Scala analysis: xen09-chalmers-tritriadic-8-14-13
Tritriadic scale built from 8:14:13
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: 169/128 481.055324 4: 91/64 609.353568 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: 2197/2048 121.5830 4: 14/13 128.2982 2/3-tone 5: 8/7 231.1741 septimal whole tone 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 : 128.3 359.5 481.1 609.4 840.5 968.8 1200.0 128.3 : 231.2 352.8 481.1 712.2 840.5 1071.7 1200.0 359.5 : 121.6 249.9 481.1 609.4 840.5 968.8 1200.0 481.1 : 128.3 359.5 487.8 718.9 847.2 1078.4 1200.0 609.4 : 231.2 359.5 590.6 718.9 950.1 1071.7 1200.0 840.5 : 128.3 359.5 487.8 718.9 840.5 968.8 1200.0 968.8 : 231.2 359.5 590.6 712.2 840.5 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 : 165.31012 cents, oct.: 1157.17085 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAB Step pattern size order : MLSMLML 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: 6 -- 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 : 0.176399 Specific harmonicity : 0.061924 Fundamental : 1/1664, -10.7004 octaves, 0.1572 Hz. Guide tone : 18928, 14.2082 octaves, 4952048.700 Hz. Exponens Consonantiae : 3.149619E+07, 24.90867 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 271.5, average 38.78571 Mersenne's string divisions : 9345105 Sum of van Prooijen's expressibility: 8.37386, average 1.19627 Sum of Tenney's harmonic distance : 16.44367, average 2.34910 Vogel's harmonic complexity : 25.00000 Wille's k value : 1098 Wilson's harmonic complexity : 46 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 135.18015, average 4.82786 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -7 .. 4 -1.71429 24 1 7: 0 .. 1 0.42857 3 1 13: -1 .. 2 0.28571 6 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 9 / 7 = 1.28571 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: 42.9570 c. M:-76.3607 c. Lebeng 10: 1 2 1 1 2 1 2 P M ME S SD: 5.8054 c. M: 9.3536 c. 37: 4 7 4 4 7 4 7 SP M DE S SD: 3.9747 c. M:-6.8626 c. 47: 5 9 5 5 9 5 9 SP M DE S SD: 2.3480 c. M:-4.0511 c. 57: 6 11 6 6 11 6 11 SP M DE S SD: 1.7072 c. M:-3.1552 c. 67: 7 13 7 7 13 7 13 SP M DE S SD: 1.7342 c. M: 2.9251 c. 110: 12 21 11 12 21 12 21 SP T3 SD: 1.4758 c. M:-2.6108 c. 120: 13 23 12 13 23 13 23 SP T3 SD: 0.9534 c. M:-1.7018 c. 130: 14 25 13 14 25 14 25 SP T3 SD: 0.6233 c. M: 1.0553 c. 140: 15 27 14 15 27 15 27 SP T3 SD: 0.5882 c. M: 1.0553 c. 177: 19 34 18 19 34 19 34 SP T3 SD: 0.4644 c. M:-0.8159 c. 187: 20 36 19 20 36 20 36 SP T3 SD: 0.1599 c. M:-0.2721 c. 384: 41 74 39 41 74 41 74 SP T3 SD: 0.1153 c. M:-0.1947 c. 514: 55 99 52 55 99 55 99 SP T3 SD: 0.0715 c. M: 0.1215 c. 701: 75 135 71 75 135 75 135 SP T3 SD: 0.0518 c. M:-0.0898 c. 711: 76 137 72 76 137 76 137 SP T3 SD: 0.0396 c. M: 0.0709 c. 898: 96 173 91 96 173 96 173 SP T3 SD: 0.0084 c. M:-0.0137 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: 46.3007 cents 3 x x 4 x 5 x 6 S SD: 15.6695 cents 4 x 5 x 6 x 7:8 S SD: 24.1033 cents 5 x 6 x 7:8:9:10 S SD: 15.1534 cents 6 x 7:8:9:10:11:12 S SD: 26.7945 cents 7:8 x 9:10:11:12:14 S SD: 21.9882 cents 8:9:10 x 11:13:14:16 SD: 16.5040 cents 9:10:11:12:13:15:16:18 SD: 11.7538 cents 12:13:15:16:17:20:21:24 SD: 7.9234 cents 13:14:16:17:18:21:23:26 SD: 7.6310 cents 16:17:20:21:23:26:28:32 SD: 5.9400 cents 21:23:26:28:30:34:37:42 SD: 5.5160 cents 22:24:27:29:31:36:39:44 SD: 5.3836 cents 24:26:30:32:34:39:42:48 SD: 4.8551 cents 25:27:31:33:36:41:44:50 SD: 4.5695 cents 26:28:32:34:37:42:46:52 SD: 3.8918 cents 31:33:38:41:44:50:54:62 SD: 3.7821 cents 35:38:43:46:50:57:61:70 SD: 2.8613 cents 38:41:47:50:54:62:67:76 SD: 2.6209 cents 40:43:49:53:57:65:70:80 SD: 1.6152 cents 66:71:81:87:94:107:116:132 SD: 1.5395 cents 69:74:85:91:98:112:121:138 SD: 1.2622 cents 78:84:96:103:111:127:137:156 SD: 1.0489 cents 88:95:108:116:125:143:154:176 SD: 1.0380 cents 91:98:112:120:129:148:159:182 SD: 0.9205 cents 104:112:128:137:148:169:182:208 SD: 0.6010 cents 144:155:177:190:205:234:252:288 SD: 0.4862 cents 168:181:207:222:239:273:294:336 SD: 0.3841 cents 221:238:272:292:314:359:387:442 SD: 0.3146 cents 256:276:315:338:364:416:448:512 SD: 0.2824 cents 272:293:335:359:387:442:476:544 SD: 0.2573 cents 299:322:368:395:425:486:523:598 SD: 0.2118 cents 325:350:400:429:462:528:569:650 SD: 0.1486 cents 403:434:496:532:573:655:705:806 SD: 0.1075 cents