Scala analysis: xen09-chalmers-tritriadic-22-24-33
Tritriadic scale built from 22:24:33
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 16/11 648.682058 undecimal semi-diminished fifth 5: 3/2 701.955001 perfect fifth 6: 18/11 852.592059 undecimal neutral sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 11/9 347.4079 undecimal neutral third 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 3: 32/27 294.1350 Pythagorean minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone 5: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 11/9 347.4079 undecimal neutral third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 32/27 294.135 cents Pythagorean minor third 1: 1 11/9 347.408 cents undecimal neutral third 2: 3 9/8 203.910 cents major whole tone 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 128/99 444.772 cents 2: 2 4/3 498.045 cents perfect fourth 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 3 4/3 498.045 cents perfect fourth 3: 2 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 4: 1 11/8 551.318 cents undecimal semi-augmented fourth 4: 2 16/11 648.682 cents undecimal semi-diminished fifth 4: 3 3/2 701.955 cents perfect fifth 4: 1 44/27 845.453 cents neutral sixth 5: 2 3/2 701.955 cents perfect fifth 5: 1 99/64 755.228 cents 5: 1 18/11 852.592 cents undecimal neutral sixth 5: 3 16/9 996.090 cents Pythagorean minor seventh 6: 1 18/11 852.592 cents undecimal neutral sixth 6: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 64/33 1146.727 cents 33rd subharmonic Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 150.6 203.9 498.0 648.7 702.0 852.6 1200.0 150.6 : 53.3 347.4 498.0 551.3 702.0 1049.4 1200.0 203.9 : 294.1 444.8 498.0 648.7 996.1 1146.7 1200.0 498.0 : 150.6 203.9 354.5 702.0 852.6 905.9 1200.0 648.7 : 53.3 203.9 551.3 702.0 755.2 1049.4 1200.0 702.0 : 150.6 498.0 648.7 702.0 996.1 1146.7 1200.0 852.6 : 347.4 498.0 551.3 845.5 996.1 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.2729 .. 347.4079 cents 32/27, 294.1350 cents 33/32, 53.2729 cents 2: 203.9100 .. 498.0450 cents 32/27, 294.1350 cents 81/88,-143.4979 cents 3: 354.5471 .. 648.6821 cents 32/27, 294.1350 cents 81/88,-143.4979 cents 4: 551.3179 .. 845.4529 cents 32/27, 294.1350 cents 121/128,-97.3641 cents 5: 701.9550 .. 996.0900 cents 32/27, 294.1350 cents 81/88,-143.4979 cents 6: 852.5921 .. 1146.7271 cents 32/27, 294.1350 cents 81/88,-143.4979 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 33/32, 53.2729 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 11/9, 347.4079 cents Average / Smallest step : 3.217929 Largest / Average step : 2.026546 Largest / Smallest step : 6.521283 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 154.80463 cents, oct.: 1083.63238 cents Scale is not proper Step pattern alph. order: ABCABAD Step pattern size order : BACBABD Scale is not a Constant Structure Scale diversity : 1.427786 Lumma stability : 0.088788 Lumma impropriety factor : 0.559463 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 243/242, 7.1391 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 150.637 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale contains a complete diamond : 1 3 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 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 99 (O: 99 U: 99) Highest odd numerator or denominator: 11 Scale harmonicity : 0.030137 Average absolute harmonicity : 0.248093 Specific harmonicity : 0.146768 Fundamental : 1/264, -8.0444 octaves, 0.9910 Hz. Guide tone : 144, 7.1699 octaves, 37674.081 Hz. Exponens Consonantiae : 3.801600E+04, 15.21432 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 55.5, average 7.92857 Mersenne's string divisions : 10715355 Sum of van Prooijen's expressibility: 5.03266, average 0.71895 Sum of Tenney's harmonic distance : 10.67845, average 1.52549 Vogel's harmonic complexity : 15.28571 Wille's k value : 148 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 86.93697, average 3.10489 Lattice compactness (without 2's) : 42.59183, average 1.52114 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.85714 14 1 3: -1 .. 2 0.71429 7 3 11: -1 .. 0 -0.42857 3 3 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 10 26| Scale is weakly epimorphic with val: <7 11 23|
FIT/MODE
7: 1 0 2 1 0 1 2 N T3 SD: 22.0614 c. M:-37.0322 c. 13: 2 0 3 2 1 1 4 N SD: 25.8426 c. M:-36.5065 c. 14: 2 0 4 2 0 2 4 N T3 SD: 22.0614 c. M:-37.0322 c. 15: 2 1 3 2 1 2 4 N SD: 20.2413 c. M:-36.0900 c. 17: 2 1 4 2 1 2 5 N SD: 7.4824 c. M: 13.3879 c. 24: 3 1 6 3 1 3 7 N SD: 2.1312 c. M: 3.9100 c. 65: 8 3 16 8 3 8 19 N SD: 1.9786 c. M: 3.3613 c. 87: 11 4 21 11 4 11 25 N SD: 1.7478 c. M:-2.9865 c. 89: 11 4 22 11 4 11 26 N SD: 1.7611 c. M: 3.1539 c. 94: 12 4 23 12 4 12 27 N SD: 1.6824 c. M:-2.7271 c. 111: 14 5 27 14 5 14 32 N SD: 0.9261 c. M:-1.4954 c. 135: 17 6 33 17 6 17 39 N SD: 0.4218 c. M:-0.7413 c. 159: 20 7 39 20 7 20 46 N SD: 0.2134 c. M:-0.3745 c. 335: 42 15 82 42 15 42 97 N SD: 0.1899 c. M: 0.3238 c. 359: 45 16 88 45 16 45 104 N SD: 0.1436 c. M: 0.2244 c. 494: 62 22 121 62 22 62 143 N SD: 0.0766 c. M:-0.1386 c. 518: 65 23 127 65 23 65 150 N SD: 0.0461 c. M: 0.0824 c. 677: 85 30 166 85 30 85 196 N SD: 0.0413 c. M: 0.0695 c. 1012: 127 45 248 127 45 127 293 N SD: 0.0368 c. M: 0.0655 c. 1171: 147 52 287 147 52 147 339 N SD: 0.0100 c. M:-0.0183 c. 1689: 212 75 414 212 75 212 489 N SD: 0.0102 c. M: 0.0166 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 0.0000 cents 3 x x 4 x x 5:6 S SD: 10.5889 cents 4 x x 5 x 6:7:8 S SD: 40.3068 cents 5 x 6 x 7 x 8:10 S SD: 33.8895 cents 6 x 7:8 x 9:10:12 S SD: 14.1042 cents 7 x 8:9:10 x 11:14 SD: 20.5859 cents 8 x 9:11 x 12:13:16 SD: 10.9244 cents 9 x 10:12:13:14:15:18 S SD: 12.4513 cents 10:11 x 13 x 15:16:20 SD: 12.0685 cents 11:12 x 15:16:17:18:22 SD: 10.7816 cents 14:15:16:19:20:21:23:28 SD: 8.6608 cents 16:17:18:21:23:24:26:32 SD: 8.3203 cents 17 x 19:23:25:26:28:34 SD: 8.1404 cents 18 x 20:24:26:27:29:36 SD: 6.0851 cents 19:21 x 25:28:29:31:38 SD: 8.3039 cents 20:22:23:27:29:30:33:40 SD: 6.9290 cents 22:24:25:29:32:33:36:44 SD: 3.7640 cents 24:26:27:32:35:36:39:48 SD: 2.5208 cents 42:46:47:56:61:63:69:84 SD: 1.9432 cents 55:60:62:73:80:83:90:110 SD: 1.9370 cents 57:62:64:76:83:86:93:114 SD: 1.8534 cents 64:70:72:85:93:96:105:128 SD: 1.3501 cents 66:72:74:88:96:99:108:132 SD: 0.8341 cents 88:96:99:117:128:132:144:176 SD: 0.7036 cents 144:157:162:192:209:216:236:288 SD: 0.6743 cents 152:166:171:203:221:228:249:304 SD: 0.5679 cents 154:168:173:205:224:231:252:308 SD: 0.5376 cents 168:183:189:224:244:252:275:336 SD: 0.5272 cents 174:190:196:232:253:261:285:348 SD: 0.4687 cents 176:192:198:235:256:264:288:352 SD: 0.3511 cents 198:216:223:264:288:297:324:396 SD: 0.2774 cents 240:262:270:320:349:360:393:480 SD: 0.2512 cents 264:288:297:352:384:396:432:528 SD: 0.0000 cents