Scala analysis: xen09-chalmers-tritriadic-16-19-24
Tritriadic scale built from 16:19:24
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: 19/16 297.513016 19th harmonic 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 19/12 795.558015 undevicesimal minor sixth 6: 57/32 999.468017 undevicesimal minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/57 200.5320 1: 9/8 203.9100 major whole tone 2: 19/18 93.6030 undevicesimal semitone 3: 64/57 200.5320 4: 9/8 203.9100 major whole tone 5: 19/18 93.6030 undevicesimal semitone 6: 9/8 203.9100 major whole tone 7: 64/57 200.5320
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 19/18 93.603 cents undevicesimal semitone 1: 2 64/57 200.532 cents 1: 3 9/8 203.910 cents major whole tone 2: 1 32/27 294.135 cents Pythagorean minor third 2: 3 19/16 297.513 cents 19th harmonic 2: 3 24/19 404.442 cents smaller undevicesimal major third 3: 5 4/3 498.045 cents perfect fourth 3: 1 171/128 501.423 cents 3: 1 27/19 608.352 cents 4: 1 38/27 591.648 cents 4: 1 256/171 698.577 cents 4: 5 3/2 701.955 cents perfect fifth 5: 3 19/12 795.558 cents undevicesimal minor sixth 5: 3 32/19 902.487 cents 19th subharmonic 5: 1 27/16 905.865 cents Pythagorean major sixth 6: 3 16/9 996.090 cents Pythagorean minor seventh 6: 2 57/32 999.468 cents undevicesimal minor seventh 6: 2 36/19 1106.397 cents smaller undevicesimal major 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 : 203.9 297.5 498.0 702.0 795.6 999.5 1200.0 203.9 : 93.6 294.1 498.0 591.6 795.6 996.1 1200.0 297.5 : 200.5 404.4 498.0 702.0 902.5 1106.4 1200.0 498.0 : 203.9 297.5 501.4 702.0 905.9 999.5 1200.0 702.0 : 93.6 297.5 498.0 702.0 795.6 996.1 1200.0 795.6 : 203.9 404.4 608.4 702.0 902.5 1106.4 1200.0 999.5 : 200.5 404.4 498.0 698.6 902.5 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 93.6030 .. 203.9100 cents 81/76, 110.3070 cents 19/18, 93.6030 cents 2: 294.1350 .. 404.4420 cents 81/76, 110.3070 cents 256/243, 90.2250 cents 3: 498.0450 .. 608.3520 cents 81/76, 110.3070 cents 19/18, 93.6030 cents 4: 591.6480 .. 701.9550 cents 81/76, 110.3070 cents 722/729,-16.7040 cents 5: 795.5580 .. 905.8650 cents 81/76, 110.3070 cents 19/18, 93.6030 cents 6: 996.0900 .. 1106.3970 cents 81/76, 110.3070 cents 256/243, 90.2250 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 19/18, 93.6030 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.831443 Largest / Average step : 1.189475 Largest / Smallest step : 2.178456 Median interval of one step : 64/57, 200.5320 cents, amount: 2 Most common interval of one step : 9/8, 203.9100 cents, amount: 3 Least squares average step : 167.68207 cents, oct.: 1173.77446 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : LSMLSLM Scale is a Constant Structure, by a margin of 16.70397 cents Scale diversity : 1.304744 Lumma stability : 0.462385 Lumma impropriety factor : 0.013920 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 : 513/512, 3.3780 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 297.513 701.955 cents Most common triad is 0.0 498.045 701.955 cents, amount: 3 Number of recognisable fifths : 6, average 701.3920 cents Scale is Lydian octave species of abstract tetrachord 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 differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval class 3 Limited inverse transpositions with margin 110.3070 cents: 6 -- Rational properties -- Prime limit : 19 Odd number limit : 171 (O: 171 U: 171) Highest odd numerator or denominator: 57 Scale harmonicity : 0.020364 Average absolute harmonicity : 0.240426 Specific harmonicity : 0.093261 Fundamental : 1/96, -6.5850 octaves, 2.7253 Hz. Guide tone : 684, 9.4179 octaves, 178951.887 Hz. Exponens Consonantiae : 6.566400E+04, 16.00282 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 93.5, average 13.35714 Mersenne's string divisions : 4924815 Sum of van Prooijen's expressibility: 6.22187, average 0.88884 Sum of Tenney's harmonic distance : 12.11753, average 1.73108 Vogel's harmonic complexity : 15.28571 Wille's k value : 85 Wilson's harmonic complexity : 28 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 97.39627, average 3.47844 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 -1.71429 18 1 3: -1 .. 2 0.28571 6 3 19: 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 33| Scale is JI-epimorphic with val: <7 11 30| = patent Scale is weakly epimorphic with val: <7 12 27|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 34.3893 c. M:-61.5848 c. Lebeng 10: 2 0 2 2 1 1 2 P D3 S SD: 35.4447 c. M: 57.5130 c. 12: 2 1 2 2 1 2 2 P M ME S SD: 2.6493 c. M:-4.4420 c. G.M.Hypodorian, G.M.Aeolian, G.Hyperphrygian, Natural Minor, Melodic Minor descending, Asavari That, Mela Natabhairavi, Raga Jaunpuri, Adana, Darbari, Dhanyasi, Jingla, Gregorian nr.2, Makam Buselik, Nihavend, Peruvian Minor, Se, Chiao: China, Geez, Ezel: Ethiopia, Kiourdi descending: Greece, Cushak: Armenia 53: 9 4 9 9 4 9 9 N M DE S SD: 2.0788 c. M: 3.2416 c. Makam Nihavend, Muberka, Fifty-three tone Minor 65: 11 5 11 11 5 11 11 N M DE S SD: 1.4628 c. M: 2.5449 c. 77: 13 6 13 13 6 13 13 N M DE S SD: 1.1590 c. M: 2.0654 c. 89: 15 7 15 15 7 15 15 N M DE S SD: 1.0605 c. M: 1.7152 c. 166: 28 13 28 28 13 28 28 N M DE S SD: 1.0899 c. M: 1.8777 c. 181: 31 14 30 31 14 31 30 N T3 SD: 1.0198 c. M:-1.6370 c. 193: 33 15 32 33 15 33 32 N T3 SD: 0.9135 c. M:-1.5683 c. 205: 35 16 34 35 16 35 34 N T3 SD: 0.8466 c. M:-1.5076 c. 217: 37 17 36 37 17 37 36 N T3 SD: 0.8137 c. M:-1.4536 c. 222: 38 17 37 38 17 38 37 N T3 SD: 0.8117 c. M:-1.4954 c. 229: 39 18 38 39 18 39 38 N T3 SD: 0.8083 c. M:-1.4053 c. 234: 40 18 39 40 18 40 39 N T3 SD: 0.6531 c. M:-1.2182 c. 246: 42 19 41 42 19 42 41 N T3 SD: 0.5184 c. M:-0.9680 c. 258: 44 20 43 44 20 44 43 N T3 SD: 0.4100 c. M:-0.7412 c. 270: 46 21 45 46 21 46 45 N T3 SD: 0.3341 c. M:-0.5344 c. 282: 48 22 47 48 22 48 47 N T3 SD: 0.2990 c. M:-0.5320 c. 294: 50 23 49 50 23 50 49 N T3 SD: 0.3062 c. M:-0.5320 c. 323: 55 25 54 55 25 55 54 N T3 SD: 0.2998 c. M: 0.5116 c. 335: 57 26 56 57 26 57 56 N T3 SD: 0.1943 c. M: 0.3341 c. 347: 59 27 58 59 27 59 58 N T3 SD: 0.0965 c. M: 0.1690 c. 359: 61 28 60 61 28 61 60 N T3 SD: 0.0142 c. M: 0.0251 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: 29.6002 cents 4 x 5 x 6 x 7:8 S SD: 23.4847 cents 5 x 6:7 x 8:9:10 S SD: 18.0229 cents 6 x 7:8:9:10:11:12 S SD: 17.7279 cents 7:8 x 9 x 11:12:14 SD: 19.2655 cents 8:9:10:11:12:13:14:16 S SD: 16.7117 cents 9:10:11:12 x 14:16:18 S SD: 10.4115 cents 10:11:12:13:15:16:18:20 SD: 9.4984 cents 11:12:13:15 x 17:20:22 SD: 14.3761 cents 12 x 14:16:18:19:21:24 SD: 7.2224 cents 13:15 x 17:20:21:23:26 SD: 13.2430 cents 14:16:17:19:21:22:25:28 SD: 8.2845 cents 15:17:18:20:23:24:27:30 SD: 7.2801 cents 16:18:19:21:24:25:29:32 SD: 6.6635 cents 21:24:25:28:32:33:37:42 SD: 6.4421 cents 22:25:26:29:33:35:39:44 SD: 4.2867 cents 26:29:31:35:39:41:46:52 SD: 3.8623 cents 31:35:37:41:47:49:55:62 SD: 3.8091 cents 32:36:38:43:48:51:57:64 SD: 2.5168 cents 42:47:50:56:63:67:75:84 SD: 2.4331 cents 48:54:57:64:72:76:86:96 SD: 1.4421 cents 64:72:76:85:96:101:114:128 SD: 1.2653 cents 86:97:102:115:129:136:153:172 SD: 1.0945 cents 96:108:114:128:144:152:171:192 SD: 0.0000 cents