Scala analysis: xen09-chalmers-tritriadic-26-32-39
Tritriadic scale built from 26:32:39
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: 16/13 359.472338 tridecimal neutral third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 64/39 857.517337 39th subharmonic 6: 24/13 1061.427339 tridecimal neutral seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 13/12 138.5727 tridecimal 2/3-tone 1: 9/8 203.9100 major whole tone 2: 128/117 155.5623 3: 13/12 138.5727 tridecimal 2/3-tone 4: 9/8 203.9100 major whole tone 5: 128/117 155.5623 6: 9/8 203.9100 major whole tone 7: 13/12 138.5727 tridecimal 2/3-tone
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 : 203.9 359.5 498.0 702.0 857.5 1061.4 1200.0 203.9 : 155.6 294.1 498.0 653.6 857.5 996.1 1200.0 359.5 : 138.6 342.5 498.0 702.0 840.5 1044.4 1200.0 498.0 : 203.9 359.5 563.4 702.0 905.9 1061.4 1200.0 702.0 : 155.6 359.5 498.0 702.0 857.5 996.1 1200.0 857.5 : 203.9 342.5 546.4 702.0 840.5 1044.4 1200.0 1061.4: 138.6 342.5 498.0 636.6 840.5 996.1 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 : 173.43543 cents, oct.: 1214.04802 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : LMSLMLS 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 0.0 359.472 701.955 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 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: 39 Scale harmonicity : 0.025540 Average absolute harmonicity : 0.244805 Specific harmonicity : 0.122846 Fundamental : 1/312, -8.2854 octaves, 0.8385 Hz. Guide tone : 576, 9.1699 octaves, 150696.326 Hz. Exponens Consonantiae : 1.797120E+05, 17.45533 octaves Euler's gradus suavitatis : 28 Sum of Mann's harmonic distance : 100.5, average 14.35714 Mersenne's string divisions : 197276415 Sum of van Prooijen's expressibility: 5.72744, average 0.81821 Sum of Tenney's harmonic distance : 12.22516, average 1.74645 Vogel's harmonic complexity : 16.00000 Wille's k value : 175 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 108.46081, average 3.87360 Lattice compactness (without 2's) : 41.76998, average 1.49178 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 6 1.71429 20 1 3: -1 .. 2 0.28571 6 3 13: -1 .. 0 -0.42857 3 3 Average exponent except 2's :-1 / 7 =-0.14286 Average absolute exponent except 2's: 9 / 7 = 1.28571 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: 20.4879 c. M: 32.8559 c. Lebeng 10: 2 1 1 2 1 2 1 P M ME S SD: 19.2940 c. M:-36.0900 c. Sethares Neutral, Beatles-7, Dichotic-7 16: 3 2 2 2 2 3 2 P D3 S SD: 21.8011 c. M: 32.5173 c. 17: 3 2 2 3 2 3 2 SP M ME S SD: 5.9924 c. M: 10.4585 c. Beatles-7, Dichotic-7 24: 4 3 3 4 3 4 3 SP M ME S SD: 6.5438 c. M: 11.4273 c. Neutral Lydian, Iced Major 36: 6 5 4 6 5 6 4 SP T3 SD: 5.1527 c. M:-9.1493 c. 41: 7 5 5 7 5 7 5 SP M DE S SD: 5.4275 c. M: 8.7368 c. Beatles-7, Dichotic-7 43: 7 6 5 7 6 7 5 SP T3 SD: 5.0656 c. M: 8.5612 c. 46: 8 6 5 8 6 8 5 SP T3 SD: 4.5485 c. M:-8.1379 c. 53: 9 7 6 9 7 9 6 SP T3 SD: 1.8291 c. M:-2.8600 c. 70: 12 9 8 12 9 12 8 SP T3 SD: 1.0244 c. M:-1.8043 c. 77: 13 10 9 13 10 13 9 SP T3 SD: 0.9735 c. M: 1.6871 c. 130: 22 17 15 22 17 22 15 SP T3 SD: 0.5636 c. M:-0.9442 c. 147: 25 19 17 25 19 25 17 SP T3 SD: 0.2101 c. M: 0.3745 c. 277: 47 36 32 47 36 47 32 SP T3 SD: 0.1718 c. M: 0.2999 c. 347: 59 45 40 59 45 59 40 SP T3 SD: 0.1364 c. M:-0.2441 c. 424: 72 55 49 72 55 72 49 SP T3 SD: 0.0771 c. M: 0.1364 c. 571: 97 74 66 97 74 97 66 SP T3 SD: 0.0739 c. M: 0.1314 c. 771: 131 100 89 131 100 131 89 SP T3 SD: 0.0410 c. M:-0.0702 c. 918: 156 119 106 156 119 156 106 SP T3 SD: 0.0069 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: 8.9471 cents 4 x 5 x 6 x 7:8 S SD: 24.1033 cents 5 x 6:7 x 8:9:10 S SD: 22.7140 cents 6:7 x 8:9:10:11:12 S SD: 11.5831 cents 7:8 x 9 x 11:13:14 SD: 20.4370 cents 8:9:10:11:12:13:15:16 SD: 9.6548 cents 14:16:17:19:21:23:26:28 SD: 6.9053 cents 18:20:22:24:27:30:33:36 S SD: 5.4848 cents 22:25:27:29:33:36:41:44 SD: 4.5378 cents 26:29:32:35:39:43:48:52 SD: 3.7165 cents 30:34:37:40:45:49:55:60 SD: 2.8137 cents 39:44:48:52:59:64:72:78 SD: 2.2193 cents 48:54:59:64:72:79:89:96 SD: 1.3321 cents 64:72:79:85:96:105:118:128 SD: 1.2522 cents 72:81:89:96:108:118:133:144 SD: 1.1276 cents 78:88:96:104:117:128:144:156 SD: 0.7036 cents 126:142:155:168:189:207:233:252 SD: 0.6694 cents 144:162:177:192:216:236:266:288 SD: 0.4777 cents 168:189:207:224:252:276:310:336 SD: 0.4090 cents 200:225:246:267:300:328:369:400 SD: 0.4089 cents 208:234:256:277:312:341:384:416 SD: 0.3832 cents 216:243:266:288:324:354:399:432 SD: 0.3805 cents 234:263:288:312:351:384:432:468 SD: 0.2350 cents 312:351:384:416:468:512:576:624 SD: 0.0000 cents