Scala analysis: xen15-chalmers-triadic-diamond-35-27
Triadic diamond for M=35/27, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 81/70 252.680383 Al-Hwarizmi's lute middle finger 2: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 54/35 750.725382 septimal semi-augmented fifth 6: 140/81 947.319617 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 81/70 252.6804 Al-Hwarizmi's lute middle finger 1: 81/70 252.6804 Al-Hwarizmi's lute middle finger 2: 2450/2187 196.5942 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 9/8 203.9100 major whole tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 2450/2187 196.5942 7: 81/70 252.6804 Al-Hwarizmi's lute middle finger
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 2450/2187 196.594 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 2 280/243 245.365 cents 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 2: 1 6561/4900 505.361 cents two (Al-Hwarizmi's lute middle finger) 3: 1 1458/1225 301.451 cents 3: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 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 54/35 750.725 cents septimal semi-augmented fifth 4: 1 1225/729 898.549 cents two (septimal semi-diminished fourth, 9/4-tone) 5: 1 9800/6561 694.639 cents 5: 2 54/35 750.725 cents septimal semi-augmented fifth 5: 2 140/81 947.320 cents 5: 2 243/140 954.635 cents 6: 2 140/81 947.320 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 2187/1225 1003.406 cents 6: 2 35/18 1151.230 cents septimal semi-diminished octave 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 : 252.7 449.3 498.0 702.0 750.7 947.3 1200.0 252.7 : 196.6 245.4 449.3 498.0 694.6 947.3 1200.0 449.3 : 48.8 252.7 301.5 498.0 750.7 1003.4 1200.0 498.0 : 203.9 252.7 449.3 702.0 954.6 1151.2 1200.0 702.0 : 48.8 245.4 498.0 750.7 947.3 996.1 1200.0 750.7 : 196.6 449.3 702.0 898.5 947.3 1151.2 1200.0 947.3 : 252.7 505.4 702.0 750.7 954.6 1003.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 48.7704 .. 252.6804 cents 9/8, 203.9100 cents 36/35, 48.7704 cents 2: 245.3646 .. 505.3608 cents 1594323/1372000, 259.9962 cents 19600/19683,-7.3158 cents 3: 301.4508 .. 701.9550 cents 1225/972, 400.5042 cents 8/9,-203.9100 cents 4: 498.0450 .. 898.5492 cents 1225/972, 400.5042 cents 8/9,-203.9100 cents 5: 694.6392 .. 954.6354 cents 1594323/1372000, 259.9962 cents 8/9,-203.9100 cents 6: 947.3196 .. 1151.2296 cents 9/8, 203.9100 cents 19600/19683,-7.3158 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 36/35, 48.7704 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 81/70, 252.6804 cents Average / Smallest step : 3.515014 Largest / Average step : 1.473969 Largest / Smallest step : 5.181021 Median interval of one step : 2450/2187, 196.5942 cents, amount: 2 Least squares average step : 166.36235 cents, oct.: 1164.53646 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.193155 Lumma stability : 0.081284 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 : 19683/19600, 7.3158 cents Number of recognisable fifths : 5, average 700.4918 cents Scale is a complete diamond : 27 35 81 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 : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.017330 Average absolute harmonicity : 0.233684 Specific harmonicity : 0.093323 Fundamental : 1/5670, -12.4691 octaves, 0.0461 Hz. Guide tone : 11340, 13.4691 octaves, 2966833.911 Hz. Exponens Consonantiae : 6.429780E+07, 25.93827 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 269.0, average 38.42857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.85935, average 1.12276 Sum of Tenney's harmonic distance : 16.21845, average 2.31692 Vogel's harmonic complexity : 25.57143 Wille's k value : 4252 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 112.65369, average 4.02335 Lattice compactness (without 2's) : 98.86508, average 3.53090 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 8 1 3: -4 .. 4 0.00000 16 2 5: -1 .. 1 0.00000 4 7: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 24 / 7 = 3.42857 Scale is weakly epimorphic with val: <7 10 16 22| Scale is weakly epimorphic with val: <7 10 17 21| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 18 20| Scale is weakly epimorphic with val: <7 10 18 21| Scale is weakly epimorphic with val: <7 11 16 22| Scale is weakly epimorphic with val: <7 11 17 21| Scale is weakly epimorphic with val: <7 11 17 22| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 11 18 21| Scale is weakly epimorphic with val: <7 12 15 18| Scale is weakly epimorphic with val: <7 12 15 22| Scale is weakly epimorphic with val: <7 12 16 21| Scale is weakly epimorphic with val: <7 12 17 20| Scale is weakly epimorphic with val: <7 12 18 19| Scale is weakly epimorphic with val: <7 12 18 22|
FIT/MODE
7: 1 2 0 1 0 2 1 N T3 I SD: 56.2953 c. M: 81.2518 c. 8: 2 1 0 2 0 1 2 N I SD: 36.0476 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 33.2474 c. M: 49.2746 c. 10: 2 2 0 2 0 2 2 N D3 I SD: 20.2164 c. M:-30.7254 c. 14: 3 2 1 2 1 2 3 N G I SD: 14.2658 c. M: 20.7032 c. 19: 4 3 1 3 1 3 4 N G I SD: 5.4381 c. M:-7.2182 c. 24: 5 4 1 4 1 4 5 N G I SD: 1.8152 c. M: 2.6804 c. 94: 20 15 4 16 4 15 20 N I SD: 1.9328 c. M:-2.6388 c. 99: 21 16 4 17 4 16 21 N I SD: 1.2257 c. M:-1.8651 c. 118: 25 19 5 20 5 19 25 N I SD: 1.2865 c. M: 1.8170 c. 123: 26 20 5 21 5 20 26 N I SD: 0.6404 c. M:-0.9782 c. 147: 31 24 6 25 6 24 31 N I SD: 0.2616 c. M: 0.3808 c. 171: 36 28 7 29 7 28 36 N I SD: 0.1370 c. M:-0.2006 c. 470: 99 77 19 80 19 77 99 N I SD: 0.1130 c. M:-0.1727 c. 494: 104 81 20 84 20 81 104 N I SD: 0.0777 c. M: 0.1181 c. 641: 135 105 26 109 26 105 135 N I SD: 0.0489 c. M:-0.0731 c. 665: 140 109 27 113 27 109 140 N I SD: 0.0368 c. M: 0.0488 c. 812: 171 133 33 138 33 133 171 N I SD: 0.0190 c. M:-0.0290 c. 1477: 311 242 60 251 60 242 311 N I SD: 0.0095 c. M: 0.0145 c. 1648: 347 270 67 280 67 270 347 N I SD: 0.0092 c. M:-0.0133 c. 2289: 482 375 93 389 93 375 482 N I SD: 0.0072 c. M: 0.0109 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: 20.9870 cents 4 x 5 x 6 x 7:8 S SD: 16.6332 cents 5:6 x 7 x 8:9:10 S SD: 28.2855 cents 6:7 x 8:9 x 10:12 S SD: 12.9081 cents 7:8:9 x x 11:12:14 SD: 8.6588 cents 8:9:10:11:12 x 14:16 S SD: 16.3666 cents 9:10 x 12 x 14:16:18 S SD: 17.3421 cents 10:12:13 x 15 x 17:20 SD: 13.8721 cents 11:13:14:15 x 17:19:22 SD: 10.3641 cents 12:14 x 16:18:19:21:24 SD: 8.6182 cents 13:15:17 x x 20:22:26 SD: 8.0319 cents 14:16:18:19:21:22:24:28 SD: 7.5773 cents 15:17:19:20 x 23:26:30 SD: 9.1853 cents 16:19:21 x 24:25:28:32 SD: 9.7392 cents 17:20:22:23 x 26:29:34 SD: 7.8431 cents 18:21:23:24:27:28:31:36 SD: 4.6547 cents 19:22 x 25 x 29:33:38 SD: 6.1532 cents 20:23:26:27:30:31:35:40 SD: 4.7986 cents 21:24:27:28 x 32:36:42 S SD: 6.0731 cents 22:25 x 29:33:34:38:44 SD: 6.2034 cents 23:27:30:31 x 35:40:46 SD: 7.0118 cents 24:28:31:32:36:37:41:48 SD: 3.6423 cents 26:30:34:35:39:40:45:52 SD: 3.3762 cents 30:35:39:40:45:46:52:60 SD: 2.7296 cents 40:46:52:53:60:62:69:80 SD: 2.6055 cents 44:51:57:59:66:68:76:88 SD: 1.5366 cents 64:74:83:85:96:99:111:128 SD: 1.4591 cents 70:81:91:93:105:108:121:140 SD: 1.1320 cents 78:90:101:104:117:120:135:156 SD: 1.0886 cents 84:97:109:112:126:130:145:168 SD: 1.0018 cents 88:102:114:117:132:136:152:176 SD: 0.9449 cents 96:111:124:128:144:148:166:192 SD: 0.9317 cents 102:118:132:136:153:157:176:204 SD: 0.8314 cents 108:125:140:144:162:167:187:216 SD: 0.7079 cents 114:132:148:152:171:176:197:228 SD: 0.4380 cents 192:222:249:256:288:296:332:384 SD: 0.3119 cents 210:243:272:280:315:324:363:420 SD: 0.2035 cents 324:375:420:432:486:500:560:648 SD: 0.0800 cents 516:597:669:688:774:796:892:1032 SD: 0.0768 cents