Scala analysis: xen15-chalmers-triadic-reversed-diamond-13-11
Triadic reversed 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: 44/39 208.835280 2: 13/11 289.209719 tridecimal minor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 22/13 910.790281 tridecimal major sixth 6: 39/22 991.164720 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 44/39 208.8353 1: 44/39 208.8353 2: 507/484 80.3744 3: 44/39 208.8353 4: 9/8 203.9100 major whole tone 5: 44/39 208.8353 6: 507/484 80.3744 7: 44/39 208.8353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 507/484 80.374 cents 1: 1 9/8 203.910 cents major whole tone 1: 4 44/39 208.835 cents 2: 4 13/11 289.210 cents tridecimal minor third 2: 2 33/26 412.745 cents tridecimal major third 2: 1 1936/1521 417.671 cents 3: 2 117/88 493.120 cents tridecimal gentle fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 242/169 621.581 cents 4: 1 169/121 578.419 cents two (tridecimal minor third) 4: 4 3/2 701.955 cents perfect fifth 4: 2 176/117 706.880 cents 5: 1 1521/968 782.329 cents 5: 2 52/33 787.255 cents tridecimal minor sixth 5: 4 22/13 910.790 cents tridecimal major sixth 6: 4 39/22 991.165 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 968/507 1119.626 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 : 208.8 289.2 498.0 702.0 910.8 991.2 1200.0 208.8 : 80.4 289.2 493.1 702.0 782.3 991.2 1200.0 289.2 : 208.8 412.7 621.6 702.0 910.8 1119.6 1200.0 498.0 : 203.9 412.7 493.1 702.0 910.8 991.2 1200.0 702.0 : 208.8 289.2 498.0 706.9 787.3 996.1 1200.0 910.8 : 80.4 289.2 498.0 578.4 787.3 991.2 1200.0 991.2 : 208.8 417.7 498.0 706.9 910.8 1119.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 80.3744 .. 208.8353 cents 21296/19773, 128.4608 cents 507/484, 80.3744 cents 2: 289.2097 .. 417.6706 cents 21296/19773, 128.4608 cents 507/484, 80.3744 cents 3: 493.1197 .. 621.5806 cents 21296/19773, 128.4608 cents 177957/170368, 75.4492 cents 4: 578.4194 .. 706.8803 cents 21296/19773, 128.4608 cents 28561/29282,-43.1611 cents 5: 782.3294 .. 910.7903 cents 21296/19773, 128.4608 cents 177957/170368, 75.4492 cents 6: 991.1647 .. 1119.6256 cents 21296/19773, 128.4608 cents 507/484, 80.3744 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 507/484, 80.3744 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 44/39, 208.8353 cents Average / Smallest step : 2.132874 Largest / Average step : 1.218206 Largest / Smallest step : 2.598280 Median interval of one step : 44/39, 208.8353 cents, amount: 4 Most common interval of one step : 44/39, 208.8353 cents, amount: 4 Least squares average step : 171.35821 cents, oct.: 1199.50747 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : LSLMLSL Scale is a Constant Structure, by a margin of 43.16112 cents Scale diversity : 1.306977 Lumma stability : 0.393663 Lumma impropriety factor : 0.035968 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 : 352/351, 4.9253 cents Number of recognisable fifths : 6, average 703.5968 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete diamond : 11 13 39 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 : 0.011235 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 : 4252920 Sum of van Prooijen's expressibility: 6.36426, average 0.90918 Sum of Tenney's harmonic distance : 12.93807, average 1.84830 Vogel's harmonic complexity : 28.57143 Wille's k value : 760 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 64.97815, average 2.32065 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 27| Scale is weakly epimorphic with val: <7 10 22 28| Scale is weakly epimorphic with val: <7 10 23 28| Scale is weakly epimorphic with val: <7 10 23 29| Scale is weakly epimorphic with val: <7 10 24 29| Scale is JI-epimorphic with val: <7 11 22 24| Scale is weakly epimorphic with val: <7 11 23 24| Scale is JI-epimorphic with val: <7 11 23 25| Scale is weakly epimorphic with val: <7 11 24 25| Scale is JI-epimorphic with val: <7 11 24 26| = patent Scale is weakly epimorphic with val: <7 11 25 26| Scale is JI-epimorphic with val: <7 11 25 27| Scale is weakly epimorphic with val: <7 11 26 27| Scale is JI-epimorphic with val: <7 11 26 28| Scale is weakly epimorphic with val: <7 12 22 25| Scale is weakly epimorphic with val: <7 12 22 28| Scale is weakly epimorphic with val: <7 12 23 26| Scale is weakly epimorphic with val: <7 12 23 29| Scale is weakly epimorphic with val: <7 12 24 27| Scale is weakly epimorphic with val: <7 12 25 28| Scale is weakly epimorphic with val: <7 12 26 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 36.0201 c. M: 53.6474 c. Lebeng 10: 2 0 2 2 2 0 2 N M DE I SD: 32.5947 c. M: 49.2097 c. 12: 2 1 2 2 2 1 2 P M ME I SD: 7.5274 c. M: 10.7903 c. G.Phrygian, M.Dorian, M.Hypomixolydian, Kafi That, Mela Kharaharapriya, Raga Bageshri, Bhimpalasi, Huseni, Kanara, Kapi, Nayaki Kanada, Ritigaula, Sriraga, Mischung 5, Gregorian nr.8, Eskimo Heptatonic, Yu: China, Hyojo, Oshikicho, Banshikicho: Japan, Nam: Vietnam 17: 3 1 3 3 3 1 3 N M DE I SD: 4.5046 c. M: 6.8568 c. Supra-7 29: 5 2 5 5 5 2 5 N M DE I SD: 1.3296 c. M:-1.9387 c. 104: 18 7 18 18 18 7 18 N M DE I SD: 1.2470 c. M:-1.8912 c. 133: 23 9 23 23 23 9 23 N M DE I SD: 1.2221 c. M: 1.8044 c. 137: 24 9 24 23 24 9 24 N T3 I SD: 0.9915 c. M:-1.3837 c. 149: 26 10 26 25 26 10 26 N T3 I SD: 0.8427 c. M:-1.2839 c. 166: 29 11 29 28 29 11 29 N T3 I SD: 0.5882 c. M:-0.8033 c. 178: 31 12 31 30 31 12 31 N T3 I SD: 0.5793 c. M:-0.8314 c. 195: 34 13 34 33 34 13 34 N T3 I SD: 0.3072 c. M:-0.4165 c. 224: 39 15 39 38 39 15 39 N T3 I SD: 0.1110 c. M: 0.1693 c. 253: 44 17 44 43 44 17 44 N T3 I SD: 0.0985 c. M: 0.1396 c. 477: 83 32 83 81 83 32 83 N T3 I SD: 0.0660 c. M: 0.0985 c. 718: 125 48 125 122 125 48 125 N T3 I SD: 0.0574 c. M:-0.0784 c. 747: 130 50 130 127 130 50 130 N T3 I SD: 0.0401 c. M: 0.0531 c. 971: 169 65 169 165 169 65 169 N T3 I SD: 0.0170 c. M: 0.0233 c. 1224: 213 82 213 208 213 82 213 N T3 I SD: 0.0077 c. M:-0.0118 c. 2195: 382 147 382 373 382 147 382 N T3 I SD: 0.0046 c. M: 0.0070 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: 8.8105 cents 4 x 5 x 6 x 7:8 S SD: 24.9101 cents 5 x 6:7 x 8:9:10 S SD: 26.8038 cents 6 x 7:8:9:10:11:12 S SD: 11.2850 cents 7:8 x 9:11:12 x 14 SD: 21.3994 cents 8:9 x 11:12 x 14:16 SD: 11.5953 cents 10:11:12:13:15:17:18:20 SD: 10.4014 cents 12 x 14:16:18:20:21:24 S SD: 6.8651 cents 13:15 x 17:20:22:23:26 SD: 11.2751 cents 14:16:17:19:21:24:25:28 SD: 9.3657 cents 15:17:18:20:23:25:27:30 SD: 8.5778 cents 16:18:19:21:24:27:28:32 SD: 5.2680 cents 22:25:26:29:33:37:39:44 SD: 3.6783 cents 30:34:35:40:45:51:53:60 SD: 3.6630 cents 32:36:38:43:48:54:57:64 SD: 2.7402 cents 38:43:45:51:57:64:67:76 SD: 2.5739 cents 39:44:46:52:59:66:69:78 SD: 2.2152 cents 48:54:57:64:72:81:85:96 SD: 1.5707 cents 54:61:64:72:81:91:96:108 SD: 1.4750 cents 62:70:73:83:93:105:110:124 SD: 1.3959 cents 72:81:85:96:108:122:128:144 SD: 1.0758 cents 78:88:92:104:117:132:138:156 SD: 0.6905 cents 110:124:130:147:165:186:195:220 SD: 0.6315 cents 126:142:149:168:189:213:223:252 SD: 0.5732 cents 132:149:156:176:198:223:234:264 SD: 0.4449 cents 186:210:220:248:279:315:330:372 SD: 0.3864 cents 204:230:241:272:306:345:362:408 SD: 0.3538 cents 258:291:305:344:387:437:457:516 SD: 0.3096 cents 264:298:312:352:396:447:468:528 SD: 0.1806 cents 374:422:442:499:561:633:663:748 SD: 0.1706 cents 390:440:461:520:585:660:691:780 SD: 0.1390 cents 462:521:546:616:693:782:819:924 SD: 0.1198 cents 468:528:553:624:702:792:830:936 SD: 0.1158 cents 546:616:645:728:819:924:968:1092 SD: 0.1071 cents 594:670:702:792:891:1005:1053:1188 SD: 0.0803 cents