Scala analysis: xen15-chalmers-triadic-reversed-diamond-64-51-tetrachord
Tetrachord 17/16 * 1024/867 * 17/16 of triadic reversed diamond for M=64/51, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 64/51 393.089590 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 17/16 104.9554 17th harmonic 1: 17/16 104.9554 17th harmonic 2: 1024/867 288.1342 3: 17/16 104.9554 17th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 17/16 104.955 cents 17th harmonic 1: 1 1024/867 288.134 cents 2: 1 289/256 209.911 cents two (17th harmonic) 2: 2 64/51 393.090 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 : 105.0 393.1 498.0 105.0: 288.1 393.1 498.0 393.1: 105.0 209.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 104.9554 .. 288.1342 cents 16384/14739, 183.1788 cents 17/16, 104.9554 cents 2: 209.9108 .. 393.0896 cents 16384/14739, 183.1788 cents 250563/262144,-78.2234 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 17/16, 104.9554 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1024/867, 288.1342 cents Average / Smallest step : 1.581767 Largest / Average step : 1.735591 Largest / Smallest step : 2.745301 Median interval of one step : 17/16, 104.9554 cents, amount: 2 Most common interval of one step : 17/16, 104.9554 cents, amount: 2 Least squares average step : 170.37640 cents, oct.: 511.12920 cents Scale is not proper Scale has Myhill's property chromas: 16384/14739, 183.1788 cents and 262144/250563, 78.2234 cents, ratio: 2.341740 generators: 1 of 104.95541 cents and 2 of 393.08959 cents ET pair of linear temperament : 28&38 Scale is distributional even Scale is a mode of a 242-tone equal temperament with octave 4/3 degrees: 51 191 242 generators: 51 and 191 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Scale is a Constant Structure, by a margin of 78.22336 cents Scale diversity : 1.102169 Lumma stability : 0.421470 Lumma impropriety factor : 0.157061 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 : 262144/250563, 78.2234 cents Most common intervals : 17/16, 104.9554 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 : 867 (O: 289 U: 867) Highest odd numerator or denominator: 51 Scale harmonicity : 0.013717 Average absolute harmonicity : 0.089793 Specific harmonicity : 0.071629 Fundamental : 1/816, -9.6724 octaves, 0.3206 Hz. Guide tone : 1088, 10.0875 octaves, 284648.615 Hz. Exponens Consonantiae : 8.878080E+05, 19.75989 octaves Euler's gradus suavitatis : 45 Sum of Mann's harmonic distance : 77.5, average 25.83333 Mersenne's string divisions : 26565 Sum of van Prooijen's expressibility: 3.41514, average 1.13838 Sum of Tenney's harmonic distance : 7.02750, average 2.34250 Vogel's harmonic complexity : 23.33333 Wille's k value : 433 Wilson's harmonic complexity : 37 Rectangular lattice diameter : 3 Triangular lattice diameter : 3 Lattice compactness : 33.05806, average 5.50968 Lattice compactness (without 2's) : 8.06450, average 1.34408 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 6 1.33333 12 3: -1 .. 0 -0.66667 2 1 17: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 4 / 3 = 1.33333 Scale is weakly epimorphic with val: <7 11 27| Scale is JI-epimorphic with val: <7 11 29| Scale is weakly epimorphic with val: <7 11 30| = patent Scale is weakly epimorphic with val: <7 11 32| Scale is weakly epimorphic with val: <7 11 33|
FIT/MODE
3: 0 2 1 N G T3 SD: 70.1045 c. M: 104.9554 c. 4: 1 2 1 P M ME I SD: 15.9673 c. M: 19.5558 c. 5: 1 3 1 N M DE I SD: 4.3653 c. M: 5.3464 c. 14: 3 8 3 N M DE I SD: 1.4440 c. M: 1.7685 c. 19: 4 11 4 N M DE I SD: 0.0848 c. M: 0.1038 c. 128: 27 74 27 N M DE I SD: 0.0824 c. M: 0.1010 c. 147: 31 85 31 N M DE I SD: 0.0608 c. M: 0.0745 c. 166: 35 96 35 N M DE I SD: 0.0442 c. M: 0.0541 c. 185: 39 107 39 N M DE I SD: 0.0309 c. M: 0.0379 c. 204: 43 118 43 N M DE I SD: 0.0201 c. M:-0.0247 c. 223: 47 129 47 N M DE I SD: 0.0112 c. M: 0.0137 c. 242: 51 140 51 N M DE I SD: 0.0037 c. M: 0.0045 c. 261: 55 151 55 N M DE I SD: 0.0028 c. M: 0.0034 c. 503: 106 291 106 N M DE I SD: 0.0003 c. M: 0.0004 c. 1267: 267 733 267 N M DE I SD: 0.0003 c. M: 0.0004 c. 1770: 373 1024 373 N M DE I SD: 0.0001 c. M: 0.0002 c. 2273: 479 1315 479 N M DE I SD: 0.0000 c. M:-0.0000 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: 6.7759 cents 5 x 6:7 S SD: 57.2995 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 66.5107 cents 8:9:10:11 H SD: 37.5291 cents 9:10:11:12 H SD: 29.9723 cents 10:11 x 13 SD: 37.1720 cents 11:12:14:15 S SD: 21.5941 cents 12:13:15:16 SD: 11.4311 cents 15:16:19:20 SD: 5.8394 cents 31:33:39:41 SD: 5.0141 cents 36:38:45:48 SD: 4.4069 cents 47:50:59:63 SD: 3.1512 cents 48:51:60:64 SD: 2.2586 cents 51:54:64:68 SD: 2.0003 cents 63:67:79:84 SD: 0.6889 cents 114:121:143:152 SD: 0.6414 cents 129:137:162:172 SD: 0.4950 cents 177:188:222:236 SD: 0.3609 cents 192:204:241:256 SD: 0.1409 cents 255:271:320:340 SD: 0.1331 cents 369:392:463:492 SD: 0.1176 cents 447:475:561:596 SD: 0.0971 cents 561:596:704:748 SD: 0.0605 cents