Scala analysis: xen15-chalmers-triadic-diamond-16-13
Triadic diamond for M=16/13, D=3/2
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 2: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 64/39 857.517337 39th subharmonic 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina 1: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina 2: 512/507 16.9897 tridecimal neutral third comma 3: 13/12 138.5727 tridecimal 2/3-tone 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 512/507 16.9897 tridecimal neutral third comma 7: 39/32 342.4827 39th harmonic, Zalzal wosta of Ibn Sina
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 512/507 16.990 cents tridecimal neutral third comma 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 1 9/8 203.910 cents major whole tone 1: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 128/117 155.562 cents 2: 2 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 2 16/13 359.472 cents tridecimal neutral third 2: 1 1521/1024 684.965 cents two (39th harmonic, Zalzal wosta of Ibn Sina) 3: 2 16/13 359.472 cents tridecimal neutral third 3: 1 169/128 481.055 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: 1 256/169 718.945 cents two (tridecimal neutral third) 4: 2 13/8 840.528 cents tridecimal neutral sixth 5: 1 2048/1521 515.035 cents 5: 2 13/8 840.528 cents tridecimal neutral sixth 5: 2 64/39 857.517 cents 39th subharmonic 5: 2 117/64 1044.438 cents 6: 2 64/39 857.517 cents 39th subharmonic 6: 1 16/9 996.090 cents Pythagorean minor seventh 6: 2 24/13 1061.427 cents tridecimal neutral seventh 6: 2 507/256 1183.010 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 : 342.5 359.5 498.0 702.0 840.5 857.5 1200.0 342.5 : 17.0 155.6 359.5 498.0 515.0 857.5 1200.0 359.5 : 138.6 342.5 481.1 498.0 840.5 1183.0 1200.0 498.0 : 203.9 342.5 359.5 702.0 1044.4 1061.4 1200.0 702.0 : 138.6 155.6 498.0 840.5 857.5 996.1 1200.0 840.5 : 17.0 359.5 702.0 718.9 857.5 1061.4 1200.0 857.5 : 342.5 685.0 702.0 840.5 1044.4 1183.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 16.9897 .. 342.4827 cents 19773/16384, 325.4930 cents 512/507, 16.9897 cents 2: 155.5623 .. 684.9653 cents 177957/131072, 529.4030 cents 4096/4563,-186.9203 cents 3: 359.4723 .. 701.9550 cents 39/32, 342.4827 cents 16384/19773,-325.4930 cents 4: 498.0450 .. 840.5277 cents 39/32, 342.4827 cents 8/9,-203.9100 cents 5: 515.0347 .. 1044.4377 cents 177957/131072, 529.4030 cents 16384/19773,-325.4930 cents 6: 857.5173 .. 1183.0103 cents 19773/16384, 325.4930 cents 4096/4563,-186.9203 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 512/507, 16.9897 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 39/32, 342.4827 cents Average / Smallest step : 10.090162 Largest / Average step : 1.997816 Largest / Smallest step : 20.158281 Median interval of one step : 13/12, 138.5727 cents, amount: 2 Least squares average step : 165.07946 cents, oct.: 1155.55623 cents Scale is not proper Scale is a mode of a 918-tone equal temperament with octave 2/1 degrees: 262 275 381 537 643 656 918 Least number of segments generator : 461 of 602.614 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 709 of 926.797 cents and inv. generated superset size: 95 = 88 more = 1357.143% 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 : 1.220388 Lumma stability : 0.028316 Lumma impropriety factor : 0.712413 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 : 512/507, 16.9897 cents Number of recognisable fifths : 5, average 705.3529 cents Number of appreciable fifths : 4, average 701.9550 cents Scale is a complete diamond : 1 3 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 : 13 Odd number limit : 1521 (O: 1521 U: 1521) Highest odd numerator or denominator: 39 Scale harmonicity : 0.016490 Average absolute harmonicity : 0.232997 Specific harmonicity : 0.089174 Fundamental : 1/1248, -10.2854 octaves, 0.2096 Hz. Guide tone : 2496, 11.2854 octaves, 653017.411 Hz. Exponens Consonantiae : 3.115008E+06, 21.57080 octaves Euler's gradus suavitatis : 40 Sum of Mann's harmonic distance : 119.5, average 17.07143 Mersenne's string divisions : 22268085 Sum of van Prooijen's expressibility: 6.36426, average 0.90918 Sum of Tenney's harmonic distance : 12.98692, average 1.85527 Vogel's harmonic complexity : 21.57143 Wille's k value : 760 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 129.08975, average 4.61035 Lattice compactness (without 2's) : 39.08641, average 1.39594 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.57143 22 1 3: -1 .. 1 0.00000 4 2 13: -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 26| Scale is weakly epimorphic with val: <7 10 27| Scale is weakly epimorphic with val: <7 11 29| Scale is weakly epimorphic with val: <7 12 24| Scale is weakly epimorphic with val: <7 12 27|
FIT/MODE
7: 2 0 1 1 1 0 2 N T3 I SD: 12.4208 c. M: 16.6152 c. 17: 5 0 2 3 2 0 5 N I SD: 6.9171 c. M: 10.4585 c. 24: 7 0 3 4 3 0 7 N I SD: 6.5478 c. M: 9.4723 c. 36: 10 1 4 6 4 1 10 N I SD: 6.3085 c. M: 9.1493 c. 41: 12 0 5 7 5 0 12 N I SD: 6.4293 c. M:-8.7368 c. 43: 12 1 5 7 5 1 12 N I SD: 4.9880 c. M: 7.5989 c. 46: 13 1 5 8 5 1 13 N I SD: 3.7785 c. M: 5.7451 c. 53: 15 1 6 9 6 1 15 N I SD: 2.1367 c. M: 2.8600 c. 60: 17 1 7 10 7 1 17 N I SD: 1.7125 c. M: 2.4827 c. 70: 20 1 8 12 8 1 20 N I SD: 0.5934 c. M:-0.9021 c. 147: 42 2 17 25 17 2 42 N I SD: 0.2569 c. M:-0.3745 c. 277: 79 4 32 47 32 4 79 N I SD: 0.1614 c. M:-0.2444 c. 347: 99 5 40 59 40 5 99 N I SD: 0.1210 c. M: 0.1818 c. 424: 121 6 49 72 49 6 121 N I SD: 0.0448 c. M:-0.0682 c. 918: 262 13 106 156 106 13 262 N I SD: 0.0040 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: 8.9471 cents 4 x 5 x 6 x 7:8 S SD: 28.6248 cents 5:6 x 7 x 8 x 10 S SD: 23.1512 cents 6:7 x 8:9 x 10:12 S SD: 16.0469 cents 7 x x 9 x 11 x 14 SD: 28.5428 cents 8 x 10:11:12:13 x 16 SD: 11.9306 cents 9:11 x 12:14 x 15:18 SD: 13.7241 cents 10:12 x 13:15:16 x 20 SD: 11.5967 cents 11:13:14:15:17 x 18:22 SD: 17.0091 cents 12 x 15:16:18 x 20:24 S SD: 7.5919 cents 13 x 16:17:20:21 x 26 SD: 11.2372 cents 14:17 x 19:21 x 23:28 SD: 6.2707 cents 15:18 x 20:23:24:25:30 SD: 10.0128 cents 16 x 20:21:24:26 x 32 SD: 7.6519 cents 17 x 21:23:26 x 28:34 SD: 8.6014 cents 18:22 x 24:27:29:30:36 SD: 5.1789 cents 19:23 x 25:29:31 x 38 SD: 8.0466 cents 20:24:25:27:30 x 33:40 SD: 7.4397 cents 21 x 26:28:32:34 x 42 SD: 5.9641 cents 22 x 27:29:33 x 36:44 SD: 4.1952 cents 23:28 x 31:35:37:38:46 SD: 6.2732 cents 24:29:30:32:36:39 x 48 SD: 5.1134 cents 25:30:31:33:38 x 41:50 SD: 6.9072 cents 26 x 32:35:39:42:43:52 SD: 3.9495 cents 27:33 x 36:41:44 x 54 SD: 4.4710 cents 28:34 x 37:42 x 46:56 SD: 3.3774 cents 30 x 37:40:45 x 49:60 SD: 1.7793 cents 31 x 38:41:47:50:51:62 SD: 4.6386 cents 32:39 x 43:48:52:53:64 SD: 3.4845 cents 33:40:41:44:50 x 54:66 SD: 4.3538 cents 34:41:42:45:51:55:56:68 SD: 3.6233 cents 35 x 43:47:53:57 x 70 SD: 4.2197 cents 36:44 x 48:54 x 59:72 SD: 1.0834 cents 38:46:47:51:57:62 x 76 SD: 3.2821 cents 39 x 48:52:59:63:64:78 SD: 2.9938 cents 40 x 49:53:60:65:66:80 SD: 2.7544 cents 41:50 x 55:62 x 67:82 SD: 3.8018 cents 42:51:52:56:63:68:69:84 SD: 1.9692 cents 44 x 54:59:66 x 72:88 SD: 2.4061 cents 45:55 x 60:68:73:74:90 SD: 2.4110 cents 46:56:57:61:69:75 x 92 SD: 2.7057 cents 48 x 59:64:72:78:79:96 SD: 0.9240 cents 49:60 x 65:74:80 x 98 SD: 3.7337 cents 50:61:62:67:75:81:82:100 SD: 2.3676 cents 51:62:63:68:77:83:84:102 SD: 2.1840 cents 52:63:64:69:78 x 85:104 SD: 2.4782 cents 53 x 65:71:80:86:87:106 SD: 2.5189 cents 54:66 x 72:81:88:89:108 SD: 1.7057 cents 56:68:69:75:84:91:92:112 SD: 1.4797 cents 58:71 x 77:87:94:95:116 SD: 2.0143 cents 60:73:74:80:90 x 98:120 SD: 1.5628 cents 62 x 76:83:93:101:102:124 SD: 1.9355 cents 64:78:79:85:96:104:105:128 SD: 1.2100 cents 67:82 x 89:101:109:110:134 SD: 2.1934 cents 68:83:84:91:102:111:112:136 SD: 1.9639 cents 69:84:85:92:104:112:113:138 SD: 1.3702 cents 71 x 87:95:107:115:117:142 SD: 2.6090 cents 72:88:89:96:108:117:118:144 SD: 1.3214 cents 78:95:96:104:117:127:128:156 SD: 0.5138 cents 80 x 98:107:120:130:131:160 SD: 1.7417 cents 81:99:100:108:122:132:133:162 SD: 1.6196 cents 82:100:101:109:123:133:135:164 SD: 1.2187 cents 86:105:106:115:129:140:141:172 SD: 1.0420 cents 96:117:118:128:144:156:158:192 SD: 0.7920 cents 114:139:140:152:171:185:187:228 SD: 0.6550 cents 142:173:175:189:213:231:233:284 SD: 0.6139 cents 156:190:192:208:234:254:256:312 SD: 0.5138 cents 168:205:207:224:252:273:276:336 SD: 0.4932 cents 178:217:219:237:267:289:292:356 SD: 0.4321 cents 192:234:236:256:288:312:315:384 SD: 0.3278 cents 234:285:288:312:351:380:384:468 SD: 0.2300 cents 312:380:384:416:468:507:512:624 SD: 0.1627 cents 438:534:539:584:657:712:719:876 SD: 0.1505 cents 480:585:591:640:720:780:788:960 SD: 0.1366 cents 498:607:613:664:747:809:817:996 SD: 0.1110 cents 576:702:709:768:864:936:945:1152 SD: 0.0661 cents