Scala analysis: xen10-chalmers-tritriadic-3-11-15
Tritriadic scale built from 3:11:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 55/48 235.676655 undecimal semi-augmented whole tone 2: 5/4 386.313714 major third 3: 22/15 663.049228 undecimal diminished fifth 4: 25/16 772.627428 classic augmented fifth 5: 8/5 813.686286 minor sixth 6: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 55/48 235.6767 undecimal semi-augmented whole tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 88/75 276.7355 4: 375/352 109.5782 5: 128/125 41.0589 minor diesis, diesis 6: 55/48 235.6767 undecimal semi-augmented whole tone 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 128/125 41.059 cents minor diesis, diesis 1: 1 375/352 109.578 cents 1: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 2 55/48 235.677 cents undecimal semi-augmented whole tone 1: 1 88/75 276.736 cents 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 88/75 276.736 cents 2: 4 5/4 386.314 cents major third 2: 1 32/25 427.373 cents classic diminished fourth 3: 1 5/4 386.314 cents major third 3: 2 32/25 427.373 cents classic diminished fourth 3: 2 15/11 536.951 cents undecimal augmented fourth 3: 1 275/192 621.990 cents 3: 1 22/15 663.049 cents undecimal diminished fifth 4: 1 15/11 536.951 cents undecimal augmented fourth 4: 1 384/275 578.010 cents 4: 2 22/15 663.049 cents undecimal diminished fifth 4: 2 25/16 772.627 cents classic augmented fifth 4: 1 8/5 813.686 cents minor sixth 5: 1 25/16 772.627 cents classic augmented fifth 5: 4 8/5 813.686 cents minor sixth 5: 1 75/44 923.264 cents 5: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 75/44 923.264 cents 6: 2 96/55 964.323 cents 6: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 1 704/375 1090.422 cents 6: 1 125/64 1158.941 cents classic augmented seventh, octave - minor diesis Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 235.7 386.3 663.0 772.6 813.7 1049.4 1200.0 235.7 : 150.6 427.4 537.0 578.0 813.7 964.3 1200.0 386.3 : 276.7 386.3 427.4 663.0 813.7 1049.4 1200.0 663.0 : 109.6 150.6 386.3 537.0 772.6 923.3 1200.0 772.6 : 41.1 276.7 427.4 663.0 813.7 1090.4 1200.0 813.7 : 235.7 386.3 622.0 772.6 1049.4 1158.9 1200.0 1049.4: 150.6 386.3 537.0 813.7 923.3 964.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 41.0589 .. 276.7355 cents 55/48, 235.6767 cents 128/125, 41.0589 cents 2: 150.6371 .. 427.3726 cents 88/75, 276.7355 cents 225/242,-126.0985 cents 3: 386.3137 .. 663.0492 cents 88/75, 276.7355 cents 125/128,-41.0589 cents 4: 536.9508 .. 813.6863 cents 88/75, 276.7355 cents 225/242,-126.0985 cents 5: 772.6274 .. 1049.3629 cents 88/75, 276.7355 cents 125/128,-41.0589 cents 6: 923.2645 .. 1158.9411 cents 55/48, 235.6767 cents 225/242,-126.0985 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 : 88/75, 276.7355 cents Average / Smallest step : 4.175191 Largest / Average step : 1.614290 Largest / Smallest step : 6.739971 Median interval of one step : 12/11, 150.6371 cents, amount: 2 Least squares average step : 177.51836 cents, oct.: 1242.62853 cents Scale is not proper Step pattern alph. order: ABCDEAB Step pattern size order : DCEBADC Scale is not a Constant Structure Scale diversity : 1.420987 Lumma stability : 0.068431 Lumma impropriety factor : 0.383678 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 : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 128/125, 41.0589 cents Most common intervals : 5/4, 386.3137 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 663.049 813.686 cents Most common triad is 0.0 386.314 813.686 cents, amount: 3 Number of recognisable fifths : 0 Scale contains two identical disjunct "tetrachords" of 3 notes Scale contains a complete diamond : 1 5 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 375 (O: 375 U: 375) Highest odd numerator or denominator: 55 Scale harmonicity : 0.021255 Average absolute harmonicity : 0.199732 Specific harmonicity : 0.104179 Fundamental : 1/240, -7.9069 octaves, 1.0901 Hz. Guide tone : 2200, 11.1033 octaves, 575576.244 Hz. Exponens Consonantiae : 5.280000E+05, 19.01018 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 111.5, average 15.92857 Mersenne's string divisions : 310783239 Sum of van Prooijen's expressibility: 6.75373, average 0.96482 Sum of Tenney's harmonic distance : 13.56584, average 1.93798 Vogel's harmonic complexity : 16.00000 Wille's k value : 187 Wilson's harmonic complexity : 29 Rectangular lattice diameter : 5 Triangular lattice diameter : 4 Lattice compactness : 99.39060, average 3.54966 Lattice compactness (without 2's) : 46.44630, average 1.65880 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 3 -0.85714 16 1 3: -1 .. 0 -0.42857 3 5: -1 .. 2 0.28571 6 3 11: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 12 / 7 = 1.71429 Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 11 15 22| Scale is weakly epimorphic with val: <7 11 16 26| Scale is weakly epimorphic with val: <7 11 17 23| Scale is weakly epimorphic with val: <7 12 15 23| Scale is weakly epimorphic with val: <7 12 17 24|
FIT/MODE
7: 1 1 2 1 0 1 1 N T3 SD: 47.7996 c. M:-84.5154 c. 9: 2 1 2 1 0 2 1 N T3 SD: 18.5039 c. M:-30.9900 c. 15: 3 2 3 2 0 3 2 N T3 SD: 15.8633 c. M:-27.3726 c. 16: 3 2 4 1 1 3 2 N SD: 12.1021 c. M: 22.6274 c. 22: 4 3 5 2 1 4 3 N SD: 9.7733 c. M: 17.4948 c. 25: 5 3 6 2 1 5 3 N SD: 4.9997 c. M:-8.9508 c. 31: 6 4 7 3 1 6 4 N SD: 2.8752 c. M: 4.9847 c. 56: 11 7 13 5 2 11 7 N SD: 0.7646 c. M:-1.2365 c. 87: 17 11 20 8 3 17 11 N SD: 0.7208 c. M: 1.1939 c. 143: 28 18 33 13 5 28 18 N SD: 0.4188 c. M: 0.7116 c. 199: 39 25 46 18 7 39 25 N SD: 0.4176 c. M: 0.7681 c. 239: 47 30 55 22 8 47 30 N SD: 0.3177 c. M:-0.5943 c. 295: 58 37 68 27 10 58 37 N SD: 0.1597 c. M:-0.2555 c. 351: 69 44 81 32 12 69 44 N SD: 0.1378 c. M:-0.2208 c. 382: 75 48 88 35 13 75 48 N SD: 0.1250 c. M: 0.2220 c. 438: 86 55 101 40 15 86 55 N SD: 0.0340 c. M: 0.0602 c. 1171: 230 147 270 107 40 230 147 N SD: 0.0244 c. M:-0.0455 c. 1227: 241 154 283 112 42 241 154 N SD: 0.0179 c. M:-0.0315 c. 1609: 316 202 371 147 55 316 202 N SD: 0.0174 c. M: 0.0287 c. 1665: 327 209 384 152 57 327 209 N SD: 0.0090 c. M: 0.0148 c. 2103: 413 264 485 192 72 413 264 N SD: 0.0096 c. M: 0.0169 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x x 4 S SD: 19.4529 cents 3 x 4 x x 5 x 6 S SD: 44.0687 cents 4 x 5:6 x x 7:8 S SD: 22.3605 cents 5 x 6:7 x 8:9:10 S SD: 22.3517 cents 6:7:8:9 x 10:11:12 S SD: 23.5497 cents 7:8:9:10:11 x 13:14 SD: 11.8685 cents 8:9:10:12 x 13:15:16 SD: 11.4950 cents 9:10:11:13:14 x 17:18 SD: 14.7015 cents 10:11:13:15 x 16:18:20 SD: 18.3544 cents 11:13:14:16:17:18:20:22 SD: 11.1812 cents 12:14:15:18 x 19:22:24 SD: 8.8434 cents 13:15:16:19:20:21:24:26 SD: 6.4575 cents 14:16:18:21:22 x 26:28 SD: 11.1913 cents 15:17:19:22:23:24:28:30 SD: 7.7245 cents 17:19:21:25 x 27:31:34 SD: 8.4159 cents 18:21:23:26:28:29:33:36 SD: 8.2345 cents 19:22:24:28:30 x 35:38 SD: 5.5839 cents 20:23:25:29:31:32:37:40 SD: 4.2132 cents 24:28:30:35 x 38:44:48 SD: 6.2339 cents 25:29:31:37:39:40:46:50 SD: 4.3765 cents 27:31:34:40:42:43:50:54 SD: 4.2975 cents 28:32:35:41:44:45:51:56 SD: 2.5240 cents 41:47:51:60:64:66:75:82 SD: 2.0967 cents 48:55:60:70:75:77:88:96 SD: 1.5491 cents 55:63:69:81:86:88:101:110 SD: 1.4324 cents 60:69:75:88:94:96:110:120 SD: 1.1134 cents 96:110:120:141:150:154:176:192 SD: 0.7328 cents 103:118:129:151:161:165:189:206 SD: 0.6251 cents 137:157:171:201:214:219:251:274 SD: 0.4706 cents 180:206:225:264:281:288:330:360 SD: 0.3720 cents 212:243:265:311:331:339:389:424 SD: 0.3333 cents 240:275:300:352:375:384:440:480 SD: 0.0000 cents