Scala analysis: xen15-chalmers-triadic-diamond-19-16
Triadic diamond for M=19/16, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 19/16 297.513016 19th harmonic 2: 24/19 404.441985 smaller undevicesimal major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 19/12 795.558015 undevicesimal minor sixth 6: 32/19 902.486984 19th subharmonic 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 19/16 297.5130 19th harmonic 1: 19/16 297.5130 19th harmonic 2: 384/361 106.9290 3: 19/18 93.6030 undevicesimal semitone 4: 9/8 203.9100 major whole tone 5: 19/18 93.6030 undevicesimal semitone 6: 384/361 106.9290 7: 19/16 297.5130 19th harmonic
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 19/18 93.603 cents undevicesimal semitone 1: 2 384/361 106.929 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 19/16 297.513 cents 19th harmonic 2: 2 64/57 200.532 cents 2: 2 19/16 297.513 cents 19th harmonic 2: 2 24/19 404.442 cents smaller undevicesimal major third 2: 1 361/256 595.026 cents two (19th harmonic) 3: 1 361/288 391.116 cents 3: 2 24/19 404.442 cents smaller undevicesimal 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 19/12 795.558 cents undevicesimal minor sixth 4: 1 576/361 808.884 cents two (smaller undevicesimal major third) 5: 1 512/361 604.974 cents 5: 2 19/12 795.558 cents undevicesimal minor sixth 5: 2 32/19 902.487 cents 19th subharmonic 5: 2 57/32 999.468 cents undevicesimal minor seventh 6: 2 32/19 902.487 cents 19th subharmonic 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 361/192 1093.071 cents 6: 2 36/19 1106.397 cents smaller undevicesimal major seventh 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 : 297.5 404.4 498.0 702.0 795.6 902.5 1200.0 297.5 : 106.9 200.5 404.4 498.0 605.0 902.5 1200.0 404.4 : 93.6 297.5 391.1 498.0 795.6 1093.1 1200.0 498.0 : 203.9 297.5 404.4 702.0 999.5 1106.4 1200.0 702.0 : 93.6 200.5 498.0 795.6 902.5 996.1 1200.0 795.6 : 106.9 404.4 702.0 808.9 902.5 1106.4 1200.0 902.5 : 297.5 595.0 702.0 795.6 999.5 1093.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 297.5130 cents 9/8, 203.9100 cents 19/18, 93.6030 cents 2: 200.5320 .. 595.0260 cents 20577/16384, 394.4940 cents 1024/1083,-96.9810 cents 3: 391.1160 .. 701.9550 cents 432/361, 310.8390 cents 8/9,-203.9100 cents 4: 498.0450 .. 808.8840 cents 432/361, 310.8390 cents 8/9,-203.9100 cents 5: 604.9740 .. 999.4680 cents 20577/16384, 394.4940 cents 8/9,-203.9100 cents 6: 902.4870 .. 1106.3970 cents 9/8, 203.9100 cents 1024/1083,-96.9810 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 19/16, 297.5130 cents Average / Smallest step : 1.831443 Largest / Average step : 1.735493 Largest / Smallest step : 3.178456 Median interval of one step : 384/361, 106.9290 cents, amount: 2 Least squares average step : 165.72189 cents, oct.: 1160.05320 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DBACABD Scale is not a Constant Structure Scale diversity : 1.334677 Lumma stability : 0.156005 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 : 513/512, 3.3780 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 1 3 19 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 : 19 Odd number limit : 361 (O: 361 U: 361) Highest odd numerator or denominator: 19 Scale harmonicity : 0.012115 Average absolute harmonicity : 0.227109 Specific harmonicity : 0.065271 Fundamental : 1/912, -9.8329 octaves, 0.2869 Hz. Guide tone : 1824, 10.8329 octaves, 477205.031 Hz. Exponens Consonantiae : 1.663488E+06, 20.66578 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 87.5, average 12.50000 Mersenne's string divisions : 2379405 Sum of van Prooijen's expressibility: 6.06926, average 0.86704 Sum of Tenney's harmonic distance : 12.44204, average 1.77743 Vogel's harmonic complexity : 26.57143 Wille's k value : 541 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 108.12304, average 3.86154 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.57143 18 1 3: -1 .. 1 0.00000 4 2 19: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 8 / 7 = 1.14286 Scale is weakly epimorphic with val: <7 10 29| Scale is weakly epimorphic with val: <7 10 30| Scale is weakly epimorphic with val: <7 11 27| Scale is weakly epimorphic with val: <7 11 33| Scale is weakly epimorphic with val: <7 12 29| Scale is weakly epimorphic with val: <7 12 32|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 41.7904 c. M:-61.5848 c. 8: 2 1 0 2 0 1 2 N I SD: 35.4161 c. M:-48.0450 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 25.1651 c. M:-35.2883 c. 12: 3 1 1 2 1 1 3 N I SD: 2.9149 c. M:-4.4420 c. Mela Yagapriya, Raga Kalahamsa 53: 13 5 4 9 4 5 13 N I SD: 2.3735 c. M: 3.1734 c. 65: 16 6 5 11 5 6 16 N I SD: 1.4769 c. M:-2.1284 c. 77: 19 7 6 13 6 7 19 N I SD: 0.9232 c. M:-1.4091 c. 89: 22 8 7 15 7 8 22 N I SD: 0.6492 c. M: 0.8838 c. 101: 25 9 8 17 8 9 25 N I SD: 0.6317 c. M:-0.9649 c. 181: 45 16 14 31 14 16 45 N I SD: 0.6189 c. M:-0.8295 c. 190: 47 17 15 32 15 17 47 N I SD: 0.6136 c. M:-0.9024 c. 234: 58 21 18 40 18 21 58 N I SD: 0.4922 c. M:-0.6862 c. 246: 61 22 19 42 19 22 61 N I SD: 0.3492 c. M:-0.4840 c. 258: 64 23 20 44 20 23 64 N I SD: 0.2433 c. M:-0.3706 c. 270: 67 24 21 46 21 24 67 N I SD: 0.2011 c. M:-0.2672 c. 347: 86 31 27 59 27 31 86 N I SD: 0.1119 c. M:-0.1690 c. 359: 89 32 28 61 28 32 89 N I SD: 0.0136 c. M:-0.0200 c. 1807: 448 161 141 307 141 161 448 N I SD: 0.0126 c. M: 0.0181 c. 2166: 537 193 169 368 169 193 537 N I SD: 0.0105 c. M:-0.0159 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: 6.0428 cents 4 x 5 x 6 x 7:8 S SD: 17.1928 cents 5:6 x 7 x 8 x 10 S SD: 22.0680 cents 6:7 x 8:9 x 10:12 S SD: 7.1206 cents 7:8:9 x x 11:12:14 SD: 16.0617 cents 8 x 10:11:12:13 x 16 SD: 14.4068 cents 9:11 x 12 x 14:15:18 SD: 12.2590 cents 10:12 x 13:15:16:17:20 SD: 8.8810 cents 11:13:14:15 x 17:19:22 SD: 12.2713 cents 12:14:15:16:18:19:20:24 S SD: 5.7075 cents 22:26:28:29:33:35:37:44 SD: 3.7944 cents 26:31:33:35:39:41:44:52 SD: 3.2281 cents 38:45:48:51:57:60:64:76 SD: 1.8898 cents 48:57:61:64:72:76:81:96 SD: 1.5741 cents 60:71:76:80:90:95:101:120 SD: 1.1149 cents 84:100:106:112:126:133:141:168 SD: 1.0637 cents 96:114:121:128:144:152:162:192 SD: 0.7222 cents 118:140:149:157:177:187:199:236 SD: 0.6980 cents 132:157:167:176:198:209:222:264 SD: 0.6565 cents 144:171:182:192:216:228:243:288 SD: 0.5033 cents 156:185:197:208:234:247:263:312 SD: 0.4210 cents 202:240:255:269:303:320:340:404 SD: 0.4170 cents 224:266:283:299:336:355:377:448 SD: 0.4025 cents 228:271:288:304:342:361:384:456 SD: 0.2283 cents 240:285:303:320:360:380:404:480 SD: 0.1822 cents 288:342:364:384:432:456:485:576 SD: 0.1456 cents 384:456:485:512:576:608:647:768 SD: 0.1041 cents 528:627:667:704:792:836:889:1056 SD: 0.0758 cents