Scala analysis: xen10-chalmers-tritriadic-13-23-21
Tritriadic scale built from 13:23:21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 23/21 157.493440 2: 26/21 369.746754 3: 441/338 460.506491 4: 483/338 617.999931 5: 21/13 830.253246 6: 23/13 987.746685 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 26/23 212.2533 1: 23/21 157.4934 2: 26/23 212.2533 3: 9261/8788 90.7597 4: 23/21 157.4934 5: 26/23 212.2533 6: 23/21 157.4934 7: 26/23 212.2533
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9261/8788 90.760 cents 1: 3 23/21 157.493 cents 1: 3 26/23 212.253 cents 2: 1 10143/8788 248.253 cents 2: 1 9261/7774 303.013 cents 2: 5 26/21 369.747 cents 3: 3 441/338 460.506 cents 3: 2 598/441 527.240 cents 3: 2 676/483 582.000 cents 4: 2 483/338 618.000 cents 4: 2 441/299 672.760 cents 4: 3 676/441 739.494 cents 5: 5 21/13 830.253 cents 5: 1 15548/9261 896.987 cents 5: 1 17576/10143 951.747 cents 6: 3 23/13 987.747 cents 6: 3 42/23 1042.507 cents 6: 1 17576/9261 1109.240 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 : 157.5 369.7 460.5 618.0 830.3 987.7 1200.0 157.5 : 212.3 303.0 460.5 672.8 830.3 1042.5 1200.0 369.7 : 90.8 248.3 460.5 618.0 830.3 987.7 1200.0 460.5 : 157.5 369.7 527.2 739.5 897.0 1109.2 1200.0 618.0 : 212.3 369.7 582.0 739.5 951.7 1042.5 1200.0 830.3 : 157.5 369.7 527.2 739.5 830.3 987.7 1200.0 987.7 : 212.3 369.7 582.0 672.8 830.3 1042.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.7597 .. 212.2533 cents 228488/213003, 121.4936 cents 9261/8788, 90.7597 cents 2: 248.2532 .. 369.7468 cents 228488/213003, 121.4936 cents 233289/228488, 35.9999 cents 3: 460.5065 .. 582.0001 cents 228488/213003, 121.4936 cents 9261/8788, 90.7597 cents 4: 617.9999 .. 739.4935 cents 228488/213003, 121.4936 cents 233289/228488, 35.9999 cents 5: 830.2532 .. 951.7468 cents 228488/213003, 121.4936 cents 9261/8788, 90.7597 cents 6: 987.7467 .. 1109.2403 cents 228488/213003, 121.4936 cents 233289/228488, 35.9999 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 9261/8788, 90.7597 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 26/23, 212.2533 cents Average / Smallest step : 1.888817 Largest / Average step : 1.238144 Largest / Smallest step : 2.338629 Median interval of one step : 23/21, 157.4934 cents, amount: 3 Least squares average step : 165.91609 cents, oct.: 1161.41262 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 35.99986 cents Scale diversity : 1.475499 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.392532 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 : 233289/228488, 35.9999 cents Most common intervals : 26/21, 369.7468 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 157.493 369.747 cents Most common triad is 0.0 369.747 830.253 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 : 13 21 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 10143 (O: 10143 U: 10143) Highest odd numerator or denominator: 483 Scale harmonicity : 0.006693 Average absolute harmonicity : 0.159132 Specific harmonicity : 0.034205 Fundamental : 1/7098, -12.7932 octaves, 0.0369 Hz. Guide tone : 263718, 18.0086 octaves, 68995370.830 Hz. Exponens Consonantiae : 1.871870E+09, 30.80183 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 882.0, average 126.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.69628, average 1.52804 Sum of Tenney's harmonic distance : 21.02022, average 3.00289 Vogel's harmonic complexity : 40.42857 Wille's k value : 5071 Wilson's harmonic complexity : 92 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 73.42887, average 2.62246 Lattice compactness (without 2's) : 67.06225, average 2.39508 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 4 1 3: -1 .. 2 0.28571 6 7: -1 .. 2 0.28571 6 13: -2 .. 1 -0.71429 7 3 23: 0 .. 1 0.42857 3 3 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is weakly epimorphic with val: <7 10 18 24 33| Scale is weakly epimorphic with val: <7 10 18 25 30| Scale is weakly epimorphic with val: <7 10 18 26 34| Scale is weakly epimorphic with val: <7 10 18 27 31| Scale is weakly epimorphic with val: <7 10 18 29 32| Scale is JI-epimorphic with val: <7 10 19 24 30| Scale is weakly epimorphic with val: <7 10 19 25 34| Scale is weakly epimorphic with val: <7 10 19 26 31| Scale is weakly epimorphic with val: <7 10 19 27 35| Scale is weakly epimorphic with val: <7 10 19 28 32| Scale is weakly epimorphic with val: <7 10 20 24 34| Scale is JI-epimorphic with val: <7 10 20 25 31| Scale is weakly epimorphic with val: <7 10 20 26 35| Scale is weakly epimorphic with val: <7 10 20 27 32| Scale is weakly epimorphic with val: <7 10 20 28 29| Scale is weakly epimorphic with val: <7 10 20 29 33| Scale is weakly epimorphic with val: <7 10 21 25 35| Scale is JI-epimorphic with val: <7 10 21 26 32| Scale is weakly epimorphic with val: <7 10 21 27 29| Scale is weakly epimorphic with val: <7 10 21 28 33| Scale is weakly epimorphic with val: <7 10 21 29 30| Scale is weakly epimorphic with val: <7 10 22 24 35| Scale is weakly epimorphic with val: <7 10 22 26 29| Scale is JI-epimorphic with val: <7 10 22 27 33| Scale is weakly epimorphic with val: <7 10 22 28 30| Scale is weakly epimorphic with val: <7 10 22 29 34| Scale is JI-epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 28 32| Scale is weakly epimorphic with val: <7 11 19 24 34| Scale is JI-epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 26 35| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 20 25 35| Scale is JI-epimorphic with val: <7 11 20 26 32| = patent Scale is weakly epimorphic with val: <7 11 20 27 29| Scale is weakly epimorphic with val: <7 11 20 28 33| Scale is weakly epimorphic with val: <7 11 20 29 30| Scale is weakly epimorphic with val: <7 11 21 24 35| Scale is weakly epimorphic with val: <7 11 21 26 29| Scale is JI-epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 21 28 30| Scale is weakly epimorphic with val: <7 11 21 29 34| Scale is weakly epimorphic with val: <7 11 22 24 32| Scale is weakly epimorphic with val: <7 11 22 25 29| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is JI-epimorphic with val: <7 11 22 28 34| Scale is weakly epimorphic with val: <7 11 22 29 31| Scale is weakly epimorphic with val: <7 12 18 24 34| Scale is JI-epimorphic with val: <7 12 18 25 31| Scale is weakly epimorphic with val: <7 12 18 26 35| Scale is weakly epimorphic with val: <7 12 18 27 32| Scale is weakly epimorphic with val: <7 12 18 28 29| Scale is weakly epimorphic with val: <7 12 18 29 33| Scale is weakly epimorphic with val: <7 12 19 25 35| Scale is JI-epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <7 12 19 27 29| Scale is weakly epimorphic with val: <7 12 19 28 33| Scale is weakly epimorphic with val: <7 12 19 29 30| Scale is weakly epimorphic with val: <7 12 20 24 35| Scale is weakly epimorphic with val: <7 12 20 26 29| Scale is JI-epimorphic with val: <7 12 20 27 33| Scale is weakly epimorphic with val: <7 12 20 28 30| Scale is weakly epimorphic with val: <7 12 20 29 34| Scale is weakly epimorphic with val: <7 12 21 24 32| Scale is weakly epimorphic with val: <7 12 21 25 29| Scale is weakly epimorphic with val: <7 12 21 27 30| Scale is JI-epimorphic with val: <7 12 21 28 34| Scale is weakly epimorphic with val: <7 12 21 29 31| Scale is weakly epimorphic with val: <7 12 22 24 29| Scale is weakly epimorphic with val: <7 12 22 25 33| Scale is weakly epimorphic with val: <7 12 22 26 30| Scale is weakly epimorphic with val: <7 12 22 28 31| Scale is JI-epimorphic with val: <7 12 22 29 35|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 39.2508 c. M:-67.7144 c. Lebeng 10: 1 2 1 1 2 1 2 P M ME S SD: 20.9408 c. M: 37.4934 c. 13: 2 2 1 2 2 2 2 SP M ME S SD: 18.1017 c. M:-28.1539 c. Oukranian 16: 2 3 1 2 3 2 3 P T3 SD: 10.0584 c. M: 17.9999 c. 23: 3 4 2 3 4 3 4 SP T3 SD: 5.3731 c. M:-9.0587 c. 29: 4 5 2 4 5 4 5 SP T3 SD: 4.5196 c. M:-8.0238 c. 39: 5 7 3 5 7 5 7 SP T3 SD: 2.1228 c. M: 3.6473 c. 68: 9 12 5 9 12 9 12 SP T3 SD: 0.9548 c. M: 1.6830 c. 91: 12 16 7 12 16 12 16 SP T3 SD: 0.9947 c. M:-1.7803 c. 107: 14 19 8 14 19 14 19 SP T3 SD: 0.6582 c. M: 1.1775 c. 130: 17 23 10 17 23 17 23 SP T3 SD: 0.5528 c. M:-1.0320 c. 159: 21 28 12 21 28 21 28 SP T3 SD: 0.6144 c. M:-0.9971 c. 175: 23 31 13 23 31 23 31 SP T3 SD: 0.6127 c. M: 1.0779 c. 198: 26 35 15 26 35 26 35 SP T3 SD: 0.1015 c. M:-0.1819 c. 503: 66 89 38 66 89 66 89 SP T3 SD: 0.0603 c. M: 0.1073 c. 701: 92 124 53 92 124 92 124 SP T3 SD: 0.0151 c. M: 0.0256 c. 899: 118 159 68 118 159 118 159 SP T3 SD: 0.0118 c. M:-0.0201 c. 1600: 210 283 121 210 283 210 283 SP T3 SD: 0.0041 c. M:-0.0066 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: 41.9775 cents 3 x x 4 x 5 x 6 S SD: 21.9508 cents 4 x 5 x 6 x 7:8 S SD: 21.9102 cents 5 x 6 x 7:8:9:10 S SD: 14.6318 cents 6 x 7:8:9:10:11:12 S SD: 26.7525 cents 7:8 x 9:10:11:12:14 S SD: 17.7479 cents 8:9:10 x 11:13:14:16 SD: 14.2780 cents 9:10:11:12:13:15:16:18 SD: 10.9473 cents 10:11:12:13:14:16:18:20 S SD: 10.5446 cents 11:12 x 14:16:18:19:22 SD: 11.8589 cents 12:13:15:16:17:19:21:24 SD: 8.8391 cents 13:14:16:17:19:21:23:26 SD: 7.1331 cents 19:21:24:25:27:31:34:38 SD: 7.0642 cents 20:22:25:26:29:32:35:40 SD: 5.7874 cents 21:23:26:27:30:34:37:42 SD: 3.8160 cents 30:33:37:39:43:48:53:60 SD: 3.0265 cents 33:36:41:43:47:53:58:66 SD: 2.6850 cents 39:43:48:51:56:63:69:78 SD: 2.5705 cents 42:46:52:55:60:68:74:84 SD: 1.4811 cents 63:69:78:82:90:102:111:126 SD: 1.3149 cents 72:79:89:94:103:116:127:144 SD: 1.2014 cents 75:82:93:98:107:121:133:150 SD: 1.0263 cents 96:105:119:125:137:155:170:192 SD: 0.7931 cents 105:115:130:137:150:170:186:210 SD: 0.6430 cents 135:148:167:176:193:218:239:270 SD: 0.4301 cents 177:194:219:231:253:286:313:354 SD: 0.2954 cents 252:276:312:329:360:407:446:504 SD: 0.1977 cents 273:299:338:356:390:441:483:546 SD: 0.1523 cents 450:493:557:587:643:727:796:900 SD: 0.1244 cents 525:575:650:685:750:848:929:1050 SD: 0.0870 cents