Scala analysis: xen09-chalmers-tritriadic-8-11-12
Tritriadic scale built from 8:11:12
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 9/8 203.910002 major whole tone 3: 4/3 498.044999 perfect fourth 4: 11/8 551.317942 undecimal semi-augmented fourth 5: 3/2 701.955001 perfect fifth 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: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 12/11 150.6371 undecimal neutral second, 3/4-tone 3: 32/27 294.1350 Pythagorean minor third 4: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 5: 12/11 150.6371 undecimal neutral second, 3/4-tone 6: 11/9 347.4079 undecimal neutral third 7: 12/11 150.6371 undecimal neutral second, 3/4-tone
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 : 53.3 203.9 498.0 551.3 702.0 1049.4 1200.0 53.3 : 150.6 444.8 498.0 648.7 996.1 1146.7 1200.0 203.9 : 294.1 347.4 498.0 845.5 996.1 1049.4 1200.0 498.0 : 53.3 203.9 551.3 702.0 755.2 905.9 1200.0 551.3 : 150.6 498.0 648.7 702.0 852.6 1146.7 1200.0 702.0 : 347.4 498.0 551.3 702.0 996.1 1049.4 1200.0 1049.4: 150.6 203.9 354.5 648.7 702.0 852.6 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 : 159.76037 cents, oct.: 1118.32262 cents Scale is not proper Step pattern alph. order: ABCABDB Step pattern size order : ABCABDB 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 0.0 551.318 701.955 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 n-1 differentially coherent in interval class 2 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: 33 Scale harmonicity : 0.030137 Average absolute harmonicity : 0.248382 Specific harmonicity : 0.144995 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 3.801600E+04, 15.21432 octaves Euler's gradus suavitatis : 24 Sum of Mann's harmonic distance : 66.5, average 9.50000 Mersenne's string divisions : 440895 Sum of van Prooijen's expressibility: 5.50978, average 0.78711 Sum of Tenney's harmonic distance : 10.80339, average 1.54334 Vogel's harmonic complexity : 12.14286 Wille's k value : 49 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 92.76536, average 3.31305 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.42857 16 1 3: -1 .. 2 0.28571 6 3 11: 0 .. 1 0.42857 3 3 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 10 26| Scale is weakly epimorphic with val: <7 11 23|
FIT/MODE
7: 0 1 2 0 1 2 1 N T3 SD: 29.8191 c. M: 53.2729 c. 15: 1 2 3 1 2 4 2 N SD: 20.1108 c. M:-36.0900 c. 16: 1 2 4 0 2 5 2 N SD: 20.9183 c. M:-26.9550 c. 17: 1 2 4 1 2 5 2 N SD: 9.7182 c. M:-17.3153 c. 22: 1 3 5 1 3 6 3 N SD: 8.5399 c. M:-14.2718 c. 24: 1 3 6 1 3 7 3 N SD: 2.2611 c. M: 3.9100 c. 65: 3 8 16 3 8 19 8 N SD: 1.7140 c. M:-2.9448 c. 87: 4 11 21 4 11 25 11 N SD: 1.6184 c. M:-2.9865 c. 89: 4 11 22 4 11 26 11 N SD: 1.3201 c. M:-2.3225 c. 94: 4 12 23 4 12 27 12 N SD: 1.5701 c. M: 2.5544 c. 111: 5 14 27 5 14 32 14 N SD: 0.7996 c. M:-1.4954 c. 135: 6 17 33 6 17 39 17 N SD: 0.3161 c. M:-0.5344 c. 159: 7 20 39 7 20 46 20 N SD: 0.2558 c. M: 0.4428 c. 294: 13 37 72 13 37 85 37 N SD: 0.2153 c. M: 0.3833 c. 359: 16 45 88 16 45 104 45 N SD: 0.1403 c. M:-0.2192 c. 494: 22 62 121 22 62 143 62 N SD: 0.0985 c. M:-0.1684 c. 518: 23 65 127 23 65 150 65 N SD: 0.0341 c. M:-0.0579 c. 1171: 52 147 287 52 147 339 147 N SD: 0.0105 c. M:-0.0183 c. 1689: 75 212 414 75 212 489 212 N SD: 0.0094 c. M:-0.0154 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 x 6 S SD: 0.0000 cents 4 x x 5 x 6:7:8 S SD: 34.4330 cents 5 x 6 x 7:8:9:10 S SD: 32.8329 cents 6 x 7:8 x 9:11:12 SD: 12.5922 cents 7 x 8:9:10:11:13:14 SD: 21.1286 cents 8 x 9 x 11:12:15:16 SD: 7.7812 cents 9 x 10:12 x 14:17:18 SD: 16.8495 cents 10 x 11:13:14:15:18:20 SD: 12.2667 cents 11 x 12 x 15:17:20:22 SD: 15.3908 cents 12 x 14:16:17:18:22:24 SD: 13.5761 cents 14:15:16 x 19:21:26:28 SD: 13.0522 cents 15:16:17:20:21:23:28:30 SD: 11.9306 cents 16:17:18:21:22:24:29:32 SD: 8.8131 cents 17:18:19:23 x 26:31:34 SD: 10.6337 cents 18:19:20:24:25:27:33:36 SD: 6.9865 cents 22:23:25:29:30:33:40:44 SD: 5.8344 cents 24:25:27:32:33:36:44:48 SD: 2.4856 cents 30:31:34:40:41:45:55:60 SD: 2.4168 cents 32:33:36:43:44:48:59:64 SD: 2.3807 cents 54:56:61:72:74:81:99:108 SD: 1.9086 cents 56:58:63:75:77:84:103:112 SD: 1.7314 cents 62:64:70:83:85:93:114:124 SD: 1.6982 cents 64:66:72:85:88:96:117:128 SD: 1.1967 cents 66:68:74:88:91:99:121:132 SD: 1.1001 cents 72:74:81:96:99:108:132:144 SD: 0.8341 cents 96:99:108:128:132:144:176:192 SD: 0.0000 cents