Scala analysis: xen15-chalmers-triadic-reversed-diamond-13-10
Triadic reversed diamond for M=13/10, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 40/39 43.831051 tridecimal minor diesis 2: 13/10 454.213948 tridecimal semi-diminished fourth 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 20/13 745.786052 tridecimal semi-augmented fifth 6: 39/20 1156.168949 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 40/39 43.8311 tridecimal minor diesis 1: 40/39 43.8311 tridecimal minor diesis 2: 507/400 410.3829 3: 40/39 43.8311 tridecimal minor diesis 4: 9/8 203.9100 major whole tone 5: 40/39 43.8311 tridecimal minor diesis 6: 507/400 410.3829 7: 40/39 43.8311 tridecimal minor diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 40/39 43.831 cents tridecimal minor diesis 1: 1 9/8 203.910 cents major whole tone 1: 2 507/400 410.383 cents 2: 1 1600/1521 87.662 cents two (tridecimal minor diesis) 2: 2 15/13 247.741 cents tridecimal 5/4-tone 2: 4 13/10 454.214 cents tridecimal semi-diminished fourth 3: 1 200/169 291.572 cents 3: 4 4/3 498.045 cents perfect fourth 3: 2 117/80 658.124 cents 4: 2 160/117 541.876 cents 4: 4 3/2 701.955 cents perfect fifth 4: 1 169/100 908.428 cents two (tridecimal semi-diminished fourth) 5: 4 20/13 745.786 cents tridecimal semi-augmented fifth 5: 2 26/15 952.259 cents tridecimal semi-augmented sixth 5: 1 1521/800 1112.338 cents 6: 2 800/507 789.617 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 4 39/20 1156.169 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 43.8 454.2 498.0 702.0 745.8 1156.2 1200.0 43.8 : 410.4 454.2 658.1 702.0 1112.3 1156.2 1200.0 454.2 : 43.8 247.7 291.6 702.0 745.8 789.6 1200.0 498.0 : 203.9 247.7 658.1 702.0 745.8 1156.2 1200.0 702.0 : 43.8 454.2 498.0 541.9 952.3 996.1 1200.0 745.8 : 410.4 454.2 498.0 908.4 952.3 1156.2 1200.0 1156.2: 43.8 87.7 498.0 541.9 745.8 789.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 43.8311 .. 410.3829 cents 19773/16000, 366.5518 cents 40/39, 43.8311 cents 2: 87.6621 .. 454.2139 cents 19773/16000, 366.5518 cents 640000/771147,-322.7208 cents 3: 291.5721 .. 658.1239 cents 19773/16000, 366.5518 cents 2000/2197,-162.6418 cents 4: 541.8761 .. 908.4279 cents 19773/16000, 366.5518 cents 12800/13689,-116.2479 cents 5: 745.7861 .. 1112.3379 cents 19773/16000, 366.5518 cents 2000/2197,-162.6418 cents 6: 789.6171 .. 1156.1689 cents 19773/16000, 366.5518 cents 640000/771147,-322.7208 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 40/39, 43.8311 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 507/400, 410.3829 cents Average / Smallest step : 3.911122 Largest / Average step : 2.393900 Largest / Smallest step : 9.362835 Median interval of one step : 40/39, 43.8311 cents, amount: 4 Most common interval of one step : 40/39, 43.8311 cents, amount: 4 Least squares average step : 173.71541 cents, oct.: 1216.00790 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1889-tone equal temperament with octave 2/1 degrees: 69 715 784 1105 1174 1820 1889 Least number of segments generator : 945 of 600.318 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1824 of 1158.708 cents and inv. generated superset size: 57 = 50 more = 814.286% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABACABA Step pattern size order : SLSMSLS Scale is a Constant Structure, by a margin of 43.83105 cents Scale diversity : 1.393438 Lumma stability : 0.073052 Lumma impropriety factor : 0.707793 Rothenberg efficiency : 0.506122 redundancy: 0.493878 Efficiency x scale size : 3.542857 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 40/39, 43.8311 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Scale is a complete diamond : 5 13 39 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 100.0000% Scale is differentially coherent in interval classes 3 and 4 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 3-4 -- Rational properties -- Prime limit : 13 Odd number limit : 1521 (O: 1521 U: 1521) Highest odd numerator or denominator: 39 Scale harmonicity : 0.014828 Average absolute harmonicity : 0.230414 Specific harmonicity : 0.079081 Fundamental : 1/780, -9.6073 octaves, 0.3354 Hz. Guide tone : 1560, 10.6073 octaves, 408135.882 Hz. Exponens Consonantiae : 1.216800E+06, 20.21466 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 104.5, average 14.92857 Mersenne's string divisions : 123819465 Sum of van Prooijen's expressibility: 6.36426, average 0.90918 Sum of Tenney's harmonic distance : 12.77250, average 1.82464 Vogel's harmonic complexity : 23.57143 Wille's k value : 760 Wilson's harmonic complexity : 42 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 78.76043, average 2.81287 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 12 1 3: -1 .. 1 0.00000 4 2 5: -1 .. 1 0.00000 4 13: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 15 27| Scale is weakly epimorphic with val: <7 10 15 28| Scale is weakly epimorphic with val: <7 10 16 28| Scale is weakly epimorphic with val: <7 10 16 29| Scale is weakly epimorphic with val: <7 10 17 29| Scale is weakly epimorphic with val: <7 10 18 24| Scale is JI-epimorphic with val: <7 11 15 24| Scale is weakly epimorphic with val: <7 11 16 24| Scale is JI-epimorphic with val: <7 11 16 25| Scale is weakly epimorphic with val: <7 11 17 25| Scale is JI-epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 18 26| Scale is JI-epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 12 15 25| Scale is weakly epimorphic with val: <7 12 15 28| Scale is weakly epimorphic with val: <7 12 16 26| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 17 27| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 18 28|
FIT/MODE
7: 0 3 0 1 0 3 0 N T3 I SD: 40.6853 c. M: 60.0718 c. 8: 0 3 0 2 0 3 0 N T3 I SD: 34.8353 c. M:-48.0450 c. 10: 0 4 0 2 0 4 0 N T3 I SD: 28.8429 c. M:-43.8311 c. 16: 1 5 1 2 1 5 1 N T3 I SD: 22.1413 c. M:-31.1689 c. 19: 1 6 1 3 1 6 1 N T3 I SD: 12.7867 c. M:-19.3268 c. 21: 1 7 1 3 1 7 1 N T3 I SD: 11.3332 c. M:-16.2407 c. 24: 1 8 1 4 1 8 1 N T3 I SD: 4.1278 c. M:-6.1689 c. 29: 1 10 1 5 1 10 1 N T3 I SD: 1.6177 c. M:-2.4517 c. 53: 2 18 2 9 2 18 2 N T3 I SD: 1.0727 c. M:-1.4520 c. 82: 3 28 3 14 3 28 3 N T3 I SD: 0.3956 c. M: 0.5554 c. 272: 10 93 10 46 10 93 10 N T3 I SD: 0.3189 c. M:-0.4844 c. 301: 11 103 11 51 11 103 11 N T3 I SD: 0.2141 c. M:-0.2939 c. 354: 13 121 13 60 13 121 13 N T3 I SD: 0.1884 c. M:-0.2601 c. 383: 14 131 14 65 14 131 14 N T3 I SD: 0.0865 c. M:-0.1273 c. 465: 17 159 17 79 17 159 17 N T3 I SD: 0.0261 c. M:-0.0399 c. 959: 35 328 35 163 35 328 35 N T3 I SD: 0.0241 c. M:-0.0354 c. 1342: 49 459 49 228 49 459 49 N T3 I SD: 0.0219 c. M:-0.0334 c. 1424: 52 487 52 242 52 487 52 N T3 I SD: 0.0084 c. M: 0.0113 c. 1889: 69 646 69 321 69 646 69 N T3 I SD: 0.0036 c. M: 0.0054 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 46.1909 cents 4 x 5 x 6 x x 8 S SD: 22.6334 cents 5 x x 7 x 8 x 10 SD: 36.1250 cents 6 x x 8:9 x x 12 S SD: 0.0000 cents 7:8:9 x x 11 x 14 SD: 47.9653 cents 8:9:10:11:12 x x 16 S SD: 36.3724 cents 9:10 x 12 x 14 x 18 SD: 34.9717 cents 10:11:13 x 15 x x 20 SD: 30.2933 cents 11:12:14:15 x 17:21:22 SD: 20.8683 cents 12:13 x 16:18 x 23:24 SD: 19.8665 cents 13:14:17 x x 20:25:26 SD: 17.6843 cents 14:15:18:19:21:22:27:28 SD: 13.3518 cents 15:16 x 20 x 23:29:30 SD: 13.9495 cents 16:17:21 x 24:25:31:32 SD: 11.6130 cents 17:18:22:23 x 26:33:34 SD: 10.4150 cents 18:19:23:24:27:28:35:36 SD: 8.7582 cents 19:20:25 x x 29:37:38 SD: 10.3012 cents 20:21:26:27:30:31:39:40 SD: 6.8231 cents 21:22:27:28 x 32:41:42 SD: 7.4390 cents 22:23 x 29:33:34:43:44 SD: 6.5968 cents 23:24:30:31 x 35:45:46 SD: 6.8030 cents 24:25:31:32:36:37:47:48 SD: 4.3139 cents 25:26 x 33 x 38:49:50 SD: 7.4761 cents 26:27:34:35:39:40:51:52 SD: 4.3930 cents 30:31:39:40:45:46:59:60 SD: 2.9202 cents 36:37:47:48:54:55:70:72 SD: 2.2013 cents 44:45:57:59:66:68:86:88 SD: 2.1906 cents 46:47:60:61:69:71:90:92 SD: 2.1719 cents 54:55:70:72:81:83:105:108 SD: 2.0047 cents 66:68:86:88:99:102:129:132 SD: 1.7831 cents 70:72:91:93:105:108:137:140 SD: 1.6114 cents 72:74:94:96:108:111:140:144 SD: 1.4629 cents 74:76:96:99:111:114:144:148 SD: 1.2036 cents 76:78:99:101:114:117:148:152 SD: 1.0386 cents 78:80:101:104:117:120:152:156 SD: 0.9910 cents 80:82:104:107:120:123:156:160 SD: 0.8021 cents 114:117:148:152:171:175:222:228 SD: 0.7378 cents 120:123:156:160:180:185:234:240 SD: 0.5374 cents 156:160:203:208:234:240:304:312 SD: 0.2931 cents 234:240:304:312:351:360:456:468 SD: 0.2300 cents 240:246:312:320:360:369:468:480 SD: 0.2187 cents 360:369:468:480:540:554:702:720 SD: 0.1692 cents 390:400:507:520:585:600:761:780 SD: 0.1625 cents 420:431:546:560:630:646:819:840 SD: 0.1450 cents 540:554:702:720:810:831:1053:1080 SD: 0.0971 cents