Scala analysis: xen15-chalmers-triadic-reversed-diamond-57-46-tetrachord
Tetrachord 184/171 * 9747/8464 * 184/171 of triadic reversed diamond for M=57/46, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 184/171 126.851329 2: 57/46 371.193670 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 184/171 126.8513 1: 184/171 126.8513 2: 9747/8464 244.3423 3: 184/171 126.8513
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 184/171 126.851 cents 1: 1 9747/8464 244.342 cents 2: 1 33856/29241 253.703 cents 2: 2 57/46 371.194 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 : 126.9 371.2 498.0 126.9: 244.3 371.2 498.0 371.2: 126.9 253.7 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.8513 .. 244.3423 cents 1666737/1557376, 117.4910 cents 184/171, 126.8513 cents 2: 253.7027 .. 371.1937 cents 1666737/1557376, 117.4910 cents 286557184/285012027, 9.3603 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 184/171, 126.8513 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 9747/8464, 244.3423 cents Average / Smallest step : 1.308737 Largest / Average step : 1.471809 Largest / Smallest step : 1.926210 Median interval of one step : 184/171, 126.8513 cents, amount: 2 Most common interval of one step : 184/171, 126.8513 cents, amount: 2 Least squares average step : 168.81240 cents, oct.: 506.43721 cents Scale is strictly proper Scale has Myhill's property chromas: 1666737/1557376, 117.4910 cents and 286557184/285012027, 9.3603 cents, ratio: 12.552031 generators: 1 of 126.85133 cents and 2 of 371.19367 cents ET pair of linear temperament : 102&110 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 373-tone equal temperament with octave 4/3 degrees: 95 278 373 generators: 95 and 278 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 9.36032 cents Scale diversity : 1.140676 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.528191 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 : 286557184/285012027, 9.3603 cents Most common intervals : 184/171, 126.8513 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 23 Odd number limit : 29241 (O: 9747 U: 29241) Highest odd numerator or denominator: 171 Scale harmonicity : 0.006083 Average absolute harmonicity : 0.079546 Specific harmonicity : 0.032140 Fundamental : 1/7866, -12.9414 octaves, 0.0333 Hz. Guide tone : 10488, 13.3565 octaves, 2743928.929 Hz. Exponens Consonantiae : 8.249861E+07, 26.29787 octaves Euler's gradus suavitatis : 91 Sum of Mann's harmonic distance : 232.5, average 77.50000 Mersenne's string divisions : 255955 Sum of van Prooijen's expressibility: 4.46599, average 1.48866 Sum of Tenney's harmonic distance : 8.99563, average 2.99854 Vogel's harmonic complexity : 48.33333 Wille's k value : 4873 Wilson's harmonic complexity : 93 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 19.72660, average 3.28777 Lattice compactness (without 2's) : 13.48619, average 2.24770 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 1.33333 6 3: -2 .. 1 -0.66667 4 1 19: -1 .. 1 0.00000 2 23: -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 JI-epimorphic with val: <7 11 28 30| Scale is weakly epimorphic with val: <7 11 28 31| Scale is weakly epimorphic with val: <7 11 28 33| Scale is weakly epimorphic with val: <7 11 28 34| Scale is weakly epimorphic with val: <7 11 28 36| Scale is JI-epimorphic with val: <7 11 29 31| Scale is weakly epimorphic with val: <7 11 29 32| Scale is weakly epimorphic with val: <7 11 29 34| Scale is weakly epimorphic with val: <7 11 29 35| Scale is weakly epimorphic with val: <7 11 30 30| Scale is JI-epimorphic with val: <7 11 30 32| Scale is weakly epimorphic with val: <7 11 30 33| Scale is weakly epimorphic with val: <7 11 30 35| Scale is weakly epimorphic with val: <7 11 30 36| Scale is weakly epimorphic with val: <7 11 31 31| Scale is JI-epimorphic with val: <7 11 31 33| = patent Scale is weakly epimorphic with val: <7 11 31 34| Scale is weakly epimorphic with val: <7 11 31 36| Scale is weakly epimorphic with val: <7 11 32 32| Scale is JI-epimorphic with val: <7 11 32 34| Scale is weakly epimorphic with val: <7 11 32 35| Scale is weakly epimorphic with val: <7 11 33 33| Scale is JI-epimorphic with val: <7 11 33 35| Scale is weakly epimorphic with val: <7 11 33 36| Scale is weakly epimorphic with val: <7 11 34 34| Scale is JI-epimorphic with val: <7 11 34 36|
FIT/MODE
3: 1 1 1 SP B ME I SD: 31.9770 c. M:-39.1637 c. 4: 1 2 1 P M ME I SD: 1.9107 c. M:-2.3401 c. 27: 7 13 7 SP M DE I SD: 1.8546 c. M:-2.2714 c. 31: 8 15 8 SP M DE I SD: 1.3688 c. M:-1.6764 c. 35: 9 17 9 SP M DE I SD: 0.9940 c. M:-1.2174 c. 39: 10 19 10 SP M DE I SD: 0.6961 c. M:-0.8525 c. 43: 11 21 11 SP M DE I SD: 0.4536 c. M:-0.5555 c. 47: 12 23 12 SP M DE I SD: 0.2524 c. M:-0.3091 c. 51: 13 25 13 SP M DE I SD: 0.0827 c. M:-0.1013 c. 55: 14 27 14 SP M DE I SD: 0.0622 c. M:-0.0762 c. 106: 27 52 27 SP M DE I SD: 0.0075 c. M:-0.0092 c. 267: 68 131 68 SP M DE I SD: 0.0069 c. M:-0.0084 c. 373: 95 183 95 SP M DE I SD: 0.0028 c. M:-0.0034 c. 479: 122 235 122 SP M DE I SD: 0.0005 c. M:-0.0006 c. 1064: 271 522 271 SP M DE I SD: 0.0003 c. M:-0.0004 c. 1543: 393 757 393 SP M DE I SD: 0.0000 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: 15.1200 cents 5 x 6:7 S SD: 50.5489 cents 6 x 7:8 S SD: 52.1614 cents 7:8 x 9 S SD: 60.9248 cents 8:9:10:11 H SD: 31.6310 cents 9:10:11:12 H SD: 20.1435 cents 12:13:15:16 SD: 6.3771 cents 25:27:31:33 SD: 6.1914 cents 30:32:37:40 SD: 5.7206 cents 37:40:46:49 SD: 5.1270 cents 38:41:47:51 SD: 4.2320 cents 39:42:48:52 S SD: 3.9368 cents 42:45:52:56 SD: 2.5162 cents 51:55:63:68 SD: 2.2059 cents 54:58:67:72 SD: 1.2871 cents 93:100:115:124 SD: 1.2652 cents 105:113:130:140 SD: 0.4906 cents 117:126:145:156 SD: 0.4900 cents 159:171:197:212 SD: 0.3027 cents 171:184:212:228 SD: 0.2960 cents 264:284:327:352 SD: 0.2707 cents 276:297:342:368 SD: 0.0341 cents