Scala analysis: xen15-chalmers-triadic-diamond-17-14
Triadic diamond for M=17/14, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/14 336.129503 supraminor third 2: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 34/21 834.174502 supraminor sixth 6: 28/17 863.870497 submajor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 17/14 336.1295 supraminor third 2: 294/289 29.6960 3: 68/63 132.2195 supraminor second 4: 9/8 203.9100 major whole tone 5: 68/63 132.2195 supraminor second 6: 294/289 29.6960 7: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 294/289 29.696 cents 1: 2 68/63 132.220 cents supraminor second 1: 1 9/8 203.910 cents major whole tone 1: 2 17/14 336.130 cents supraminor third 2: 2 56/51 161.915 cents 2: 2 17/14 336.130 cents supraminor third 2: 2 21/17 365.825 cents submajor third 2: 1 289/196 672.259 cents two (supraminor third) 3: 2 21/17 365.825 cents submajor third 3: 1 578/441 468.349 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: 1 441/289 731.651 cents two (submajor third) 4: 2 34/21 834.175 cents supraminor sixth 5: 1 392/289 527.741 cents 5: 2 34/21 834.175 cents supraminor sixth 5: 2 28/17 863.870 cents submajor sixth 5: 2 51/28 1038.085 cents 6: 2 28/17 863.870 cents submajor sixth 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 63/34 1067.780 cents submajor seventh 6: 2 289/147 1170.304 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 : 336.1 365.8 498.0 702.0 834.2 863.9 1200.0 336.1 : 29.7 161.9 365.8 498.0 527.7 863.9 1200.0 365.8 : 132.2 336.1 468.3 498.0 834.2 1170.3 1200.0 498.0 : 203.9 336.1 365.8 702.0 1038.1 1067.8 1200.0 702.0 : 132.2 161.9 498.0 834.2 863.9 996.1 1200.0 834.2 : 29.7 365.8 702.0 731.7 863.9 1067.8 1200.0 863.9 : 336.1 672.3 702.0 834.2 1038.1 1170.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.6960 .. 336.1295 cents 4913/4116, 306.4335 cents 294/289, 29.6960 cents 2: 161.9155 .. 672.2590 cents 14739/10976, 510.3435 cents 784/867,-174.2140 cents 3: 365.8255 .. 701.9550 cents 17/14, 336.1295 cents 4116/4913,-306.4335 cents 4: 498.0450 .. 834.1745 cents 17/14, 336.1295 cents 8/9,-203.9100 cents 5: 527.7410 .. 1038.0845 cents 14739/10976, 510.3435 cents 4116/4913,-306.4335 cents 6: 863.8705 .. 1170.3040 cents 4913/4116, 306.4335 cents 784/867,-174.2140 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 294/289, 29.6960 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 5.772784 Largest / Average step : 1.960755 Largest / Smallest step : 11.319018 Median interval of one step : 68/63, 132.2195 cents, amount: 2 Least squares average step : 165.17022 cents, oct.: 1156.19155 cents Scale is not proper Scale is a mode of a 2142-tone equal temperament with octave 2/1 degrees: 600 653 889 1253 1489 1542 2142 Least number of segments generator : 1073 of 601.120 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1403 of 785.994 cents and inv. generated superset size: 63 = 56 more = 900.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDCBA Step pattern size order : DABCBAD Scale is not a Constant Structure Scale diversity : 1.320588 Lumma stability : 0.049493 Lumma impropriety factor : 0.680648 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 : 294/289, 29.6960 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 7 17 21 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 : 441 (O: 441 U: 441) Highest odd numerator or denominator: 21 Scale harmonicity : 0.011218 Average absolute harmonicity : 0.225808 Specific harmonicity : 0.059608 Fundamental : 1/714, -9.4798 octaves, 0.3664 Hz. Guide tone : 1428, 10.4798 octaves, 373601.307 Hz. Exponens Consonantiae : 1.019592E+06, 19.95956 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 92.0, average 13.14286 Mersenne's string divisions : 4081770 Sum of van Prooijen's expressibility: 6.05958, average 0.86565 Sum of Tenney's harmonic distance : 12.61891, average 1.80270 Vogel's harmonic complexity : 28.57143 Wille's k value : 535 Wilson's harmonic complexity : 54 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 66.43961, average 2.37284 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 7: -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 18 26| Scale is weakly epimorphic with val: <7 10 18 27| Scale is weakly epimorphic with val: <7 10 19 27| Scale is weakly epimorphic with val: <7 10 19 28| Scale is weakly epimorphic with val: <7 10 20 28| Scale is weakly epimorphic with val: <7 10 20 29| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 10 21 30| Scale is weakly epimorphic with val: <7 10 22 30| Scale is weakly epimorphic with val: <7 10 22 31| Scale is weakly epimorphic with val: <7 11 18 30| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 32| Scale is weakly epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 20 32| Scale is weakly epimorphic with val: <7 11 21 26| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 11 22 27| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 18 29| Scale is weakly epimorphic with val: <7 12 19 27| Scale is weakly epimorphic with val: <7 12 19 30| Scale is weakly epimorphic with val: <7 12 20 28| Scale is weakly epimorphic with val: <7 12 20 31| Scale is weakly epimorphic with val: <7 12 21 29| Scale is weakly epimorphic with val: <7 12 21 32| Scale is weakly epimorphic with val: <7 12 22 26| Scale is weakly epimorphic with val: <7 12 22 30|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 15.4602 c. M: 22.9684 c. 17: 5 0 2 3 2 0 5 N I SD: 11.5147 c. M:-16.8117 c. 22: 6 1 2 4 2 1 6 N I SD: 10.4899 c. M: 15.9927 c. 24: 7 0 3 4 3 0 7 N I SD: 11.2968 c. M: 15.8255 c. 26: 7 1 3 4 3 1 7 N I SD: 8.8646 c. M:-13.0526 c. 29: 8 1 3 5 3 1 8 N I SD: 4.5228 c. M: 6.5883 c. 36: 10 1 4 6 4 1 10 N I SD: 1.8783 c. M:-2.7962 c. 75: 21 2 8 13 8 2 21 N I SD: 1.5971 c. M: 2.1745 c. 82: 23 2 9 14 9 2 23 N I SD: 0.3557 c. M:-0.4840 c. 118: 33 3 13 20 13 3 33 N I SD: 0.3511 c. M:-0.5363 c. 200: 56 5 22 34 22 5 56 N I SD: 0.1186 c. M: 0.1745 c. 282: 79 7 31 48 31 7 79 N I SD: 0.1182 c. M:-0.1727 c. 482: 135 12 53 82 53 12 135 N I SD: 0.1037 c. M: 0.1496 c. 607: 170 15 67 103 67 15 170 N I SD: 0.0948 c. M:-0.1428 c. 689: 193 17 76 117 76 17 193 N I SD: 0.0556 c. M: 0.0780 c. 771: 216 19 85 131 85 19 216 N I SD: 0.0473 c. M: 0.0667 c. 889: 249 22 98 151 98 22 249 N I SD: 0.0280 c. M:-0.0427 c. 971: 272 24 107 165 107 24 272 N I SD: 0.0136 c. M:-0.0188 c. 1171: 328 29 129 199 129 29 328 N I SD: 0.0103 c. M: 0.0157 c. 2060: 577 51 227 350 227 51 577 N I SD: 0.0099 c. M:-0.0133 c. 2142: 600 53 236 364 236 53 600 N I SD: 0.0041 c. M:-0.0058 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: 6.8294 cents 4 x 5 x 6 x 7:8 S SD: 26.7341 cents 5:6 x 7 x 8 x 10 S SD: 22.3247 cents 6:7 x 8:9 x 10:12 S SD: 14.4451 cents 7 x x 9 x 11:12:14 SD: 26.7300 cents 8 x 10:11:12:13 x 16 SD: 11.4859 cents 9:11 x 12:14 x 15:18 SD: 13.4329 cents 10:12 x 13:15:16 x 20 SD: 10.5085 cents 11:13:14:15:17 x 18:22 SD: 15.9726 cents 12 x 15:16:18:19:20:24 S SD: 8.0463 cents 13 x 16:17:20:21 x 26 SD: 11.1481 cents 14:17 x 19:21 x 23:28 SD: 6.1919 cents 16:19:20:21:24:26 x 32 SD: 8.6517 cents 17 x 21:23:26 x 28:34 SD: 8.4116 cents 18:22 x 24:27:29:30:36 SD: 4.1478 cents 19:23 x 25:29:31 x 38 SD: 8.0978 cents 20:24:25:27:30:32:33:40 SD: 5.9442 cents 21 x 26:28:32:34:35:42 SD: 5.7215 cents 22 x 27:29:33 x 36:44 SD: 5.0828 cents 23:28 x 31:35:37:38:46 SD: 5.6335 cents 24:29:30:32:36:39:40:48 SD: 4.4084 cents 26 x 32:35:39:42:43:52 SD: 3.2527 cents 27:33 x 36:41:44 x 54 SD: 5.3128 cents 28:34:35:37:42:45:46:56 SD: 4.1494 cents 30:36:37:40:45 x 49:60 SD: 4.2072 cents 31 x 38:41:47:50:51:62 SD: 4.6093 cents 32:39:40:43:48:52:53:64 SD: 3.9765 cents 33:40:41:44:50:53:54:66 SD: 3.8682 cents 34:41:42:45:51:55:56:68 SD: 2.5154 cents 35 x 43:47:53:57:58:70 SD: 4.4881 cents 36:44 x 48:54:58:59:72 SD: 2.7573 cents 40 x 49:53:60:65:66:80 SD: 3.2387 cents 42:51:52:56:63:68:69:84 SD: 0.8443 cents 102:124:126:136:153:165:168:204 SD: 0.3565 cents 144:175:178:192:216:233:237:288 SD: 0.3527 cents 192:233:237:256:288:311:316:384 SD: 0.3220 cents 234:284:289:312:351:379:385:468 SD: 0.3108 cents 252:306:311:336:378:408:415:504 SD: 0.2364 cents 294:357:363:392:441:476:484:588 SD: 0.1700 cents 378:459:467:504:567:612:623:756 SD: 0.1665 cents 396:481:489:528:594:641:652:792 SD: 0.1561 cents 420:510:519:560:630:680:692:840 SD: 0.1189 cents 522:634:645:696:783:845:860:1044 SD: 0.1184 cents 570:692:704:760:855:923:939:1140 SD: 0.0891 cents