Scala analysis: xen15-chalmers-triadic-diamond-17-13
Triadic diamond for M=17/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/34 237.527253 2: 17/13 464.427748 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 26/17 735.572252 6: 68/39 962.472747 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 39/34 237.5273 1: 39/34 237.5273 2: 578/507 226.9005 3: 52/51 33.6173 4: 9/8 203.9100 major whole tone 5: 52/51 33.6173 6: 578/507 226.9005 7: 39/34 237.5273
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 52/51 33.617 cents 1: 1 9/8 203.910 cents major whole tone 1: 2 578/507 226.900 cents 1: 2 39/34 237.527 cents 2: 2 39/34 237.527 cents 2: 2 136/117 260.518 cents 2: 2 17/13 464.428 cents 2: 1 1521/1156 475.055 cents 3: 1 338/289 271.145 cents 3: 2 17/13 464.428 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: 2 26/17 735.572 cents 4: 1 289/169 928.855 cents 5: 1 2312/1521 724.945 cents 5: 2 26/17 735.572 cents 5: 2 117/68 939.482 cents 5: 2 68/39 962.473 cents 6: 2 68/39 962.473 cents 6: 2 507/289 973.100 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 51/26 1166.383 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 : 237.5 464.4 498.0 702.0 735.6 962.5 1200.0 237.5 : 226.9 260.5 464.4 498.0 724.9 962.5 1200.0 464.4 : 33.6 237.5 271.1 498.0 735.6 973.1 1200.0 498.0 : 203.9 237.5 464.4 702.0 939.5 1166.4 1200.0 702.0 : 33.6 260.5 498.0 735.6 962.5 996.1 1200.0 735.6 : 226.9 464.4 702.0 928.9 962.5 1166.4 1200.0 962.5 : 237.5 475.1 702.0 735.6 939.5 973.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 33.6173 .. 237.5273 cents 9/8, 203.9100 cents 52/51, 33.6173 cents 2: 237.5273 .. 475.0545 cents 39/34, 237.5273 cents 1/1, 0.0000 cents 3: 271.1445 .. 701.9550 cents 867/676, 430.8105 cents 8/9,-203.9100 cents 4: 498.0450 .. 928.8555 cents 867/676, 430.8105 cents 8/9,-203.9100 cents 5: 724.9455 .. 962.4727 cents 39/34, 237.5273 cents 8/9,-203.9100 cents 6: 962.4727 .. 1166.3827 cents 9/8, 203.9100 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 52/51, 33.6173 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 39/34, 237.5273 cents Average / Smallest step : 5.099423 Largest / Average step : 1.385576 Largest / Smallest step : 7.065636 Median interval of one step : 578/507, 226.9005 cents, amount: 2 Least squares average step : 166.57882 cents, oct.: 1166.05177 cents Scale is not proper Step pattern alph. order: ABCDCBA Step pattern size order : DCABACD Scale is not a Constant Structure Scale diversity : 1.067468 Lumma stability : 0.056029 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 : 19773/19652, 10.6268 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 13 17 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 : 17 Odd number limit : 1521 (O: 1521 U: 1521) Highest odd numerator or denominator: 39 Scale harmonicity : 0.008859 Average absolute harmonicity : 0.222907 Specific harmonicity : 0.047110 Fundamental : 1/1326, -10.3729 octaves, 0.1973 Hz. Guide tone : 2652, 11.3729 octaves, 693830.999 Hz. Exponens Consonantiae : 3.516552E+06, 21.74573 octaves Euler's gradus suavitatis : 64 Sum of Mann's harmonic distance : 134.0, average 19.14286 Mersenne's string divisions : 70533330 Sum of van Prooijen's expressibility: 6.59727, average 0.94247 Sum of Tenney's harmonic distance : 13.69429, average 1.95633 Vogel's harmonic complexity : 34.57143 Wille's k value : 994 Wilson's harmonic complexity : 66 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 65.73531, average 2.34769 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 13: -1 .. 1 0.00000 4 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 24 26| Scale is weakly epimorphic with val: <7 10 24 32| Scale is weakly epimorphic with val: <7 10 25 26| Scale is weakly epimorphic with val: <7 10 25 27| Scale is weakly epimorphic with val: <7 10 26 27| Scale is weakly epimorphic with val: <7 10 26 28| Scale is weakly epimorphic with val: <7 10 27 28| Scale is weakly epimorphic with val: <7 10 27 29| Scale is weakly epimorphic with val: <7 10 28 29| Scale is weakly epimorphic with val: <7 10 28 30| Scale is weakly epimorphic with val: <7 10 29 30| Scale is weakly epimorphic with val: <7 10 29 31| Scale is weakly epimorphic with val: <7 11 24 29| Scale is weakly epimorphic with val: <7 11 24 30| Scale is weakly epimorphic with val: <7 11 25 30| Scale is weakly epimorphic with val: <7 11 25 31| Scale is weakly epimorphic with val: <7 11 26 31| Scale is weakly epimorphic with val: <7 11 26 32| Scale is weakly epimorphic with val: <7 11 27 32| Scale is weakly epimorphic with val: <7 12 24 28| Scale is weakly epimorphic with val: <7 12 24 32| Scale is weakly epimorphic with val: <7 12 25 26| Scale is weakly epimorphic with val: <7 12 25 29| Scale is weakly epimorphic with val: <7 12 26 27| Scale is weakly epimorphic with val: <7 12 26 30| Scale is weakly epimorphic with val: <7 12 27 28| Scale is weakly epimorphic with val: <7 12 27 31| Scale is weakly epimorphic with val: <7 12 28 29| Scale is weakly epimorphic with val: <7 12 28 32| Scale is weakly epimorphic with val: <7 12 29 30|
FIT/MODE
7: 1 2 0 1 0 2 1 N T3 I SD: 45.0987 c. M:-66.0987 c. 8: 2 1 0 2 0 1 2 N I SD: 42.8263 c. M:-62.4727 c. 10: 2 2 0 2 0 2 2 N D3 I SD: 12.8088 c. M:-18.0450 c. 15: 3 3 0 3 0 3 3 N D3 I SD: 12.8088 c. M:-18.0450 c. 21: 4 4 1 3 1 4 4 N G I SD: 10.6508 c. M:-16.2407 c. 24: 5 4 1 4 1 4 5 N G I SD: 10.2477 c. M:-14.4277 c. 26: 5 5 1 4 1 5 5 N G I SD: 6.4827 c. M:-9.6473 c. 31: 6 6 1 5 1 6 6 N G I SD: 3.9502 c. M:-5.2692 c. 36: 7 7 1 6 1 7 7 N G I SD: 2.7477 c. M: 4.1939 c. 41: 8 8 1 7 1 8 8 N G I SD: 2.7569 c. M:-3.8649 c. 65: 13 12 2 11 2 12 13 N I SD: 2.0449 c. M:-2.8893 c. 70: 14 13 2 12 2 13 14 N I SD: 1.6384 c. M:-2.4727 c. 96: 19 18 3 16 3 18 19 N I SD: 1.4676 c. M: 1.9550 c. 101: 20 19 3 17 3 19 20 N I SD: 0.7685 c. M:-1.0614 c. 106: 21 20 3 18 3 20 21 N I SD: 0.1888 c. M:-0.2768 c. 323: 64 61 9 55 9 61 64 N I SD: 0.1735 c. M:-0.2436 c. 359: 71 68 10 61 10 68 71 N I SD: 0.1503 c. M:-0.2013 c. 460: 91 87 13 78 13 87 91 N I SD: 0.1429 c. M:-0.2159 c. 465: 92 88 13 79 13 88 92 N I SD: 0.0753 c. M:-0.1079 c. 571: 113 108 16 97 16 108 113 N I SD: 0.0323 c. M:-0.0491 c. 677: 134 128 19 115 19 128 134 N I SD: 0.0237 c. M:-0.0348 c. 1248: 247 236 35 212 35 236 247 N I SD: 0.0226 c. M:-0.0319 c. 1359: 269 257 38 231 38 257 269 N I SD: 0.0239 c. M:-0.0318 c. 1465: 290 277 41 249 41 277 290 N I SD: 0.0162 c. M: 0.0245 c. 2036: 403 385 57 346 57 385 403 N I SD: 0.0085 c. M:-0.0123 c. 2142: 424 405 60 364 60 405 424 N I SD: 0.0053 c. M:-0.0078 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: 26.0380 cents 4 x 5 x 6 x 7:8 S SD: 19.5930 cents 5:6 x 7 x 8:9:10 S SD: 29.9178 cents 6:7 x 8:9 x 10:12 S SD: 16.6887 cents 7:8:9 x x 11:12:14 SD: 12.5919 cents 8:9:10:11:12 x 14:16 S SD: 16.7583 cents 9:10 x 12 x 14:16:18 S SD: 14.1842 cents 10:11:13 x 15 x 17:20 SD: 17.0705 cents 11:13:14:15 x 17:19:22 SD: 13.9219 cents 12:14 x 16:18 x 21:24 S SD: 6.0047 cents 13:15:17 x x 20:23:26 SD: 5.8221 cents 14:16:18:19:21 x 24:28 SD: 8.6625 cents 15:17 x 20 x 23:26:30 SD: 4.7257 cents 16:18:21 x 24 x 28:32 S SD: 6.9594 cents 17:20:22:23 x 26:30:34 SD: 9.6041 cents 18:21 x 24:27:28:31:36 SD: 7.7778 cents 19:22:25 x x 29:33:38 SD: 4.1787 cents 21:24:27:28 x 32:37:42 SD: 5.9373 cents 22:25:29 x 33:34:38:44 SD: 5.3894 cents 23:26:30:31 x 35:40:46 SD: 5.5382 cents 25:29:33 x x 38:44:50 SD: 6.3796 cents 26:30:34:35:39:40:45:52 SD: 3.6319 cents 27:31:35:36 x 41:47:54 SD: 3.3060 cents 28:32 x 37:42:43:49:56 SD: 3.2167 cents 29:33:38:39 x 44:51:58 SD: 4.8207 cents 30:34:39:40:45:46:52:60 SD: 3.6774 cents 31:36 x 41 x 47:54:62 SD: 5.9429 cents 32:37:42:43:48:49:56:64 SD: 3.0555 cents 33:38:43:44 x 50:58:66 SD: 3.8644 cents 34:39:44:45:51:52:59:68 SD: 3.3739 cents 36:41:47:48:54:55:63:72 SD: 2.0451 cents 42:48:55:56:63:64:73:84 SD: 1.5416 cents 62:71:81:83:93:95:108:124 SD: 1.2165 cents 74:85:97:99:111:113:129:148 SD: 1.1452 cents 90:103:118:120:135:138:157:180 SD: 1.0730 cents 94:108:123:125:141:144:164:188 SD: 0.8994 cents 102:117:133:136:153:156:178:204 SD: 0.7455 cents 108:124:141:144:162:165:188:216 SD: 0.6724 cents 130:149:170:173:195:199:227:260 SD: 0.6671 cents 136:156:178:181:204:208:237:272 SD: 0.5203 cents 156:179:204:208:234:239:272:312 SD: 0.4341 cents 198:227:259:264:297:303:345:396 SD: 0.2644 cents 300:344:392:400:450:459:523:600 SD: 0.2349 cents 306:351:400:408:459:468:534:612 SD: 0.2340 cents 312:358:408:416:468:477:544:624 SD: 0.1224 cents 468:537:612:624:702:716:816:936 SD: 0.1150 cents 504:578:659:672:756:771:879:1008 SD: 0.1039 cents 510:585:667:680:765:780:889:1020 SD: 0.0702 cents