Scala analysis: xen15-chalmers-triadic-diamond-26-21
Triadic diamond for M=26/21, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 63/52 332.208246 2: 26/21 369.746754 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 21/13 830.253246 6: 104/63 867.791754 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 63/52 332.2082 1: 63/52 332.2082 2: 1352/1323 37.5385 3: 14/13 128.2982 2/3-tone 4: 9/8 203.9100 major whole tone 5: 14/13 128.2982 2/3-tone 6: 1352/1323 37.5385 7: 63/52 332.2082
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 1352/1323 37.539 cents 1: 2 14/13 128.298 cents 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 63/52 332.208 cents 2: 2 208/189 165.837 cents 2: 2 63/52 332.208 cents 2: 2 26/21 369.747 cents 2: 1 3969/2704 664.416 cents 3: 2 26/21 369.747 cents 3: 1 441/338 460.506 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: 1 676/441 739.494 cents 4: 2 21/13 830.253 cents 5: 1 5408/3969 535.584 cents 5: 2 21/13 830.253 cents 5: 2 104/63 867.792 cents 5: 2 189/104 1034.163 cents 6: 2 104/63 867.792 cents 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 13/7 1071.702 cents 16/3-tone 6: 2 1323/676 1162.461 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 : 332.2 369.7 498.0 702.0 830.3 867.8 1200.0 332.2 : 37.5 165.8 369.7 498.0 535.6 867.8 1200.0 369.7 : 128.3 332.2 460.5 498.0 830.3 1162.5 1200.0 498.0 : 203.9 332.2 369.7 702.0 1034.2 1071.7 1200.0 702.0 : 128.3 165.8 498.0 830.3 867.8 996.1 1200.0 830.3 : 37.5 369.7 702.0 739.5 867.8 1071.7 1200.0 867.8 : 332.2 664.4 702.0 830.3 1034.2 1162.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 37.5385 .. 332.2082 cents 83349/70304, 294.6697 cents 1352/1323, 37.5385 cents 2: 165.8368 .. 664.4165 cents 750141/562432, 498.5797 cents 10816/11907,-166.3715 cents 3: 369.7468 .. 701.9550 cents 63/52, 332.2082 cents 70304/83349,-294.6697 cents 4: 498.0450 .. 830.2532 cents 63/52, 332.2082 cents 8/9,-203.9100 cents 5: 535.5835 .. 1034.1632 cents 750141/562432, 498.5797 cents 70304/83349,-294.6697 cents 6: 867.7918 .. 1162.4615 cents 83349/70304, 294.6697 cents 10816/11907,-166.3715 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1352/1323, 37.5385 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 63/52, 332.2082 cents Average / Smallest step : 4.566739 Largest / Average step : 1.937881 Largest / Smallest step : 8.849799 Median interval of one step : 14/13, 128.2982 cents, amount: 2 Least squares average step : 165.22624 cents, oct.: 1156.58368 cents Scale is not proper Scale is a mode of a 2142-tone equal temperament with octave 2/1 degrees: 593 660 889 1253 1482 1549 2142 Least number of segments generator : 1073 of 601.120 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1417 of 793.838 cents and inv. generated superset size: 121 = 114 more = 1728.571% 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 : 1.373474 Lumma stability : 0.062564 Lumma impropriety factor : 0.661041 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 : 1352/1323, 37.5385 cents Number of recognisable fifths : 4, average 701.9550 cents Scale is a complete diamond : 13 21 63 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 : 13 Odd number limit : 3969 (O: 3969 U: 3969) Highest odd numerator or denominator: 63 Scale harmonicity : 0.012415 Average absolute harmonicity : 0.227551 Specific harmonicity : 0.067376 Fundamental : 1/3276, -11.6777 octaves, 0.0799 Hz. Guide tone : 6552, 12.6777 octaves, 1714170.704 Hz. Exponens Consonantiae : 2.146435E+07, 24.35544 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 189.0, average 27.00000 Mersenne's string divisions : 644481390 Sum of van Prooijen's expressibility: 7.19736, average 1.02819 Sum of Tenney's harmonic distance : 14.66344, average 2.09478 Vogel's harmonic complexity : 28.57143 Wille's k value : 1984 Wilson's harmonic complexity : 52 Rectangular lattice diameter : 8 Triangular lattice diameter : 6 Lattice compactness : 82.89743, average 2.96062 Lattice compactness (without 2's) : 59.16021, average 2.11286 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.57143 10 1 3: -2 .. 2 0.00000 8 2 7: -1 .. 1 0.00000 4 13: -1 .. 1 0.00000 4 4 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 19 24| Scale is weakly epimorphic with val: <7 10 20 24| Scale is weakly epimorphic with val: <7 10 20 25| Scale is weakly epimorphic with val: <7 10 21 25| Scale is weakly epimorphic with val: <7 10 21 26| Scale is weakly epimorphic with val: <7 10 22 26| Scale is weakly epimorphic with val: <7 10 22 27| Scale is weakly epimorphic with val: <7 11 18 27| Scale is weakly epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 11 19 28| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 20 29| Scale is weakly epimorphic with val: <7 11 21 24| Scale is weakly epimorphic with val: <7 11 22 24| Scale is weakly epimorphic with val: <7 11 22 25| Scale is weakly epimorphic with val: <7 12 18 24| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 19 25| Scale is weakly epimorphic with val: <7 12 19 28| Scale is weakly epimorphic with val: <7 12 20 26| Scale is weakly epimorphic with val: <7 12 20 29| Scale is weakly epimorphic with val: <7 12 21 27| Scale is weakly epimorphic with val: <7 12 22 24| Scale is weakly epimorphic with val: <7 12 22 28|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 17.7298 c. M: 26.8896 c. 17: 5 0 2 3 2 0 5 N I SD: 14.4193 c. M:-20.7329 c. 19: 5 1 2 3 2 1 5 N I SD: 10.7747 c. M:-16.4188 c. 22: 6 1 2 4 2 1 6 N I SD: 7.9462 c. M: 12.0714 c. 26: 7 1 3 4 3 1 7 N I SD: 7.1057 c. M:-9.6473 c. 29: 8 1 3 5 3 1 8 N I SD: 1.7502 c. M: 2.6670 c. 65: 18 2 7 11 7 2 18 N I SD: 0.3584 c. M: 0.5160 c. 94: 26 3 10 16 10 3 26 N I SD: 0.3085 c. M: 0.4660 c. 159: 44 5 17 27 17 5 44 N I SD: 0.0869 c. M:-0.1328 c. 383: 106 12 41 65 41 12 106 N I SD: 0.0863 c. M:-0.1273 c. 542: 150 17 58 92 58 17 150 N I SD: 0.0813 c. M:-0.1100 c. 701: 194 22 75 119 75 22 194 N I SD: 0.0803 c. M:-0.1112 c. 1188: 329 37 127 202 127 37 329 N I SD: 0.0755 c. M:-0.1150 c. 1217: 337 38 130 207 130 38 337 N I SD: 0.0700 c. M: 0.0992 c. 1282: 355 40 137 218 137 40 355 N I SD: 0.0603 c. M:-0.0850 c. 1347: 373 42 144 229 144 42 373 N I SD: 0.0564 c. M:-0.0857 c. 1376: 381 43 147 234 147 43 381 N I SD: 0.0543 c. M:-0.0799 c. 1441: 399 45 154 245 154 45 399 N I SD: 0.0448 c. M:-0.0610 c. 1506: 417 47 161 256 161 47 417 N I SD: 0.0413 c. M:-0.0627 c. 1600: 443 50 171 272 171 50 443 N I SD: 0.0329 c. M:-0.0450 c. 1665: 461 52 178 283 178 52 461 N I SD: 0.0291 c. M:-0.0440 c. 1759: 487 55 188 299 188 55 487 N I SD: 0.0237 c. M: 0.0348 c. 1824: 505 57 195 310 195 57 505 N I SD: 0.0190 c. M:-0.0286 c. 1918: 531 60 205 326 205 60 531 N I SD: 0.0172 c. M:-0.0262 c. 1983: 549 62 212 337 212 62 549 N I SD: 0.0107 c. M:-0.0157 c. 2142: 593 67 229 364 229 67 593 N I SD: 0.0040 c. M:-0.0058 c. 2301: 637 72 246 391 246 72 637 N I SD: 0.0039 c. M: 0.0055 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: 5.5223 cents 4 x 5 x 6 x 7:8 S SD: 25.5959 cents 5:6 x 7 x 8 x 10 S SD: 21.9141 cents 6:7 x 8:9 x 10:12 S SD: 13.4810 cents 7:8 x 9 x 11:12:14 SD: 28.7903 cents 8 x 10:11:12:13 x 16 SD: 11.3455 cents 9:11 x 12:14 x 15:18 SD: 13.3710 cents 10:12 x 13:15:16:17:20 SD: 11.8507 cents 11:13:14:15:17 x 18:22 SD: 15.4072 cents 12 x 15:16:18:19:20:24 S SD: 6.9775 cents 13 x 16:17:20:21 x 26 SD: 11.2372 cents 14:17 x 19:21 x 23:28 SD: 6.3998 cents 16:19:20:21:24:26 x 32 SD: 8.0400 cents 17 x 21:23:26:27:28:34 SD: 8.5970 cents 18:22 x 24:27:29:30:36 SD: 3.8244 cents 19:23:24:25:29:31 x 38 SD: 9.0315 cents 20:24:25:27:30:32:33:40 SD: 5.1242 cents 22 x 27:29:33 x 36:44 SD: 5.8431 cents 23:28 x 31:35:37:38:46 SD: 5.5129 cents 24:29:30:32:36:39:40:48 SD: 3.7130 cents 26 x 32:35:39:42:43:52 SD: 3.2925 cents 27:33 x 36:41:44:45:54 SD: 5.7440 cents 28:34:35:37:42:45:46:56 SD: 3.7224 cents 31 x 38:41:47:50:51:62 SD: 4.9432 cents 32:39:40:43:48:52:53:64 SD: 3.7789 cents 33:40:41:44:50:53:54:66 SD: 3.7017 cents 34:41:42:45:51:55:56:68 SD: 2.3277 cents 42:51:52:56:63:68:69:84 SD: 1.4312 cents 66:80:82:88:99:107:109:132 SD: 1.2507 cents 72:87:89:96:108:116:119:144 SD: 1.0507 cents 80:97:99:107:120:129:132:160 SD: 0.9261 cents 104:126:129:139:156:168:172:208 SD: 0.8776 cents 114:138:141:152:171:184:188:228 SD: 0.4592 cents 138:167:171:184:207:223:228:276 SD: 0.4168 cents 180:218:223:240:270:291:297:360 SD: 0.2922 cents 198:240:245:264:297:320:327:396 SD: 0.2465 cents 294:356:364:392:441:475:485:588 SD: 0.2198 cents 312:378:386:416:468:504:515:624 SD: 0.1844 cents 378:458:468:504:567:611:624:756 SD: 0.1571 cents 444:538:550:592:666:717:733:888 SD: 0.1561 cents 450:545:557:600:675:727:743:900 SD: 0.1208 cents 492:596:609:656:738:795:812:984 SD: 0.1136 cents