Scala analysis: xen15-chalmers-triadic-reversed-diamond-27-22-tetrachord
Tetrachord 88/81 * 2187/1936 * 88/81 of triadic reversed diamond for M=27/22, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 88/81 143.497939 2nd undecimal neutral second 2: 27/22 354.547060 neutral third, Zalzal wosta of al-Farabi 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 88/81 143.4979 2nd undecimal neutral second 1: 88/81 143.4979 2nd undecimal neutral second 2: 2187/1936 211.0491 3: 88/81 143.4979 2nd undecimal neutral second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 88/81 143.498 cents 2nd undecimal neutral second 1: 1 2187/1936 211.049 cents 2: 1 7744/6561 286.996 cents two (2nd undecimal neutral second) 2: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 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 : 143.5 354.5 498.0 143.5: 211.0 354.5 498.0 354.5: 143.5 287.0 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 143.4979 .. 211.0491 cents 177147/170368, 67.5512 cents 88/81, 143.4979 cents 2: 286.9959 .. 354.5471 cents 177147/170368, 67.5512 cents 14992384/14348907, 75.9468 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 88/81, 143.4979 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 2187/1936, 211.0491 cents Average / Smallest step : 1.156916 Largest / Average step : 1.271265 Largest / Smallest step : 1.470747 Median interval of one step : 88/81, 143.4979 cents, amount: 2 Most common interval of one step : 88/81, 143.4979 cents, amount: 2 Least squares average step : 167.62336 cents, oct.: 502.87008 cents Scale is strictly proper Scale has Myhill's property chromas: 177147/170368, 67.5512 cents and 14992384/14348907, 75.9468 cents, ratio: 1.124285 generators: 1 of 143.49794 cents and 2 of 354.54706 cents ET pair of linear temperament : 118&2492 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 715-tone equal temperament with octave 4/3 degrees: 206 509 715 generators: 206 and 509 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 75.94676 cents Scale diversity : 1.333122 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.728735 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 : 177147/170368, 67.5512 cents Most common intervals : 88/81, 143.4979 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 Best fifths form a closed circle Best major thirds form a closed circle Best minor 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 : 11 Odd number limit : 6561 (O: 2187 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.016940 Average absolute harmonicity : 0.094157 Specific harmonicity : 0.088029 Fundamental : 1/1782, -10.7993 octaves, 0.1468 Hz. Guide tone : 2376, 11.2143 octaves, 621622.343 Hz. Exponens Consonantiae : 4.234032E+06, 22.01360 octaves Euler's gradus suavitatis : 39 Sum of Mann's harmonic distance : 112.5, average 37.50000 Mersenne's string divisions : 8281 Sum of van Prooijen's expressibility: 3.81697, average 1.27232 Sum of Tenney's harmonic distance : 7.70594, average 2.56865 Vogel's harmonic complexity : 23.33333 Wille's k value : 1093 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 9 Triangular lattice diameter : 7 Lattice compactness : 27.37398, average 4.56233 Lattice compactness (without 2's) : 22.85088, average 3.80848 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -4 .. 3 -0.66667 8 1 11: -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 24| Scale is weakly epimorphic with val: <7 11 25| = patent Scale is weakly epimorphic with val: <7 11 27|
FIT/MODE
3: 1 1 1 SP B ME I SD: 18.3851 c. M:-22.5171 c. 4: 1 2 1 P M ME I SD: 15.5026 c. M:-18.9867 c. 7: 2 3 2 SP M ME I SD: 0.9793 c. M: 1.1994 c. 31: 9 13 9 SP M DE I SD: 0.8947 c. M:-1.0958 c. 38: 11 16 11 SP M DE I SD: 0.5495 c. M:-0.6730 c. 45: 13 19 13 SP M DE I SD: 0.3117 c. M: 0.3817 c. 52: 15 22 15 SP M DE I SD: 0.1379 c. M: 0.1689 c. 59: 17 25 17 SP M DE I SD: 0.0053 c. M: 0.0066 c. 656: 189 278 189 SP M DE I SD: 0.0052 c. M: 0.0063 c. 715: 206 303 206 SP M DE I SD: 0.0043 c. M:-0.0053 c. 774: 223 328 223 SP M DE I SD: 0.0036 c. M: 0.0044 c. 833: 240 353 240 SP M DE I SD: 0.0029 c. M:-0.0036 c. 892: 257 378 257 SP M DE I SD: 0.0024 c. M:-0.0029 c. 951: 274 403 274 SP M DE I SD: 0.0019 c. M: 0.0023 c. 1010: 291 428 291 SP M DE I SD: 0.0015 c. M: 0.0018 c. 1069: 308 453 308 SP M DE I SD: 0.0011 c. M: 0.0013 c. 1128: 325 478 325 SP M DE I SD: 0.0008 c. M: 0.0009 c. 1187: 342 503 342 SP M DE I SD: 0.0005 c. M: 0.0006 c. 1246: 359 528 359 SP M DE I SD: 0.0002 c. M:-0.0002 c. 1305: 376 553 376 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: 31.7667 cents 5 x 6:7 S SD: 46.4983 cents 6 x 7:8 S SD: 43.8381 cents 7:8 x 9 S SD: 53.9703 cents 8:9:10:11 H SD: 28.8612 cents 9:10:11:12 H SD: 13.1851 cents 12:13:15:16 SD: 10.7154 cents 21:23:26:28 SD: 6.8872 cents 34:37:42:45 SD: 5.7620 cents 35:38:43:47 SD: 4.1693 cents 36:39:44:48 SD: 2.8911 cents 45:49:55:60 SD: 2.7165 cents 48:52:59:64 SD: 1.8674 cents 57:62:70:76 SD: 0.7851 cents 93:101:114:124 SD: 0.7216 cents 105:114:129:140 SD: 0.7163 cents 141:153:173:188 SD: 0.7143 cents 150:163:184:200 SD: 0.3138 cents 198:215:243:264 SD: 0.2982 cents 255:277:313:340 SD: 0.1139 cents 405:440:497:540 SD: 0.0528 cents