Scala analysis: xen15-chalmers-triadic-reversed-diamond-34-27-tetrachord
Tetrachord 18/17 * 289/243 * 18/17 of triadic reversed diamond for M=34/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 18/17 98.954592 Arabic lute index finger 2: 34/27 399.090407 septendecimal major third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 18/17 98.9546 Arabic lute index finger 1: 18/17 98.9546 Arabic lute index finger 2: 289/243 300.1358 3: 18/17 98.9546 Arabic lute index finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 18/17 98.955 cents Arabic lute index finger 1: 1 289/243 300.136 cents 2: 1 324/289 197.909 cents two (Arabic lute index finger) 2: 2 34/27 399.090 cents septendecimal major third 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 : 99.0 399.1 498.0 99.0 : 300.1 399.1 498.0 399.1: 99.0 197.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 98.9546 .. 300.1358 cents 4913/4374, 201.1812 cents 18/17, 98.9546 cents 2: 197.9092 .. 399.0904 cents 4913/4374, 201.1812 cents 78732/83521,-102.2266 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 18/17, 98.9546 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 289/243, 300.1358 cents Average / Smallest step : 1.677689 Largest / Average step : 1.807884 Largest / Smallest step : 3.033066 Median interval of one step : 18/17, 98.9546 cents, amount: 2 Most common interval of one step : 18/17, 98.9546 cents, amount: 2 Least squares average step : 170.80503 cents, oct.: 512.41509 cents Scale is not proper Scale has Myhill's property chromas: 4913/4374, 201.1812 cents and 83521/78732, 102.2266 cents, ratio: 1.967992 generators: 1 of 98.95459 cents and 2 of 399.09041 cents ET pair of linear temperament : 302&1218 Scale is distributional even Scale is a mode of a 151-tone equal temperament with octave 4/3 degrees: 30 121 151 generators: 30 and 121 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS 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 2 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 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 ] Scale is a Constant Structure, by a margin of 98.95459 cents Scale diversity : 1.066739 Lumma stability : 0.397372 Lumma impropriety factor : 0.205256 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 : 18/17, 98.9546 cents Most common intervals : 18/17, 98.9546 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 : 289 (O: 289 U: 289) Highest odd numerator or denominator: 27 Scale harmonicity : 0.013233 Average absolute harmonicity : 0.089094 Specific harmonicity : 0.069755 Fundamental : 1/459, -8.8424 octaves, 0.5700 Hz. Guide tone : 612, 9.2574 octaves, 160114.846 Hz. Exponens Consonantiae : 2.809080E+05, 18.09974 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 51.5, average 17.16667 Mersenne's string divisions : 2135 Sum of van Prooijen's expressibility: 3.13893, average 1.04631 Sum of Tenney's harmonic distance : 6.52775, average 2.17592 Vogel's harmonic complexity : 25.33333 Wille's k value : 144 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.15346, average 3.19224 Lattice compactness (without 2's) : 17.18186, average 2.86364 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -3 .. 2 -0.66667 6 1 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 27| Scale is JI-epimorphic with val: <7 11 28| Scale is weakly epimorphic with val: <7 11 30| = patent Scale is weakly epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 11 33|
FIT/MODE
3: 1 1 1 SP B ME I SD: 54.7546 c. M: 67.0604 c. 4: 1 2 1 P M ME I SD: 20.8669 c. M: 25.5567 c. 5: 1 3 1 N M DE I SD: 0.5343 c. M: 0.6544 c. 81: 16 49 16 N M DE I SD: 0.4698 c. M: 0.5753 c. 86: 17 52 17 N M DE I SD: 0.4114 c. M: 0.5038 c. 91: 18 55 18 N M DE I SD: 0.3594 c. M: 0.4402 c. 96: 19 58 19 N M DE I SD: 0.3129 c. M: 0.3832 c. 101: 20 61 20 N M DE I SD: 0.2709 c. M: 0.3318 c. 106: 21 64 21 N M DE I SD: 0.2329 c. M: 0.2853 c. 111: 22 67 22 N M DE I SD: 0.1984 c. M: 0.2430 c. 116: 23 70 23 N M DE I SD: 0.1668 c. M: 0.2043 c. 121: 24 73 24 N M DE I SD: 0.1378 c. M: 0.1688 c. 126: 25 76 25 N M DE I SD: 0.1112 c. M: 0.1361 c. 131: 26 79 26 N M DE I SD: 0.0865 c. M: 0.1060 c. 136: 27 82 27 N M DE I SD: 0.0637 c. M: 0.0780 c. 141: 28 85 28 N M DE I SD: 0.0425 c. M: 0.0520 c. 146: 29 88 29 N M DE I SD: 0.0227 c. M: 0.0278 c. 151: 30 91 30 N M DE I SD: 0.0043 c. M: 0.0053 c. 458: 91 276 91 N M DE I SD: 0.0016 c. M: 0.0019 c. 609: 121 367 121 N M DE I SD: 0.0001 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: 12.7767 cents 5 x 6:7 S SD: 59.3685 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 68.5156 cents 8:9:10:11 H SD: 39.4643 cents 9:10:11:12 H SD: 32.7191 cents 10:11 x 13 SD: 39.6349 cents 11:12:14:15 S SD: 22.4201 cents 12:13:15:16 SD: 13.8758 cents 15:16:19:20 SD: 5.4400 cents 34:36:43:45 SD: 4.9337 cents 35:37:44:47 SD: 4.3189 cents 49:52:62:65 SD: 4.2502 cents 50:53:63:67 SD: 2.9681 cents 51:54:64:68 SD: 2.0003 cents 54:57:68:72 SD: 1.7839 cents 66:70:83:88 SD: 1.2403 cents 69:73:87:92 SD: 0.8717 cents 120:127:151:160 SD: 0.5016 cents 135:143:170:180 SD: 0.2374 cents 255:270:321:340 SD: 0.1997 cents 324:343:408:432 SD: 0.0990 cents 459:486:578:612 SD: 0.0000 cents