Scala analysis: xen15-chalmers-triadic-reversed-diamond-39-32
Triadic reversed diamond for M=39/32, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 128/117 155.562336 2: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 64/39 857.517337 39th subharmonic 6: 117/64 1044.437664 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 128/117 155.5623 1: 128/117 155.5623 2: 4563/4096 186.9203 3: 128/117 155.5623 4: 9/8 203.9100 major whole tone 5: 128/117 155.5623 6: 4563/4096 186.9203 7: 128/117 155.5623
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 128/117 155.562 cents 1: 2 4563/4096 186.920 cents 1: 1 9/8 203.910 cents major whole tone 2: 1 16384/13689 311.125 cents 2: 4 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 3: 4 4/3 498.045 cents perfect fourth 3: 1 2048/1521 515.035 cents 3: 2 351/256 546.393 cents 4: 2 512/351 653.607 cents 4: 1 1521/1024 684.965 cents two (39th harmonic, Zalzal wosta of Ibn Sina) 4: 4 3/2 701.955 cents perfect fifth 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 4 64/39 857.517 cents 39th subharmonic 5: 1 13689/8192 888.875 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 8192/4563 1013.080 cents 6: 4 117/64 1044.438 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 : 155.6 342.5 498.0 702.0 857.5 1044.4 1200.0 155.6 : 186.9 342.5 546.4 702.0 888.9 1044.4 1200.0 342.5 : 155.6 359.5 515.0 702.0 857.5 1013.1 1200.0 498.0 : 203.9 359.5 546.4 702.0 857.5 1044.4 1200.0 702.0 : 155.6 342.5 498.0 653.6 840.5 996.1 1200.0 857.5 : 186.9 342.5 498.0 685.0 840.5 1044.4 1200.0 1044.4: 155.6 311.1 498.0 653.6 857.5 1013.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 155.5623 .. 203.9100 cents 1053/1024, 48.3477 cents 128/117, 155.5623 cents 2: 311.1247 .. 359.4723 cents 1053/1024, 48.3477 cents 131072/123201, 107.2147 cents 3: 498.0450 .. 546.3927 cents 1053/1024, 48.3477 cents 13/12, 138.5727 cents 4: 653.6073 .. 701.9550 cents 1053/1024, 48.3477 cents 131072/123201, 107.2147 cents 5: 840.5277 .. 888.8753 cents 1053/1024, 48.3477 cents 13/12, 138.5727 cents 6: 996.0900 .. 1044.4377 cents 1053/1024, 48.3477 cents 131072/123201, 107.2147 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 128/117, 155.5623 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.101993 Largest / Average step : 1.189475 Largest / Smallest step : 1.310793 Median interval of one step : 128/117, 155.5623 cents, amount: 4 Most common interval of one step : 128/117, 155.5623 cents, amount: 4 Least squares average step : 172.11925 cents, oct.: 1204.83477 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACABA Step pattern size order : SMSLSMS Scale is a Constant Structure, by a margin of 107.21467 cents Scale diversity : 1.240139 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.758262 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 : 512/507, 16.9897 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is Dorian octave species of abstract tetrachord Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale is a complete diamond : 1 3 117 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 : 13689 (O: 13689 U: 13689) Highest odd numerator or denominator: 117 Scale harmonicity : 0.014711 Average absolute harmonicity : 0.230264 Specific harmonicity : 0.079500 Fundamental : 1/7488, -12.8704 octaves, 0.0349 Hz. Guide tone : 14976, 13.8704 octaves, 3918104.466 Hz. Exponens Consonantiae : 1.121403E+08, 26.74073 octaves Euler's gradus suavitatis : 46 Sum of Mann's harmonic distance : 307.5, average 43.92857 Mersenne's string divisions : 972884955 Sum of van Prooijen's expressibility: 8.27274, average 1.18182 Sum of Tenney's harmonic distance : 16.70158, average 2.38594 Vogel's harmonic complexity : 25.57143 Wille's k value : 6844 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 165.66444, average 5.91659 Lattice compactness (without 2's) : 52.73791, average 1.88350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 7 0.57143 28 1 3: -2 .. 2 0.00000 8 2 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 24| Scale is weakly epimorphic with val: <7 11 25| Scale is JI-epimorphic with val: <7 11 26| = patent Scale is weakly epimorphic with val: <7 12 26| Scale is weakly epimorphic with val: <7 12 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 12.1378 c. M:-16.2407 c. Lebeng 17: 2 3 2 3 2 3 2 SP M ME I SD: 9.7359 c. M: 14.3859 c. Neutral Dorian, Maqamic-7 24: 3 4 3 4 3 4 3 SP M ME I SD: 5.1066 c. M: 7.5173 c. Neutral Dorian, Misaelides 2nd Byzantine mode, Iced Fridgian, Maqam Sikah Baladi, Maqamic-7 31: 4 5 4 5 4 5 4 SP M ME I SD: 4.2165 c. M:-5.9044 c. Neutral Dorian, Maqamic-7 39: 5 6 5 7 5 6 5 SP T3 I SD: 3.8557 c. M:-5.7373 c. 46: 6 7 6 8 6 7 6 SP T3 I SD: 2.2604 c. M: 3.3522 c. 53: 7 8 7 9 7 8 7 SP T3 I SD: 2.1882 c. M: 2.9282 c. 70: 9 11 9 12 9 11 9 SP T3 I SD: 0.8592 c. M: 1.2766 c. 77: 10 12 10 13 10 12 10 SP T3 I SD: 0.4311 c. M:-0.6563 c. 147: 19 23 19 25 19 23 19 SP T3 I SD: 0.3205 c. M: 0.4603 c. 224: 29 35 29 38 29 35 29 SP T3 I SD: 0.2455 c. M: 0.3745 c. 270: 35 42 35 46 35 42 35 SP T3 I SD: 0.1995 c. M:-0.2672 c. 347: 45 54 45 59 45 54 45 SP T3 I SD: 0.0783 c. M: 0.1196 c. 424: 55 66 55 72 55 66 55 SP T3 I SD: 0.0658 c. M: 0.0980 c. 494: 64 77 64 84 64 77 64 SP T3 I SD: 0.0653 c. M: 0.0967 c. 571: 74 89 74 97 74 89 74 SP T3 I SD: 0.0490 c. M: 0.0743 c. 841: 109 131 109 143 109 131 109 SP T3 I SD: 0.0435 c. M: 0.0664 c. 918: 119 143 119 156 119 143 119 SP T3 I SD: 0.0048 c. M: 0.0068 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: 8.9471 cents 4 x 5 x 6 x 7:8 S SD: 21.8493 cents 5 x 6:7 x 8:9:10 S SD: 20.4908 cents 6 x 7:8:9:10:11:12 S SD: 13.3976 cents 7:8 x 9 x 11:13:14 SD: 25.3404 cents 8:9:10:11:12:13:15:16 SD: 13.7814 cents 9:10:11:12:14:15:16:18 S SD: 12.5899 cents 10:11:12:13:15:16:18:20 SD: 10.4709 cents 12:13:15:16:18:20:22:24 SD: 7.7651 cents 18:20:22:24:27:30:33:36 S SD: 5.5133 cents 22:24:27:29:33:36:40:44 SD: 3.7107 cents 30:33:37:40:45:49:55:60 SD: 3.5098 cents 33:36:40:44:50:54:60:66 SD: 3.2874 cents 36:39:44:48:54:59:66:72 SD: 2.6429 cents 42:46:51:56:63:69:77:84 SD: 1.2129 cents 64:70:78:85:96:105:117:128 SD: 0.9717 cents 86:94:105:115:129:141:157:172 SD: 0.9646 cents 105:115:128:140:158:172:192:210 SD: 0.9451 cents 106:116:129:141:159:174:194:212 SD: 0.7474 cents 128:140:156:171:192:210:234:256 SD: 0.4901 cents 150:164:183:200:225:246:274:300 SD: 0.3887 cents 192:210:234:256:288:315:351:384 SD: 0.0854 cents