Scala analysis: xen09-chalmers-tritriadic-32-39-48
Tritriadic scale built from 32:39:48
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: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 13/8 840.527662 tridecimal neutral sixth 6: 117/64 1044.437664 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 128/117 155.5623 1: 9/8 203.9100 major whole tone 2: 13/12 138.5727 tridecimal 2/3-tone 3: 128/117 155.5623 4: 9/8 203.9100 major whole tone 5: 13/12 138.5727 tridecimal 2/3-tone 6: 9/8 203.9100 major whole tone 7: 128/117 155.5623
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 13/12 138.573 cents tridecimal 2/3-tone 1: 2 128/117 155.562 cents 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 2: 3 16/13 359.472 cents tridecimal neutral third 3: 5 4/3 498.045 cents perfect fourth 3: 1 351/256 546.393 cents 3: 1 18/13 563.382 cents tridecimal augmented fourth 4: 1 13/9 636.618 cents tridecimal diminished fifth 4: 1 512/351 653.607 cents 4: 5 3/2 701.955 cents perfect fifth 5: 3 13/8 840.528 cents tridecimal neutral sixth 5: 3 64/39 857.517 cents 39th subharmonic 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 117/64 1044.438 cents 6: 2 24/13 1061.427 cents tridecimal neutral seventh 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 : 203.9 342.5 498.0 702.0 840.5 1044.4 1200.0 203.9 : 138.6 294.1 498.0 636.6 840.5 996.1 1200.0 342.5 : 155.6 359.5 498.0 702.0 857.5 1061.4 1200.0 498.0 : 203.9 342.5 546.4 702.0 905.9 1044.4 1200.0 702.0 : 138.6 342.5 498.0 702.0 840.5 996.1 1200.0 840.5 : 203.9 359.5 563.4 702.0 857.5 1061.4 1200.0 1044.4: 155.6 359.5 498.0 653.6 857.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 138.5727 .. 203.9100 cents 27/26, 65.3373 cents 13/12, 138.5727 cents 2: 294.1350 .. 359.4723 cents 27/26, 65.3373 cents 256/243, 90.2250 cents 3: 498.0450 .. 563.3823 cents 27/26, 65.3373 cents 13/12, 138.5727 cents 4: 636.6177 .. 701.9550 cents 27/26, 65.3373 cents 169/162, 73.2353 cents 5: 840.5277 .. 905.8650 cents 27/26, 65.3373 cents 13/12, 138.5727 cents 6: 996.0900 .. 1061.4273 cents 27/26, 65.3373 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 13/12, 138.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.237102 Largest / Average step : 1.189475 Largest / Smallest step : 1.471502 Median interval of one step : 128/117, 155.5623 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 171.85782 cents, oct.: 1203.00473 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : LSMLSLM Scale is a Constant Structure, by a margin of 73.23532 cents Scale diversity : 1.302399 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.673313 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 : 512/507, 16.9897 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 342.483 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 5, average 701.9550 cents Scale is Lydian octave species of abstract tetrachord Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle 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 classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval class 4 Limited inverse transpositions with margin 65.3373 cents: 4 -- Rational properties -- Prime limit : 13 Odd number limit : 351 (O: 351 U: 351) Highest odd numerator or denominator: 117 Scale harmonicity : 0.026210 Average absolute harmonicity : 0.244309 Specific harmonicity : 0.122455 Fundamental : 1/192, -7.5850 octaves, 1.3626 Hz. Guide tone : 468, 8.8704 octaves, 122440.765 Hz. Exponens Consonantiae : 8.985600E+04, 16.45533 octaves Euler's gradus suavitatis : 27 Sum of Mann's harmonic distance : 152.5, average 21.78571 Mersenne's string divisions : 22939035 Sum of van Prooijen's expressibility: 6.68168, average 0.95453 Sum of Tenney's harmonic distance : 13.00331, average 1.85762 Vogel's harmonic complexity : 14.57143 Wille's k value : 175 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 108.46773, average 3.87385 Lattice compactness (without 2's) : 42.59183, average 1.52114 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -6 .. 2 -2.14286 21 1 3: -1 .. 2 0.71429 7 3 13: 0 .. 1 0.42857 3 3 Average exponent except 2's : 8 / 7 = 1.14286 Average absolute exponent except 2's: 10 / 7 = 1.42857 Scale is JI-epimorphic with val: <7 11 26| = patent Scale is weakly epimorphic with val: <7 12 29|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 17.3638 c. M: 32.4814 c. Lebeng 17: 3 2 2 3 2 3 2 SP M ME S SD: 8.0315 c. M:-14.3859 c. Beatles-7, Dichotic-7 24: 4 3 3 4 3 4 3 SP M ME S SD: 5.3467 c. M:-9.4723 c. Neutral Lydian, Iced Major 36: 6 4 5 6 4 6 5 SP T3 SD: 6.3438 c. M: 11.1043 c. 41: 7 5 5 7 5 7 5 SP M DE S SD: 5.7430 c. M:-9.2209 c. Beatles-7, Dichotic-7 46: 8 5 6 8 5 8 6 SP T3 SD: 3.3704 c. M: 5.7451 c. 53: 9 6 7 9 6 9 7 SP T3 SD: 1.8737 c. M: 2.9282 c. 70: 12 8 9 12 8 12 9 SP T3 SD: 0.9951 c. M:-1.8043 c. 77: 13 9 10 13 9 13 10 SP T3 SD: 0.7432 c. M: 1.3126 c. 130: 22 15 17 22 15 22 17 SP T3 SD: 0.7618 c. M: 1.3607 c. 147: 25 17 19 25 17 25 19 SP T3 SD: 0.2618 c. M:-0.4603 c. 277: 47 32 36 47 32 47 36 SP T3 SD: 0.2265 c. M: 0.3943 c. 347: 59 40 45 59 40 59 45 SP T3 SD: 0.1028 c. M: 0.1818 c. 424: 72 49 55 72 49 72 55 SP T3 SD: 0.0755 c. M: 0.1364 c. 571: 97 66 74 97 66 97 74 SP T3 SD: 0.0574 c. M:-0.1028 c. 771: 131 89 100 131 89 131 100 SP T3 SD: 0.0471 c. M: 0.0797 c. 918: 156 106 119 156 106 156 119 SP T3 SD: 0.0062 c. M:-0.0116 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 14.6104 cents 4 x 5 x 6 x 7:8 S SD: 21.8493 cents 5 x 6:7 x 8:9:10 S SD: 19.2832 cents 6:7 x 8:9:10:11:12 S SD: 12.8122 cents 7:8 x 9 x 11:13:14 SD: 18.7818 cents 8:9:10:11:12:13:15:16 SD: 11.6762 cents 10:11:12:13:15:16:18:20 SD: 10.6868 cents 14:16:17:19:21:23:26:28 SD: 7.5916 cents 18:20:22:24:27:29:33:36 SD: 3.8647 cents 24:27:29:32:36:39:44:48 SD: 2.2365 cents 40:45:49:53:60:65:73:80 SD: 2.0454 cents 42:47:51:56:63:68:77:84 SD: 1.9657 cents 54:61:66:72:81:88:99:108 SD: 1.5865 cents 64:72:78:85:96:104:117:128 SD: 0.9680 cents 88:99:107:117:132:143:161:176 SD: 0.9301 cents 96:108:117:128:144:156:176:192 SD: 0.7036 cents 120:135:146:160:180:195:219:240 SD: 0.5984 cents 128:144:156:171:192:208:234:256 SD: 0.4826 cents 168:189:205:224:252:273:307:336 SD: 0.3181 cents 192:216:234:256:288:312:351:384 SD: 0.0000 cents