Scala analysis: xen15-chalmers-triadic-reversed-diamond-22-17-tetrachord
Tetrachord 34/33 * 363/289 * 34/33 of triadic reversed diamond for M=22/17, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 34/33 51.682466 2: 22/17 446.362533 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 34/33 51.6825 1: 34/33 51.6825 2: 363/289 394.6801 3: 34/33 51.6825
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 34/33 51.682 cents 1: 1 363/289 394.680 cents 2: 1 1156/1089 103.365 cents 2: 2 22/17 446.363 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 : 51.7 446.4 498.0 51.7 : 394.7 446.4 498.0 446.4: 51.7 103.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 51.6825 .. 394.6801 cents 11979/9826, 342.9976 cents 34/33, 51.6825 cents 2: 103.3649 .. 446.3625 cents 11979/9826, 342.9976 cents 334084/395307,-291.3151 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 34/33, 51.6825 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 363/289, 394.6801 cents Average / Smallest step : 3.212211 Largest / Average step : 2.377376 Largest / Smallest step : 7.636634 Median interval of one step : 34/33, 51.6825 cents, amount: 2 Most common interval of one step : 34/33, 51.6825 cents, amount: 2 Least squares average step : 174.18161 cents, oct.: 522.54483 cents Scale is not proper Scale has Myhill's property chromas: 11979/9826, 342.9976 cents and 395307/334084, 291.3151 cents, ratio: 1.177411 generators: 1 of 51.68247 cents and 2 of 446.36253 cents ET pair of linear temperament : 20&38 Scale is distributional even Scale is a mode of a 106-tone equal temperament with octave 4/3 degrees: 11 95 106 generators: 11 and 95 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 2 0 0 0 0 0 0 0 0 0 0 1 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 0 0 ] Scale is a Constant Structure, by a margin of 51.68247 cents Scale diversity : 0.455948 Lumma stability : 0.207541 Lumma impropriety factor : 0.584917 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 : 34/33, 51.6825 cents Most common intervals : 34/33, 51.6825 cents & inv., amount: 2 Number of recognisable fifths : 0 Number of recognisable fourths : 0 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 : 17 Odd number limit : 1089 (O: 363 U: 1089) Highest odd numerator or denominator: 33 Scale harmonicity : 0.009875 Average absolute harmonicity : 0.084604 Specific harmonicity : 0.052208 Fundamental : 1/561, -9.1319 octaves, 0.4664 Hz. Guide tone : 748, 9.5469 octaves, 195695.923 Hz. Exponens Consonantiae : 4.196280E+05, 18.67875 octaves Euler's gradus suavitatis : 57 Sum of Mann's harmonic distance : 56.5, average 18.83333 Mersenne's string divisions : 18291 Sum of van Prooijen's expressibility: 3.22608, average 1.07536 Sum of Tenney's harmonic distance : 6.70205, average 2.23402 Vogel's harmonic complexity : 30.33333 Wille's k value : 181 Wilson's harmonic complexity : 59 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.70017, average 2.11669 Lattice compactness (without 2's) : 10.29253, average 1.71542 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 0 -0.66667 2 1 11: -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: 6 / 3 = 2.00000 Scale is JI-epimorphic with val: <7 11 23 28| Scale is weakly epimorphic with val: <7 11 23 29| Scale is weakly epimorphic with val: <7 11 23 31| Scale is weakly epimorphic with val: <7 11 23 32| Scale is weakly epimorphic with val: <7 11 24 27| Scale is JI-epimorphic with val: <7 11 24 29| Scale is weakly epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 24 32| Scale is weakly epimorphic with val: <7 11 24 33| Scale is weakly epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 25 28| Scale is JI-epimorphic with val: <7 11 25 30| = patent Scale is weakly epimorphic with val: <7 11 25 31| Scale is weakly epimorphic with val: <7 11 25 33| Scale is weakly epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 11 26 29| Scale is JI-epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 32| Scale is weakly epimorphic with val: <7 11 27 27| Scale is weakly epimorphic with val: <7 11 27 29| Scale is weakly epimorphic with val: <7 11 27 30| Scale is JI-epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 11 27 33|
FIT/MODE
3: 0 3 0 N M DE I SD: 42.1986 c. M: 51.6825 c. 4: 0 4 0 N M DE I SD: 42.1986 c. M: 51.6825 c. 5: 0 4 1 N G T3 SD: 40.6941 c. M: 51.6825 c. 6: 1 4 1 N M DE I SD: 25.5768 c. M: 31.3250 c. 7: 1 5 1 N M DE I SD: 15.8946 c. M: 19.4668 c. 8: 1 6 1 N M DE I SD: 8.6329 c. M: 10.5732 c. 9: 1 7 1 N M DE I SD: 2.9850 c. M: 3.6559 c. 10: 1 8 1 N M DE I SD: 1.5334 c. M: 1.8780 c. 19: 2 15 2 N M DE I SD: 0.6069 c. M: 0.7433 c. 29: 3 23 3 N M DE I SD: 0.1311 c. M: 0.1606 c. 77: 8 61 8 N M DE I SD: 0.0510 c. M: 0.0625 c. 106: 11 84 11 N M DE I SD: 0.0012 c. M: 0.0014 c. 1725: 179 1367 179 N M DE I SD: 0.0010 c. M: 0.0013 c. 1831: 190 1451 190 N M DE I SD: 0.0009 c. M: 0.0011 c. 1937: 201 1535 201 N M DE I SD: 0.0008 c. M: 0.0010 c. 2043: 212 1619 212 N M DE I SD: 0.0007 c. M: 0.0009 c. 2149: 223 1703 223 N M DE I SD: 0.0006 c. M: 0.0007 c. 2255: 234 1787 234 N M DE I SD: 0.0005 c. M: 0.0006 c. 2361: 245 1871 245 N M DE I SD: 0.0004 c. M: 0.0005 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: 60.0488 cents 5 x 6:7 S SD: 77.8183 cents 6 x x 8 S SD: 0.0000 cents 7:8:9 x S SD: 89.9228 cents 8:9:10:11 H SD: 57.3654 cents 9:10 x 12 S SD: 65.3606 cents 10:11:13 x SD: 56.7967 cents 11:12:14:15 S SD: 36.7246 cents 12:13 x 16 SD: 43.4451 cents 13:14:17 x SD: 39.3584 cents 14:15:18:19 S SD: 25.0724 cents 15:16:19:20 SD: 23.5316 cents 16:17:21 x SD: 29.3013 cents 17:18:22:23 SD: 17.8681 cents 18:19:23:24 SD: 15.7806 cents 19:20 x 25 S SD: 21.8150 cents 20:21:26:27 SD: 13.3292 cents 21:22:27:28 SD: 10.3268 cents 24:25:31:32 SD: 6.4238 cents 27:28:35:36 S SD: 3.8828 cents 30:31:39:40 SD: 3.1180 cents 61:63:79:81 SD: 2.7807 cents 64:66:83:85 SD: 2.6251 cents 65:67:84:87 SD: 2.3723 cents 68:70:88:91 SD: 2.1758 cents 69:71:89:92 SD: 2.0421 cents 72:74:93:96 SD: 1.7895 cents 95:98:123:127 SD: 1.6990 cents 96:99:124:128 SD: 1.2157 cents 99:102:128:132 SD: 0.5302 cents 102:105:132:136 SD: 0.4994 cents 129:133:167:172 SD: 0.4439 cents 201:207:260:268 SD: 0.3638 cents 228:235:295:304 SD: 0.2512 cents 231:238:299:308 SD: 0.1135 cents 330:340:427:440 SD: 0.0795 cents 561:578:726:748 SD: 0.0000 cents