Scala analysis: xen09-chalmers-tritriadic-8-9-10
Tritriadic scale built from 8:9:10
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 5/4 386.313714 major third 3: 45/32 590.223716 diatonic tritone 4: 25/16 772.627428 classic augmented fifth 5: 8/5 813.686286 minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 128/125 41.0589 minor diesis, diesis 6: 9/8 203.9100 major whole tone 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 3 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 2: 1 256/225 223.463 cents Neapolitan diminished third 2: 1 144/125 244.969 cents classic diminished third 2: 5 5/4 386.314 cents major third 3: 3 32/25 427.373 cents classic diminished fourth 3: 2 25/18 568.717 cents classic augmented fourth 3: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 2 36/25 631.283 cents classic diminished fifth 4: 3 25/16 772.627 cents classic augmented fifth 5: 5 8/5 813.686 cents minor sixth 5: 1 125/72 955.031 cents classic augmented sixth 5: 1 225/128 976.537 cents augmented sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 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 : 203.9 386.3 590.2 772.6 813.7 1017.6 1200.0 203.9 : 182.4 386.3 568.7 609.8 813.7 996.1 1200.0 386.3 : 203.9 386.3 427.4 631.3 813.7 1017.6 1200.0 590.2 : 182.4 223.5 427.4 609.8 813.7 996.1 1200.0 772.6 : 41.1 245.0 427.4 631.3 813.7 1017.6 1200.0 813.7 : 203.9 386.3 590.2 772.6 976.5 1158.9 1200.0 1017.6: 182.4 386.3 568.7 772.6 955.0 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 203.9100 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 2: 223.4626 .. 386.3137 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 3: 427.3726 .. 590.2237 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 4: 609.7763 .. 772.6274 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents 5: 813.6863 .. 976.5374 cents 1125/1024, 162.8511 cents 128/125, 41.0589 cents 6: 996.0900 .. 1158.9411 cents 1125/1024, 162.8511 cents 2048/2025, 19.5526 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 128/125, 41.0589 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 4.175191 Largest / Average step : 1.189475 Largest / Smallest step : 4.966285 Median interval of one step : 10/9, 182.4037 cents, amount: 3 Least squares average step : 174.36948 cents, oct.: 1220.58637 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABABCAB Step pattern size order : LMLMSLM Scale is a Constant Structure, by a margin of 19.55257 cents Scale diversity : 1.233743 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.185744 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 : 2048/2025, 19.5526 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 203.910 386.314 cents Most common triad is 0.0 386.314 813.686 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 1 5 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 162.8511 cents: 2 -- Rational properties -- Prime limit : 5 Odd number limit : 225 (O: 225 U: 225) Highest odd numerator or denominator: 45 Scale harmonicity : 0.030738 Average absolute harmonicity : 0.221420 Specific harmonicity : 0.164271 Fundamental : 1/160, -7.3219 octaves, 1.6352 Hz. Guide tone : 1800, 10.8138 octaves, 470926.018 Hz. Exponens Consonantiae : 2.880000E+05, 18.13571 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 87.0, average 12.42857 Mersenne's string divisions : 12558546 Sum of van Prooijen's expressibility: 6.35758, average 0.90823 Sum of Tenney's harmonic distance : 12.47509, average 1.78216 Vogel's harmonic complexity : 12.57143 Wille's k value : 112 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 111.16586, average 3.97021 Lattice compactness (without 2's) : 53.74331, average 1.91940 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -1.42857 18 1 3: 0 .. 2 0.85714 6 1 5: -1 .. 2 0.28571 6 5 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is JI-epimorphic with val: <7 11 16| = patent
FIT/MODE
7: 1 1 1 1 0 2 1 N T3 SD: 68.4119 c. M: 127.9720 c. 8: 1 1 2 1 0 2 1 N D3 SD: 47.9134 c. M: 86.3137 c. 9: 2 1 2 1 0 2 1 N T3 SD: 43.6115 c. M:-76.4430 c. 10: 2 1 2 1 1 1 2 N D3 SD: 35.5967 c. M: 57.5963 c. 11: 2 1 2 2 0 2 2 N T3 SD: 36.9550 c. M: 59.0410 c. 12: 2 2 2 2 0 2 2 P M DE S SD: 14.8535 c. M:-27.3726 c. 19: 3 3 3 3 1 3 3 SP M DE S SD: 12.3017 c. M: 21.8027 c. Glacial-7 22: 4 3 4 3 1 4 3 P T3 SD: 10.5067 c. M:-18.7673 c. 25: 4 4 4 4 1 4 4 SP M DE S SD: 8.1799 c. M: 14.2237 c. 28: 5 4 5 4 1 5 4 P T3 SD: 6.8227 c. M:-10.9751 c. 34: 6 5 6 5 1 6 5 P T3 SD: 5.5373 c. M:-9.7763 c. 47: 8 7 8 7 2 8 7 SP T3 SD: 3.5724 c. M: 6.6700 c. 53: 9 8 9 8 2 9 8 SP T3 SD: 1.5079 c. M: 2.8161 c. 59: 10 9 10 9 2 10 9 SP T3 SD: 0.3666 c. M: 0.6471 c. 230: 39 35 39 35 8 39 35 SP T3 SD: 0.3724 c. M: 0.6585 c. 289: 49 44 49 44 10 49 44 SP T3 SD: 0.3376 c. M: 0.6043 c. 323: 55 49 55 49 11 55 49 SP T3 SD: 0.2861 c. M:-0.4884 c. 376: 64 57 64 57 13 64 57 SP T3 SD: 0.2732 c. M:-0.4888 c. 382: 65 58 65 58 13 65 58 SP T3 SD: 0.1986 c. M:-0.3522 c. 435: 74 66 74 66 15 74 66 SP T3 SD: 0.1879 c. M:-0.3347 c. 441: 75 67 75 67 15 75 67 SP T3 SD: 0.1418 c. M:-0.2525 c. 494: 84 75 84 75 17 84 75 SP T3 SD: 0.1239 c. M:-0.2175 c. 500: 85 76 85 76 17 85 76 SP T3 SD: 0.1095 c. M:-0.1763 c. 553: 94 84 94 84 19 94 84 SP T3 SD: 0.0755 c. M:-0.1252 c. 612: 104 93 104 93 21 104 93 SP T3 SD: 0.0426 c. M: 0.0784 c. 671: 114 102 114 102 23 114 102 SP T3 SD: 0.0350 c. M: 0.0598 c. 1112: 189 169 189 169 38 189 169 SP T3 SD: 0.0358 c. M:-0.0641 c. 1171: 199 178 199 178 40 199 178 SP T3 SD: 0.0271 c. M:-0.0455 c. 1724: 293 262 293 262 59 293 262 SP T3 SD: 0.0227 c. M:-0.0371 c. 1783: 303 271 303 271 61 303 271 SP T3 SD: 0.0106 c. M:-0.0175 c. 1842: 313 280 313 280 63 313 280 SP T3 SD: 0.0059 c. M:-0.0110 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: 35.3362 cents 3 x x 4 x 5 x 6 S SD: 38.7176 cents 4 x 5 x 6 x 7:8 S SD: 21.4668 cents 5 x 6:7 x 8:9:10 S SD: 14.2184 cents 6:7 x 8:9:10:11:12 S SD: 25.5274 cents 7:8:9:10:11 x 13:14 SD: 13.8343 cents 8:9:10:11 x 13:14:16 SD: 11.3194 cents 9:10:11:13:14 x 16:18 SD: 11.3658 cents 10:11:13:14 x 16:18:20 SD: 13.1059 cents 12:14:15:17 x 19:22:24 SD: 12.3210 cents 13:15:16:18:20:21:23:26 SD: 10.3490 cents 14:16:18:20:22 x 25:28 SD: 10.7404 cents 15:17:19:21:23:24:27:30 SD: 6.0823 cents 17:19:21:24 x 27:31:34 SD: 5.9239 cents 19:21:24:27:30 x 34:38 SD: 7.5054 cents 20:23:25:28:31:32:36:40 SD: 5.8913 cents 23:26:29:32:36:37:41:46 SD: 4.5537 cents 24:27:30:34 x 38:43:48 SD: 3.9314 cents 25:28:31:35:39:40:45:50 SD: 2.5554 cents 32:36:40:45:50:51:58:64 SD: 1.9663 cents 55:62:69:77:86:88:99:110 SD: 1.5169 cents 64:72:80:90:100:102:115:128 SD: 1.0591 cents 89:100:111:125:139:142:160:178 SD: 1.0451 cents 96:108:120:135:150:154:173:192 SD: 0.7040 cents 128:144:160:180:200:205:230:256 SD: 0.4929 cents 135:152:169:190:211:216:243:270 SD: 0.4714 cents 160:180:200:225:250:256:288:320 SD: 0.0000 cents