Scala analysis: xen15-chalmers-triadic-diamond-13-11
Triadic diamond for M=13/11, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 13/11 289.209719 tridecimal minor third 2: 33/26 412.745281 tridecimal major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 52/33 787.254719 tridecimal minor sixth 6: 22/13 910.790281 tridecimal major sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/11 289.2097 tridecimal minor third 1: 13/11 289.2097 tridecimal minor third 2: 363/338 123.5356 3: 104/99 85.2997 4: 9/8 203.9100 major whole tone 5: 104/99 85.2997 6: 363/338 123.5356 7: 13/11 289.2097 tridecimal minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 104/99 85.300 cents 1: 2 363/338 123.536 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 13/11 289.210 cents tridecimal minor third 2: 2 44/39 208.835 cents 2: 2 13/11 289.210 cents tridecimal minor third 2: 2 33/26 412.745 cents tridecimal major third 2: 1 169/121 578.419 cents two (tridecimal minor third) 3: 1 1352/1089 374.509 cents 3: 2 33/26 412.745 cents tridecimal major third 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 2 3/2 701.955 cents perfect fifth 4: 2 52/33 787.255 cents tridecimal minor sixth 4: 1 1089/676 825.491 cents two (tridecimal major third) 5: 1 242/169 621.581 cents 5: 2 52/33 787.255 cents tridecimal minor sixth 5: 2 22/13 910.790 cents tridecimal major sixth 5: 2 39/22 991.165 cents 6: 2 22/13 910.790 cents tridecimal major sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 676/363 1076.464 cents 6: 2 99/52 1114.700 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 289.2 412.7 498.0 702.0 787.3 910.8 1200.0 289.2 : 123.5 208.8 412.7 498.0 621.6 910.8 1200.0 412.7 : 85.3 289.2 374.5 498.0 787.3 1076.5 1200.0 498.0 : 203.9 289.2 412.7 702.0 991.2 1114.7 1200.0 702.0 : 85.3 208.8 498.0 787.3 910.8 996.1 1200.0 787.3 : 123.5 412.7 702.0 825.5 910.8 1114.7 1200.0 910.8 : 289.2 578.4 702.0 787.3 991.2 1076.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 85.2997 .. 289.2097 cents 9/8, 203.9100 cents 104/99, 85.2997 cents 2: 208.8353 .. 578.4194 cents 6591/5324, 369.5842 cents 484/507,-80.3744 cents 3: 374.5094 .. 701.9550 cents 3267/2704, 327.4456 cents 8/9,-203.9100 cents 4: 498.0450 .. 825.4906 cents 3267/2704, 327.4456 cents 8/9,-203.9100 cents 5: 621.5806 .. 991.1647 cents 6591/5324, 369.5842 cents 8/9,-203.9100 cents 6: 910.7903 .. 1114.7003 cents 9/8, 203.9100 cents 484/507,-80.3744 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 104/99, 85.2997 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 13/11, 289.2097 cents Average / Smallest step : 2.009720 Largest / Average step : 1.687057 Largest / Smallest step : 3.390512 Median interval of one step : 363/338, 123.5356 cents, amount: 2 Least squares average step : 165.84050 cents, oct.: 1160.88353 cents Scale is not proper Scale is a mode of a 1224-tone equal temperament with octave 2/1 degrees: 295 421 508 716 803 929 1224 Least number of segments generator : 613 of 600.980 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1045 of 1024.510 cents and inv. generated superset size: 59 = 52 more = 842.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.423825 Lumma stability : 0.142166 Lumma impropriety factor : 0.509775 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 352/351, 4.9253 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 11 13 33 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 : 1089 (O: 1089 U: 1089) Highest odd numerator or denominator: 33 Scale harmonicity : 0.011235 Average absolute harmonicity : 0.225849 Specific harmonicity : 0.059698 Fundamental : 1/858, -9.7448 octaves, 0.3049 Hz. Guide tone : 1716, 10.7448 octaves, 448949.470 Hz. Exponens Consonantiae : 1.472328E+06, 20.48967 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 109.0, average 15.57143 Mersenne's string divisions : 842520 Sum of van Prooijen's expressibility: 6.21916, average 0.88845 Sum of Tenney's harmonic distance : 12.93807, average 1.84830 Vogel's harmonic complexity : 28.57143 Wille's k value : 643 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 65.73531, average 2.34769 Lattice compactness (without 2's) : 47.53320, average 1.69761 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -1 .. 1 0.00000 4 2 11: -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 22 24| Scale is weakly epimorphic with val: <7 10 23 24| Scale is weakly epimorphic with val: <7 10 23 25| Scale is weakly epimorphic with val: <7 10 24 25| Scale is weakly epimorphic with val: <7 10 24 26| Scale is weakly epimorphic with val: <7 10 25 26| Scale is weakly epimorphic with val: <7 10 25 27| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 26 28| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly 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 24 29| Scale is weakly epimorphic with val: <7 12 22 26| Scale is weakly epimorphic with val: <7 12 23 24| Scale is weakly epimorphic with val: <7 12 23 27| Scale is weakly epimorphic with val: <7 12 24 25| Scale is weakly epimorphic with val: <7 12 24 28| Scale is weakly epimorphic with val: <7 12 25 26| Scale is weakly epimorphic with val: <7 12 25 29| Scale is weakly epimorphic with val: <7 12 26 27|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 47.8872 c. M: 69.8881 c. 8: 2 1 0 2 0 1 2 N I SD: 33.0050 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 23.3966 c. M:-35.2883 c. 12: 3 1 1 2 1 1 3 N I SD: 8.9872 c. M:-12.7453 c. Mela Yagapriya, Raga Kalahamsa 17: 4 2 1 3 1 2 4 N I SD: 7.1462 c. M:-10.7841 c. 29: 7 3 2 5 2 3 7 N I SD: 1.0037 c. M: 1.4933 c. 125: 30 13 9 21 9 13 30 N I SD: 0.8945 c. M: 1.2097 c. 137: 33 14 10 23 10 14 33 N I SD: 0.8723 c. M:-1.2251 c. 154: 37 16 11 26 11 16 37 N I SD: 0.6084 c. M: 0.8980 c. 166: 40 17 12 28 12 17 40 N I SD: 0.5481 c. M:-0.7502 c. 183: 44 19 13 31 13 19 44 N I SD: 0.4490 c. M: 0.6851 c. 195: 47 20 14 33 14 20 47 N I SD: 0.3231 c. M:-0.4376 c. 224: 54 23 16 38 16 23 54 N I SD: 0.1644 c. M:-0.2453 c. 253: 61 26 18 43 18 26 61 N I SD: 0.0826 c. M: 0.1183 c. 689: 166 71 49 117 49 71 166 N I SD: 0.0642 c. M: 0.0951 c. 718: 173 74 51 122 51 74 173 N I SD: 0.0535 c. M: 0.0732 c. 942: 227 97 67 160 67 97 227 N I SD: 0.0312 c. M:-0.0442 c. 971: 234 100 69 165 69 100 234 N I SD: 0.0183 c. M:-0.0251 c. 1224: 295 126 87 208 87 126 295 N I SD: 0.0044 c. M: 0.0060 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 x 5:6 S SD: 8.8105 cents 4 x 5 x 6 x 7:8 S SD: 15.9428 cents 5:6 x 7 x 8 x 10 S SD: 23.0922 cents 6:7 x 8:9 x 10:12 S SD: 6.9214 cents 7:8:9 x x 11:12:14 SD: 13.2497 cents 9:11 x 12 x 14:15:18 SD: 13.5421 cents 10:12:13 x 15:16:17:20 SD: 9.3964 cents 11:13:14:15 x 17:19:22 SD: 10.4349 cents 12:14:15:16:18:19:20:24 S SD: 6.3330 cents 13:15 x 17 x 20:22:26 SD: 13.5195 cents 14:17:18:19:21:22:24:28 SD: 9.2153 cents 15:18:19:20:23:24:25:30 SD: 8.5189 cents 16:19:20:21:24:25:27:32 SD: 5.9746 cents 22:26:28:29:33:35:37:44 SD: 4.0519 cents 26:31:33:35:39:41:44:52 SD: 3.2266 cents 33:39:42:44:50:52:56:66 SD: 2.6654 cents 38:45:48:51:57:60:64:76 SD: 2.4381 cents 42:50:53:56:63:66:71:84 SD: 2.4173 cents 45:53:57:60:68:71:76:90 SD: 2.1563 cents 48:57:61:64:72:76:81:96 SD: 1.8457 cents 56:66:71:75:84:88:95:112 SD: 1.6041 cents 66:78:84:88:99:104:112:132 SD: 0.9622 cents 78:92:99:104:117:123:132:156 SD: 0.5214 cents 160:189:203:213:240:252:271:320 SD: 0.4807 cents 182:215:231:243:273:287:308:364 SD: 0.3995 cents 186:220:236:248:279:293:315:372 SD: 0.2950 cents 264:312:335:352:396:416:447:528 SD: 0.1398 cents 516:610:655:688:774:813:873:1032 SD: 0.1064 cents 594:702:754:792:891:936:1005:1188 SD: 0.0621 cents