Scala analysis: xen15-chalmers-triadic-reversed-diamond-32-27-tetrachord
Tetrachord 9/8 * 256/243 * 9/8 of triadic reversed diamond for M=32/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 32/27 294.134997 Pythagorean minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 9/8 203.9100 major whole tone 1: 9/8 203.9100 major whole tone 2: 256/243 90.2250 limma, Pythagorean minor second 3: 9/8 203.9100 major whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 256/243 90.225 cents limma, Pythagorean minor second 1: 2 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 1 81/64 407.820 cents Pythagorean 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 : 203.9 294.1 498.0 203.9: 90.2 294.1 498.0 294.1: 203.9 407.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.2250 .. 203.9100 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents 2: 294.1350 .. 407.8200 cents 2187/2048, 113.6850 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 256/243, 90.2250 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.840011 Largest / Average step : 1.228263 Largest / Smallest step : 2.260017 Median interval of one step : 9/8, 203.9100 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 2 Least squares average step : 163.30821 cents, oct.: 489.92464 cents Scale is strictly proper Scale has Myhill's property chromas: 2187/2048, 113.6850 cents and 531441/524288, 23.4600 cents, ratio: 4.845906 generators: 1 of 203.91000 cents and 2 of 294.13500 cents ET pair of linear temperament : 34&44 Scale is distributional even Scale is a mode of a 276-tone equal temperament with octave 4/3 degrees: 113 163 276 generators: 113 and 163 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 90.22500 cents Scale diversity : 1.001178 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.543475 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 : 256/243, 90.2250 cents Most common intervals : 9/8, 203.9100 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 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 : 3 Odd number limit : 243 (O: 81 U: 243) Highest odd numerator or denominator: 27 Scale harmonicity : 0.046875 Average absolute harmonicity : 0.137069 Specific harmonicity : 0.233009 Fundamental : 1/216, -7.7549 octaves, 1.2112 Hz. Guide tone : 288, 8.1699 octaves, 75348.163 Hz. Exponens Consonantiae : 6.220800E+04, 15.92481 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 41.5, average 13.83333 Mersenne's string divisions : 7021 Sum of van Prooijen's expressibility: 2.86273, average 0.95424 Sum of Tenney's harmonic distance : 5.87303, average 1.95768 Vogel's harmonic complexity : 11.33333 Wille's k value : 121 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 5 Triangular lattice diameter : 5 Lattice compactness : 30.54306, average 5.09051 Lattice compactness (without 2's) : 16.00000, average 2.66667 Number of different primes : 2 Prime exponents' range, average, count, tones@limit: 2: -3 .. 5 1.33333 10 3: -3 .. 2 -0.66667 6 3 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| = patent
FIT/MODE
3: 1 1 1 SP B ME I SD: 30.9411 c. M:-37.8950 c. 5: 2 1 2 SP M ME I SD: 3.8310 c. M: 4.6920 c. 12: 5 2 5 SP M DE I SD: 2.9465 c. M:-3.6087 c. Raga Sarvasri, Warao tritonic: South America 17: 7 3 7 SP M DE I SD: 0.9531 c. M:-1.1674 c. 22: 9 4 9 SP M DE I SD: 0.1342 c. M:-0.1643 c. 83: 34 15 34 SP M DE I SD: 0.0885 c. M:-0.1084 c. 105: 43 19 43 SP M DE I SD: 0.0419 c. M:-0.0513 c. 127: 52 23 52 SP M DE I SD: 0.0114 c. M:-0.0139 c. 149: 61 27 61 SP M DE I SD: 0.0101 c. M: 0.0124 c. 276: 113 50 113 SP M DE I SD: 0.0002 c. M: 0.0003 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: 92.1787 cents 5 x 6:7 S SD: 43.5810 cents 6 x 7:8 S SD: 13.6320 cents 7:8 x 9 S SD: 34.3053 cents 8:9 x 11 SD: 26.6365 cents 9:10:11:12 H SD: 19.1501 cents 12 x 14:16 S SD: 13.6320 cents 13:15 x 17 SD: 27.6192 cents 14:16:17:19 SD: 19.5670 cents 15:17:18:20 SD: 8.3384 cents 26:29:31:35 SD: 8.1846 cents 27:30:32:36 S SD: 7.1688 cents 31:35:37:41 SD: 6.5240 cents 32:36:38:43 SD: 4.6299 cents 33:37:39:44 SD: 2.5463 cents 48:54:57:64 SD: 1.1260 cents 81:91:96:108 SD: 0.7921 cents 129:145:153:172 SD: 0.6504 cents 135:152:160:180 SD: 0.4748 cents 168:189:199:224 SD: 0.3221 cents 216:243:256:288 SD: 0.0000 cents