Scala analysis: xen09-chalmers-tritriadic-13-14-16
Tritriadic scale built from 13:14:16
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 16/13 359.472338 tridecimal neutral third 3: 224/169 487.770583 4: 256/169 718.944676 two (tridecimal neutral third) 5: 13/8 840.527662 tridecimal neutral sixth 6: 7/4 968.825906 harmonic seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 14/13 128.2982 2/3-tone 2: 8/7 231.1741 septimal whole tone 3: 14/13 128.2982 2/3-tone 4: 8/7 231.1741 septimal whole tone 5: 2197/2048 121.5830 6: 14/13 128.2982 2/3-tone 7: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 2197/2048 121.583 cents 1: 3 14/13 128.298 cents 2/3-tone 1: 3 8/7 231.174 cents septimal whole tone 2: 1 1183/1024 249.881 cents 2: 1 2197/1792 352.757 cents 2: 5 16/13 359.472 cents tridecimal neutral third 3: 3 169/128 481.055 cents 3: 2 224/169 487.771 cents 3: 2 128/91 590.646 cents 4: 2 91/64 609.354 cents 4: 2 169/112 712.229 cents 4: 3 256/169 718.945 cents two (tridecimal neutral third) 5: 5 13/8 840.528 cents tridecimal neutral sixth 5: 1 3584/2197 847.243 cents 5: 1 2048/1183 950.119 cents 6: 3 7/4 968.826 cents harmonic seventh 6: 3 13/7 1071.702 cents 16/3-tone 6: 1 4096/2197 1078.417 cents Highest number of different intervals for one interval class: 3 Average number of different intervals per interval class: 3.00000 = 3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 128.3 359.5 487.8 718.9 840.5 968.8 1200.0 128.3 : 231.2 359.5 590.6 712.2 840.5 1071.7 1200.0 359.5 : 128.3 359.5 481.1 609.4 840.5 968.8 1200.0 487.8 : 231.2 352.8 481.1 712.2 840.5 1071.7 1200.0 718.9 : 121.6 249.9 481.1 609.4 840.5 968.8 1200.0 840.5 : 128.3 359.5 487.8 718.9 847.2 1078.4 1200.0 968.8 : 231.2 359.5 590.6 718.9 950.1 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 121.5830 .. 231.1741 cents 16384/15379, 109.5911 cents 2197/2048, 121.5830 cents 2: 249.8812 .. 359.4723 cents 16384/15379, 109.5911 cents 8281/8192, 18.7071 cents 3: 481.0553 .. 590.6464 cents 16384/15379, 109.5911 cents 2197/2048, 121.5830 cents 4: 609.3536 .. 718.9447 cents 16384/15379, 109.5911 cents 8281/8192, 18.7071 cents 5: 840.5277 .. 950.1188 cents 16384/15379, 109.5911 cents 2197/2048, 121.5830 cents 6: 968.8259 .. 1078.4170 cents 16384/15379, 109.5911 cents 8281/8192, 18.7071 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 2197/2048, 121.5830 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.409972 Largest / Average step : 1.348516 Largest / Smallest step : 1.901369 Median interval of one step : 14/13, 128.2982 cents, amount: 3 Least squares average step : 168.58519 cents, oct.: 1180.09636 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : MLMLSML Scale is a Constant Structure, by a margin of 18.70714 cents Scale diversity : 1.260343 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.452044 Rothenberg efficiency : 0.544218 redundancy: 0.455782 Efficiency x scale size : 3.809524 Number of different interval sizes : 18 = 3.00000 / class Number of one step interval sizes : 3 Highest interval variety : 3 Mean interval variety : 3.00000 = 3 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 28672/28561, 6.7153 cents Most common intervals : 16/13, 359.4723 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 128.298 359.472 cents Most common triad is 0.0 359.472 840.528 cents, amount: 3 Number of recognisable fifths : 5, average 716.2586 cents Number of appreciable fifths : 2, average 712.2294 cents Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 13 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 109.5911 cents: 3 -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.011396 Average absolute harmonicity : 0.175027 Specific harmonicity : 0.060740 Fundamental : 1/1352, -10.4009 octaves, 0.1935 Hz. Guide tone : 23296, 14.5078 octaves, 6094829.169 Hz. Exponens Consonantiae : 3.149619E+07, 24.90867 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 454.5, average 64.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.64270, average 1.23467 Sum of Tenney's harmonic distance : 17.55762, average 2.50823 Vogel's harmonic complexity : 24.71429 Wille's k value : 1098 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 133.59831, average 4.77137 Lattice compactness (without 2's) : 42.59183, average 1.52114 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 8 2.00000 24 1 7: 0 .. 1 0.42857 3 1 13: -2 .. 1 -0.71429 7 5 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is weakly epimorphic with val: <7 18 29| Scale is weakly epimorphic with val: <7 19 24| Scale is JI-epimorphic with val: <7 20 26| = patent
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.3578 c. M:-59.7455 c. Lebeng 10: 1 2 1 2 1 1 2 P M ME S SD: 5.4617 c. M: 8.8259 c. 27: 3 5 3 5 3 3 5 SP M DE S SD: 5.3290 c. M:-8.9519 c. 37: 4 7 4 7 4 4 7 SP M DE S SD: 3.0506 c. M: 5.4312 c. 47: 5 9 5 9 5 5 9 SP M DE S SD: 2.2054 c. M: 4.0511 c. 57: 6 11 6 11 6 6 11 SP M DE S SD: 2.1281 c. M: 3.5601 c. 93: 10 18 10 18 9 10 18 SP T3 SD: 2.0020 c. M:-3.6360 c. 103: 11 20 11 20 10 11 20 SP T3 SD: 1.8120 c. M:-3.3854 c. 110: 12 21 12 21 11 12 21 SP T3 SD: 1.7999 c. M:-3.1385 c. 113: 12 22 12 22 11 12 22 SP T3 SD: 1.7912 c. M:-3.1792 c. 120: 13 23 13 23 12 13 23 SP T3 SD: 1.2487 c. M:-2.2294 c. 130: 14 25 14 25 13 14 25 SP T3 SD: 0.8312 c. M:-1.4602 c. 140: 15 27 15 27 14 15 27 SP T3 SD: 0.5918 c. M:-1.0553 c. 177: 19 34 19 34 18 19 34 SP T3 SD: 0.3737 c. M:-0.6656 c. 187: 20 36 20 36 19 20 36 SP T3 SD: 0.1253 c. M: 0.2281 c. 514: 55 99 55 99 52 55 99 SP T3 SD: 0.0952 c. M:-0.1672 c. 524: 56 101 56 101 53 56 101 SP T3 SD: 0.0824 c. M:-0.1393 c. 701: 75 135 75 135 71 75 135 SP T3 SD: 0.0607 c. M:-0.1039 c. 711: 76 137 76 137 72 76 137 SP T3 SD: 0.0293 c. M: 0.0495 c. 898: 96 173 96 173 91 96 173 SP T3 SD: 0.0113 c. M: 0.0200 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: 8.4948 cents 3 x x 4 x 5 x 6 S SD: 15.0064 cents 4 x 5 x 6 x 7:8 S SD: 7.9416 cents 5 x 6:7 x 8:9:10 S SD: 23.6611 cents 6 x 7:8:9:10:11:12 S SD: 21.9701 cents 7:8 x 9 x 11:12:14 SD: 26.8341 cents 8:9:10:11:12:13:14:16 S SD: 14.8217 cents 9:10:11:12:14:15:16:18 S SD: 12.7426 cents 10:11:12:13:15:16:18:20 SD: 12.6024 cents 12:13:15:16:18:20:21:24 SD: 8.0069 cents 13:14:16:17:20:21:23:26 SD: 5.9400 cents 21:23:26:28:32:34:37:42 SD: 5.2434 cents 24:26:30:32:36:39:42:48 SD: 4.9903 cents 25:27:31:33:38:41:44:50 SD: 3.5804 cents 27:29:33:36:41:44:47:54 SD: 2.8530 cents 39:42:48:52:59:63:68:78 SD: 2.2883 cents 40:43:49:53:61:65:70:80 SD: 2.0763 cents 43:46:53:57:65:70:75:86 SD: 1.9971 cents 52:56:64:69:79:85:91:104 SD: 1.6518 cents 56:60:69:74:85:91:98:112 SD: 1.5778 cents 64:69:79:85:97:104:112:128 SD: 0.9316 cents 101:109:124:134:153:164:177:202 SD: 0.9306 cents 104:112:128:138:158:169:182:208 SD: 0.7743 cents 117:126:144:155:177:190:205:234 SD: 0.4862 cents 144:155:177:191:218:234:252:288 SD: 0.4145 cents 169:182:208:224:256:275:296:338 SD: 0.3969 cents 208:224:256:276:315:338:364:416 SD: 0.2824 cents 221:238:272:293:335:359:387:442 SD: 0.2573 cents 299:322:368:396:453:486:523:598 SD: 0.2381 cents 338:364:416:448:512:549:592:676 SD: 0.2374 cents 363:391:447:481:550:590:635:726 SD: 0.1981 cents 416:448:512:551:630:676:728:832 SD: 0.1828 cents 443:477:545:587:671:720:775:886 SD: 0.1624 cents 480:517:591:636:727:780:840:960 SD: 0.1368 cents 507:546:624:672:768:824:887:1014 SD: 0.0792 cents