Scala analysis: xen15-chalmers-triadic-reversed-diamond-21-17-tetrachord
Tetrachord 68/63 * 1323/1156 * 68/63 of triadic reversed diamond for M=21/17, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/63 132.219501 supraminor second 2: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 68/63 132.2195 supraminor second 1: 68/63 132.2195 supraminor second 2: 1323/1156 233.6060 3: 68/63 132.2195 supraminor second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 68/63 132.220 cents supraminor second 1: 1 1323/1156 233.606 cents 2: 1 4624/3969 264.439 cents two (supraminor second) 2: 2 21/17 365.825 cents submajor 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 : 132.2 365.8 498.0 132.2: 233.6 365.8 498.0 365.8: 132.2 264.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 132.2195 .. 233.6060 cents 83349/78608, 101.3865 cents 68/63, 132.2195 cents 2: 264.4390 .. 365.8255 cents 83349/78608, 101.3865 cents 5345344/5250987, 30.8330 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 68/63, 132.2195 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 1323/1156, 233.6060 cents Average / Smallest step : 1.255601 Largest / Average step : 1.407138 Largest / Smallest step : 1.766804 Median interval of one step : 68/63, 132.2195 cents, amount: 2 Most common interval of one step : 68/63, 132.2195 cents, amount: 2 Least squares average step : 168.42896 cents, oct.: 505.28689 cents Scale is strictly proper Scale has Myhill's property chromas: 83349/78608, 101.3865 cents and 5345344/5250987, 30.8330 cents, ratio: 3.288246 generators: 1 of 132.21950 cents and 2 of 365.82550 cents ET pair of linear temperament : 30&98 Scale is maximally even for L / S <= 2 Scale is distributional even Scale is a mode of a 113-tone equal temperament with octave 4/3 degrees: 30 83 113 generators: 30 and 83 Number of contiguous 1-step segments: 0 Step pattern alph. order: ABA Step pattern size order : SLS Interval vector is [ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 ] Scale is a Constant Structure, by a margin of 30.83301 cents Scale diversity : 1.228746 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.592862 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 : 5345344/5250987, 30.8330 cents Most common intervals : 68/63, 132.2195 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 : 17 Odd number limit : 3969 (O: 1323 U: 3969) Highest odd numerator or denominator: 63 Scale harmonicity : 0.011012 Average absolute harmonicity : 0.086150 Specific harmonicity : 0.057743 Fundamental : 1/1071, -10.0647 octaves, 0.2443 Hz. Guide tone : 1428, 10.4798 octaves, 373601.307 Hz. Exponens Consonantiae : 1.529388E+06, 20.54452 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 88.0, average 29.33333 Mersenne's string divisions : 34846 Sum of van Prooijen's expressibility: 3.59868, average 1.19956 Sum of Tenney's harmonic distance : 7.26370, average 2.42123 Vogel's harmonic complexity : 29.33333 Wille's k value : 661 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 7 Triangular lattice diameter : 5 Lattice compactness : 16.60730, average 2.76788 Lattice compactness (without 2's) : 13.48619, average 2.24770 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.33333 4 3: -2 .. 1 -0.66667 4 1 7: -1 .. 1 0.00000 2 17: -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 18 27| Scale is weakly epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 33| Scale is JI-epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 20 27| Scale is JI-epimorphic with val: <7 11 20 29| Scale is weakly epimorphic with val: <7 11 20 30| = patent Scale is weakly epimorphic with val: <7 11 20 32| Scale is weakly epimorphic with val: <7 11 20 33| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 21 28| Scale is JI-epimorphic with val: <7 11 21 30| Scale is weakly epimorphic with val: <7 11 21 31| Scale is weakly epimorphic with val: <7 11 21 33| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 11 22 29| Scale is JI-epimorphic with val: <7 11 22 31| Scale is weakly epimorphic with val: <7 11 22 32|
FIT/MODE
3: 1 1 1 SP B ME I SD: 27.5939 c. M:-33.7955 c. 4: 1 2 1 P M ME I SD: 6.2938 c. M: 7.7083 c. 11: 3 5 3 SP M DE I SD: 2.9483 c. M: 3.6110 c. 15: 4 7 4 SP M DE I SD: 0.4838 c. M:-0.5925 c. 34: 9 16 9 SP M DE I SD: 0.3136 c. M: 0.3841 c. 49: 13 23 13 SP M DE I SD: 0.0695 c. M: 0.0851 c. 64: 17 30 17 SP M DE I SD: 0.0602 c. M: 0.0737 c. 113: 30 53 30 SP M DE I SD: 0.0039 c. M: 0.0048 c. 501: 133 235 133 SP M DE I SD: 0.0032 c. M: 0.0040 c. 614: 163 288 163 SP M DE I SD: 0.0019 c. M: 0.0023 c. 727: 193 341 193 SP M DE I SD: 0.0010 c. M: 0.0012 c. 840: 223 394 223 SP M DE I SD: 0.0003 c. M: 0.0004 c. 953: 253 447 253 SP M DE I SD: 0.0002 c. M: 0.0002 c. 1793: 476 841 476 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: 20.4882 cents 5 x 6:7 S SD: 49.1253 cents 6 x 7:8 S SD: 49.4773 cents 7:8 x 9 S SD: 58.6432 cents 8:9:10:11 H SD: 30.5456 cents 9:10:11:12 H SD: 17.8190 cents 12:13:15:16 SD: 7.1502 cents 25:27:31:33 SD: 6.2103 cents 26:28:32:35 SD: 6.0572 cents 37:40:46:49 SD: 5.4634 cents 38:41:47:51 SD: 3.8590 cents 39:42:48:52 S SD: 2.4886 cents 51:55:63:68 SD: 0.4994 cents 213:230:263:284 SD: 0.3518 cents 264:285:326:352 SD: 0.2295 cents 276:298:341:368 SD: 0.2096 cents 315:340:389:420 SD: 0.1745 cents 327:353:404:436 SD: 0.1146 cents 378:408:467:504 SD: 0.0727 cents