: <7 11 25 33| Scale is weakly epimorphic with val: <7 11 26 28| Scale is JI-epimorphic with val: <7 11 26 29| Scale is weakly epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 32| Scale is weakly epimorphic with val: <7 11 27 27| Scale is weakly epimorphic with val: <7 11 27 29| Scale is JI-epimorphic with val: <7 11 27 30| = patent Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 27 33| Scale is weakly epimorphic with val: <7 11 28 28| Scale is weakly epimorphic with val: <7 11 28 30| Scale is JI-epimorphic with val: <7 11 28 31| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 29 29| Scale is weakly epimorphic with val: <7 11 29 31| Scale is JI-epimorphic with val: <7 11 29 32| Scale is weakly epimorphic with val: <7 11 30 30| Scale is weakly epimorphic with val: <7 11 30 32| Scale is JI-epimorphic with val: <7 11 30 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 58.3895 c. M: 71.5123 c. 4: 2 0 2 P M DE I SD: 9.3858 c. M: 11.4952 c. 6: 3 0 3 P M DE I SD: 9.3858 c. M:-11.4952 c. 10: 5 0 5 P M DE I SD: 9.3858 c. M: 11.4952 c. 11: 5 1 5 SP M DE I SD: 9.0984 c. M: 11.1432 c. 13: 6 1 6 SP M DE I SD: 6.2546 c. M: 7.6603 c. 15: 7 1 7 SP M DE I SD: 4.1692 c. M: 5.1063 c. 17: 8 1 8 SP M DE I SD: 2.5745 c. M: 3.1531 c. 19: 9 1 9 SP M DE I SD: 1.3155 c. M: 1.6112 c. 21: 10 1 10 SP M DE I SD: 0.2964 c. M: 0.3630 c. 44: 21 2 21 SP M DE I SD: 0.1437 c. M: 0.1760 c. 65: 31 3 31 SP M DE I SD: 0.0016 c. M: 0.0019 c. 2036: 971 94 971 SP M DE I SD: 0.0015 c. M: 0.0019 c. 2101: 1002 97 1002 SP M DE I SD: 0.0014 c. M: 0.0017 c. 2166: 1033 100 1033 SP M DE I SD: 0.0013 c. M: 0.0016 c. 2231: 1064 103 1064 SP M DE I SD: 0.0013 c. M: 0.0015 c. 2296: 1095 106 1095 SP M DE I SD: 0.0012 c. M: 0.0014 c. 2361: 1126 109 1126 SP M DE I SD: 0.0011 c. M: 0.0013 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 7:8 x 9 S SD: 31.6403 cents 8:9 x 11 SD: 31.4965 cents 9:10 x 12 S SD: 27.5618 cents 11 x 13:15 SD: 24.1707 cents 12 x 14:16 S SD: 3.1766 cents 13:15 x 17 SD: 17.5673 cents 14:16 x 19 SD: 15.6469 cents 15:17 x 20 SD: 10.4203 cents 17 x 20:23 SD: 16.3791 cents 18 x 21:24 S SD: 3.1766 cents 19 x 22:25 SD: 11.9465 cents 20:23 x 27 SD: 10.9792 cents 21:24 x 28 S SD: 3.1766 cents 24 x 28:32 S SD: 3.1766 cents 25 x 29:33 SD: 8.8808 cents 26:30 x 35 SD: 9.7312 cents 27:31 x 36 SD: 0.8217 cents 31 x 36:41 SD: 7.0571 cents 32 x 37:43 SD: 8.1497 cents 33:38 x 44 SD: 3.3564 cents 38 x 44:51 SD: 6.5943 cents 39:45 x 52 SD: 5.1069 cents 40:46 x 53 SD: 5.8623 cents 41:47:48:55 SD: 5.4270 cents 42:48:49:56 S SD: 2.9949 cents 45 x 52:60 SD: 5.1069 cents 46:53 x 61 SD: 6.0899 cents 47:54:55:63 SD: 5.0232 cents 48:55:56:64 SD: 2.2057 cents 51 x 59:68 SD: 4.1282 cents 52:60 x 69 SD: 6.5942 cents 53:61:62:71 SD: 4.9657 cents 54:62:63:72 SD: 2.1874 cents 58 x 67:77 SD: 6.5632 cents 59:68:69:79 SD: 5.0864 cents 60:69:70:80 SD: 2.5824 cents 61:70:71:81 SD: 2.5020 cents 68:78:79:91 SD: 2.1406 cents 69:79:80:92 SD: 1.8264 cents 75:86:87:100 SD: 1.2056 cents 81:93:94:108 SD: 1.0912 cents 117:134:136:156 SD: 0.8860 cents 123:141:143:164 SD: 0.3756 cents 129:148:150:172 SD: 0.2282 cents 252:289:293:336 SD: 0.1917 cents 333:382:387:444 SD: 0.1230 cents 456:523:530:608 SD: 0.0856 cents 462:530:537:616 SD: 0.0697 cents 585:671:680:780 SD: 0.0253 cents