Scala analysis: xen15-chalmers-triadic-reversed-diamond-27-23-tetrachord
Tetrachord 92/81 * 2187/2116 * 92/81 of triadic reversed diamond for M=27/23, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 92/81 220.454344 2: 27/23 277.590655 vicesimotertial minor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 92/81 220.4543 1: 92/81 220.4543 2: 2187/2116 57.1363 3: 92/81 220.4543
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2187/2116 57.136 cents 1: 2 92/81 220.454 cents 2: 2 27/23 277.591 cents vicesimotertial minor third 2: 1 8464/6561 440.909 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 : 220.5 277.6 498.0 220.5: 57.1 277.6 498.0 277.6: 220.5 440.9 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 57.1363 .. 220.4543 cents 194672/177147, 163.3180 cents 2187/2116, 57.1363 cents 2: 277.5907 .. 440.9087 cents 194672/177147, 163.3180 cents 2187/2116, 57.1363 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 2187/2116, 57.1363 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 92/81, 220.4543 cents Average / Smallest step : 2.905595 Largest / Average step : 1.327918 Largest / Smallest step : 3.858393 Median interval of one step : 92/81, 220.4543 cents, amount: 2 Most common interval of one step : 92/81, 220.4543 cents, amount: 2 Least squares average step : 162.12648 cents, oct.: 486.37943 cents Scale is strictly proper Scale has Myhill's property chromas: 194672/177147, 163.3180 cents and 411925952/387420489, 106.1817 cents, ratio: 1.538099 generators: 1 of 220.45434 cents and 2 of 277.59066 cents ET pair of linear temperament : 122&1970 Scale is distributional even Scale is a mode of a 619-tone equal temperament with octave 4/3 degrees: 274 345 619 generators: 274 and 345 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 57.13631 cents Scale diversity : 0.701875 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.344164 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 : 2187/2116, 57.1363 cents Most common intervals : 92/81, 220.4543 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best major thirds form a closed circle 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 : 23 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.009538 Average absolute harmonicity : 0.084171 Specific harmonicity : 0.050127 Fundamental : 1/1863, -10.8634 octaves, 0.1404 Hz. Guide tone : 2484, 11.2784 octaves, 649877.904 Hz. Exponens Consonantiae : 4.627692E+06, 22.14186 octaves Euler's gradus suavitatis : 61 Sum of Mann's harmonic distance : 115.0, average 38.33333 Mersenne's string divisions : 60550 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.74455, average 2.58152 Vogel's harmonic complexity : 34.33333 Wille's k value : 1093 Wilson's harmonic complexity : 67 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 25.27561, average 4.21260 Lattice compactness (without 2's) : 22.85088, average 3.80848 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -4 .. 3 -0.66667 8 1 23: -1 .. 1 0.00000 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 10 / 3 = 3.33333 Scale is JI-epimorphic with val: <7 11 31| Scale is weakly epimorphic with val: <7 11 32| Scale is weakly epimorphic with val: <7 11 34| Scale is weakly epimorphic with val: <7 11 35|
FIT/MODE
3: 1 1 1 SP B ME I SD: 44.4495 c. M: 54.4393 c. 4: 2 0 2 P M DE I SD: 23.3258 c. M: 28.5682 c. 5: 2 1 2 SP M ME I SD: 17.3394 c. M: 21.2363 c. 7: 3 1 3 SP M DE I SD: 5.7208 c. M: 7.0065 c. 9: 4 1 4 SP M DE I SD: 0.7340 c. M: 0.8990 c. 34: 15 4 15 SP M DE I SD: 0.5949 c. M: 0.7286 c. 43: 19 5 19 SP M DE I SD: 0.3168 c. M: 0.3879 c. 52: 23 6 23 SP M DE I SD: 0.1349 c. M: 0.1652 c. 61: 27 7 27 SP M DE I SD: 0.0067 c. M: 0.0082 c. 558: 247 64 247 SP M DE I SD: 0.0053 c. M: 0.0064 c. 619: 274 71 274 SP M DE I SD: 0.0041 c. M: 0.0050 c. 680: 301 78 301 SP M DE I SD: 0.0031 c. M: 0.0038 c. 741: 328 85 328 SP M DE I SD: 0.0023 c. M: 0.0028 c. 802: 355 92 355 SP M DE I SD: 0.0016 c. M: 0.0020 c. 863: 382 99 382 SP M DE I SD: 0.0010 c. M: 0.0013 c. 924: 409 106 409 SP M DE I SD: 0.0005 c. M: 0.0006 c. 985: 436 113 436 SP M DE I SD: 0.0001 c. M: 0.0001 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: 108.7231 cents 5 x 6:7 S SD: 46.3210 cents 6 x 7:8 S SD: 5.3599 cents 7:8 x 9 S SD: 31.9335 cents 8:9 x 11 SD: 27.8914 cents 9:10:11:12 H SD: 26.5043 cents 11 x 13:15 SD: 20.3019 cents 12 x 14:16 S SD: 5.3599 cents 13:15 x 17 SD: 21.6488 cents 14:16 x 19 SD: 16.2315 cents 15:17:18:20 SD: 12.7456 cents 16:18:19:21 SD: 12.5342 cents 19 x 22:25 SD: 16.5195 cents 20:23 x 27 SD: 15.2072 cents 21:24:25:28 SD: 8.8397 cents 22:25:26:29 SD: 7.6537 cents 23:26:27:31 SD: 6.8114 cents 24:27:28:32 S SD: 6.5712 cents 29:33:34:39 SD: 5.1233 cents 30:34:35:40 SD: 3.7875 cents 45:51:53:60 SD: 2.2748 cents 51:58:60:68 SD: 1.4564 cents 75:85:88:100 SD: 1.2878 cents 81:92:95:108 SD: 0.5280 cents 132:150:155:176 SD: 0.3278 cents 207:235:243:276 SD: 0.2728 cents 213:242:250:284 SD: 0.2032 cents 339:385:398:452 SD: 0.0840 cents 420:477:493:560 SD: 0.0678 cents 552:627:648:736 SD: 0.0341 cents