Scala analysis: xen15-chalmers-triadic-diamond-64-51
Triadic diamond for M=64/51, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 153/128 308.865411 2: 64/51 393.089590 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 51/32 806.910410 6: 256/153 891.134589 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 153/128 308.8654 1: 153/128 308.8654 2: 8192/7803 84.2242 3: 17/16 104.9554 17th harmonic 4: 9/8 203.9100 major whole tone 5: 17/16 104.9554 17th harmonic 6: 8192/7803 84.2242 7: 153/128 308.8654
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 8192/7803 84.224 cents 1: 2 17/16 104.955 cents 17th harmonic 1: 1 9/8 203.910 cents major whole tone 1: 2 153/128 308.865 cents 2: 2 512/459 189.180 cents 2: 2 153/128 308.865 cents 2: 2 64/51 393.090 cents 2: 1 23409/16384 617.731 cents 3: 2 64/51 393.090 cents 3: 1 2601/2048 413.821 cents 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: 1 4096/2601 786.179 cents 4: 2 51/32 806.910 cents 5: 1 32768/23409 582.269 cents 5: 2 51/32 806.910 cents 5: 2 256/153 891.135 cents 5: 2 459/256 1010.820 cents 6: 2 256/153 891.135 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 32/17 1095.045 cents 17th subharmonic 6: 2 7803/4096 1115.776 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 : 308.9 393.1 498.0 702.0 806.9 891.1 1200.0 308.9 : 84.2 189.2 393.1 498.0 582.3 891.1 1200.0 393.1 : 105.0 308.9 413.8 498.0 806.9 1115.8 1200.0 498.0 : 203.9 308.9 393.1 702.0 1010.8 1095.0 1200.0 702.0 : 105.0 189.2 498.0 806.9 891.1 996.1 1200.0 806.9 : 84.2 393.1 702.0 786.2 891.1 1095.0 1200.0 891.1 : 308.9 617.7 702.0 806.9 1010.8 1115.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.2242 .. 308.8654 cents 1193859/1048576, 224.6412 cents 8192/7803, 84.2242 cents 2: 189.1796 .. 617.7308 cents 10744731/8388608, 428.5512 cents 65536/70227,-119.6858 cents 3: 393.0896 .. 701.9550 cents 153/128, 308.8654 cents 1048576/1193859,-224.6412 cents 4: 498.0450 .. 806.9104 cents 153/128, 308.8654 cents 8/9,-203.9100 cents 5: 582.2692 .. 1010.8204 cents 10744731/8388608, 428.5512 cents 1048576/1193859,-224.6412 cents 6: 891.1346 .. 1115.7758 cents 1193859/1048576, 224.6412 cents 65536/70227,-119.6858 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 8192/7803, 84.2242 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 153/128, 308.8654 cents Average / Smallest step : 2.035384 Largest / Average step : 1.801715 Largest / Smallest step : 3.667182 Median interval of one step : 17/16, 104.9554 cents, amount: 2 Least squares average step : 165.55971 cents, oct.: 1158.91796 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.389638 Lumma stability : 0.140374 Lumma impropriety factor : 0.544327 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 : 4131/4096, 14.7304 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 1 3 153 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 : 17 Odd number limit : 23409 (O: 23409 U: 23409) Highest odd numerator or denominator: 153 Scale harmonicity : 0.011641 Average absolute harmonicity : 0.226547 Specific harmonicity : 0.063356 Fundamental : 1/19584, -14.2574 octaves, 0.0134 Hz. Guide tone : 39168, 15.2574 octaves, 10247350.142 Hz. Exponens Consonantiae : 7.670661E+08, 29.51478 octaves Euler's gradus suavitatis : 56 Sum of Mann's harmonic distance : 451.5, average 64.50000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.73877, average 1.24840 Sum of Tenney's harmonic distance : 17.76967, average 2.53852 Vogel's harmonic complexity : 30.57143 Wille's k value : 11704 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 6 Triangular lattice diameter : 6 Lattice compactness : 178.75210, average 6.38400 Lattice compactness (without 2's) : 52.73791, average 1.88350 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 8 0.57143 30 1 3: -2 .. 2 0.00000 8 2 17: -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 30| Scale is weakly epimorphic with val: <7 10 31| Scale is weakly epimorphic with val: <7 11 26| Scale is weakly epimorphic with val: <7 11 32| Scale is weakly epimorphic with val: <7 12 26| Scale is weakly epimorphic with val: <7 12 29|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 33.5623 c. M: 50.2324 c. 9: 2 1 1 1 1 1 2 N D3 I SD: 29.6347 c. M: 42.1987 c. 12: 3 1 1 2 1 1 3 N I SD: 6.0985 c. M: 8.8654 c. Mela Yagapriya, Raga Kalahamsa 31: 8 2 3 5 3 2 8 N I SD: 4.2566 c. M: 5.9928 c. 43: 11 3 4 7 4 3 11 N I SD: 2.8087 c. M:-4.2806 c. 46: 12 3 4 8 4 3 12 N I SD: 2.7448 c. M: 4.1781 c. 55: 14 4 5 9 5 4 14 N I SD: 2.7257 c. M:-3.7732 c. 58: 15 4 5 10 5 4 15 N I SD: 1.1236 c. M: 1.4933 c. 70: 18 5 6 12 6 5 18 N I SD: 0.8161 c. M: 1.1961 c. 101: 26 7 9 17 9 7 26 N I SD: 0.7472 c. M:-1.0104 c. 159: 41 11 14 27 14 11 41 N I SD: 0.4577 c. M:-0.6368 c. 171: 44 12 15 29 15 12 44 N I SD: 0.1314 c. M:-0.2006 c. 400: 103 28 35 68 35 28 103 N I SD: 0.0897 c. M:-0.1346 c. 412: 106 29 36 70 36 29 106 N I SD: 0.0918 c. M: 0.1275 c. 571: 147 40 50 97 50 40 147 N I SD: 0.0637 c. M: 0.0948 c. 641: 165 45 56 109 56 45 165 N I SD: 0.0484 c. M:-0.0731 c. 812: 209 57 71 138 71 57 209 N I SD: 0.0111 c. M:-0.0154 c. 1795: 462 126 157 305 157 126 462 N I SD: 0.0050 c. M: 0.0075 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: 2.2586 cents 4 x 5 x 6 x 7:8 S SD: 19.4966 cents 5:6 x 7 x 8 x 10 S SD: 21.2523 cents 6:7 x 8:9 x 10:12 S SD: 8.5075 cents 7:8:9 x x 11:12:14 SD: 20.1586 cents 8 x 10:11:12:13 x 16 SD: 12.6713 cents 9:11 x 12 x 14:15:18 SD: 11.4804 cents 10:12 x 13:15:16:17:20 SD: 8.7712 cents 11:13:14:15:17 x 18:22 SD: 13.5942 cents 12:14:15:16:18:19:20:24 S SD: 6.3635 cents 13 x 16:17:20:21:22:26 SD: 11.9171 cents 14:17:18:19:21:22:23:28 SD: 10.1480 cents 15:18:19:20:23:24:25:30 SD: 6.1388 cents 20:24:25:27:30:32:33:40 SD: 4.9171 cents 24:29:30:32:36:38:40:48 SD: 3.4182 cents 30:36:38:40:45:48:50:60 S SD: 2.8525 cents 36:43:45:48:54:57:60:72 SD: 2.1299 cents 42:50:53:56:63:67:70:84 SD: 1.9723 cents 52:62:65:69:78:83:87:104 SD: 1.6984 cents 62:74:78:83:93:99:104:124 SD: 1.4556 cents 66:79:83:88:99:105:110:132 SD: 1.2354 cents 82:98:103:109:123:131:137:164 SD: 1.0535 cents 86:103:108:115:129:137:144:172 SD: 0.9116 cents 98:117:123:131:147:156:164:196 SD: 0.7594 cents 114:136:143:152:171:182:191:228 SD: 0.7300 cents 138:165:173:184:207:220:231:276 SD: 0.2907 cents 180:215:226:240:270:287:301:360 SD: 0.2855 cents 266:318:334:355:399:424:445:532 SD: 0.2817 cents 282:337:354:376:423:449:472:564 SD: 0.2735 cents 306:366:384:408:459:488:512:612 SD: 0.2240 cents 318:380:399:424:477:507:532:636 SD: 0.1269 cents 522:624:655:696:783:832:873:1044 SD: 0.1216 cents 588:703:738:784:882:937:984:1176 SD: 0.0850 cents