Scala analysis: xen10-chalmers-tritriadic-7-3-19
Tritriadic scale built from 7:3:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57/49 261.816204 2: 24/19 404.441985 smaller undevicesimal major third 3: 19/14 528.687110 4: 28/19 671.312890 5: 12/7 933.129094 septimal major sixth 6: 361/196 1057.374219 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 392/361 142.6258 1: 57/49 261.8162 2: 392/361 142.6258 3: 361/336 124.2451 4: 392/361 142.6258 5: 57/49 261.8162 6: 361/336 124.2451 7: 392/361 142.6258
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 361/336 124.245 cents 1: 3 392/361 142.626 cents 1: 2 57/49 261.816 cents 2: 3 7/6 266.871 cents septimal minor third 2: 1 6859/5488 386.061 cents 2: 3 24/19 404.442 cents smaller undevicesimal major third 3: 1 1372/1083 409.497 cents 3: 5 19/14 528.687 cents 3: 1 9408/6859 547.068 cents 4: 1 6859/4704 652.932 cents 4: 5 28/19 671.313 cents 4: 1 1083/686 790.503 cents 5: 3 19/12 795.558 cents undevicesimal minor sixth 5: 1 10976/6859 813.939 cents 5: 3 12/7 933.129 cents septimal major sixth 6: 2 98/57 938.184 cents 6: 3 361/196 1057.374 cents 6: 2 672/361 1075.755 cents 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 : 261.8 404.4 528.7 671.3 933.1 1057.4 1200.0 261.8 : 142.6 266.9 409.5 671.3 795.6 938.2 1200.0 404.4 : 124.2 266.9 528.7 652.9 795.6 1057.4 1200.0 528.7 : 142.6 404.4 528.7 671.3 933.1 1075.8 1200.0 671.3 : 261.8 386.1 528.7 790.5 933.1 1057.4 1200.0 933.1 : 124.2 266.9 528.7 671.3 795.6 938.2 1200.0 1057.4: 142.6 404.4 547.1 671.3 813.9 1075.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 124.2451 .. 261.8162 cents 144/133, 137.5711 cents 361/336, 124.2451 cents 2: 266.8709 .. 404.4420 cents 144/133, 137.5711 cents 343/342, 5.0547 cents 3: 409.4967 .. 547.0678 cents 144/133, 137.5711 cents 343/342, 5.0547 cents 4: 652.9322 .. 790.5033 cents 144/133, 137.5711 cents 47045881/44255232, 105.8645 cents 5: 795.5580 .. 933.1291 cents 144/133, 137.5711 cents 343/342, 5.0547 cents 6: 938.1838 .. 1075.7549 cents 144/133, 137.5711 cents 343/342, 5.0547 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 361/336, 124.2451 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 57/49, 261.8162 cents Average / Smallest step : 1.379761 Largest / Average step : 1.527261 Largest / Smallest step : 2.107255 Median interval of one step : 392/361, 142.6258 cents, amount: 3 Most common interval of one step : 392/361, 142.6258 cents, amount: 3 Least squares average step : 176.79931 cents, oct.: 1237.59519 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : LMSMLSM Scale is a Constant Structure, by a margin of 5.05470 cents Scale diversity : 1.238041 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.312145 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 : 343/342, 5.0547 cents Most common intervals : 19/14, 528.6871 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 404.442 671.313 cents Most common triad is 0.0 528.687 671.313 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 7 19 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 137.5711 cents: 5 -- Rational properties -- Prime limit : 19 Odd number limit : 6859 (O: 6859 U: 6859) Highest odd numerator or denominator: 361 Scale harmonicity : 0.007100 Average absolute harmonicity : 0.166294 Specific harmonicity : 0.039589 Fundamental : 1/3724, -11.8626 octaves, 0.0703 Hz. Guide tone : 60648, 15.8882 octaves, 15867067.284 Hz. Exponens Consonantiae : 2.258532E+08, 27.75081 octaves Euler's gradus suavitatis : 80 Sum of Mann's harmonic distance : 404.0, average 57.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.99474, average 1.28496 Sum of Tenney's harmonic distance : 18.33090, average 2.61870 Vogel's harmonic complexity : 37.42857 Wille's k value : 3429 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 83.53212, average 2.98329 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 3 0.71429 11 1 3: 0 .. 1 0.42857 3 7: -2 .. 1 -0.71429 7 1 19: -1 .. 2 0.28571 6 5 Average exponent except 2's : 0 / 7 = 0.00000 Average absolute exponent except 2's: 16 / 7 = 2.28571 Scale is weakly epimorphic with val: <7 10 18 30| Scale is JI-epimorphic with val: <7 10 19 29| Scale is weakly epimorphic with val: <7 10 20 28| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 10 22 33| Scale is weakly epimorphic with val: <7 11 19 31| Scale is JI-epimorphic with val: <7 11 20 30| = patent Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 11 22 28| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 20 32| Scale is JI-epimorphic with val: <7 12 21 31| Scale is weakly epimorphic with val: <7 12 22 30|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 52.0727 c. M: 90.3876 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 4.9688 c. M:-9.2924 c. 32: 7 4 3 4 7 3 4 P T3 SD: 4.8708 c. M:-8.0580 c. 41: 9 5 4 5 9 4 5 P T3 SD: 3.0107 c. M:-5.3141 c. 50: 11 6 5 6 11 5 6 P T3 SD: 2.0179 c. M:-3.5580 c. 59: 13 7 6 7 13 6 7 P T3 SD: 1.6188 c. M:-2.5906 c. 68: 15 8 7 8 15 7 8 P T3 SD: 1.6152 c. M:-2.8897 c. 125: 27 15 13 15 27 13 15 SP T3 SD: 1.4610 c. M: 2.6162 c. 134: 29 16 14 16 29 14 16 SP T3 SD: 1.2208 c. M: 2.1147 c. 143: 31 17 15 17 31 15 17 SP T3 SD: 1.0872 c. M: 1.6763 c. 152: 33 18 16 18 33 16 18 SP T3 SD: 1.0523 c. M: 1.8104 c. 175: 38 21 18 21 38 18 21 SP T3 SD: 0.8203 c. M: 1.3742 c. 184: 40 22 19 22 40 19 22 SP T3 SD: 0.5689 c. M: 0.9466 c. 193: 42 23 20 23 42 20 23 SP T3 SD: 0.3776 c. M: 0.6763 c. 202: 44 24 21 24 44 21 24 SP T3 SD: 0.2997 c. M: 0.4816 c. 252: 55 30 26 30 55 26 30 SP T3 SD: 0.1821 c. M:-0.3199 c. 261: 57 31 27 31 57 27 31 SP T3 SD: 0.1434 c. M:-0.2528 c. 454: 99 54 47 54 99 47 54 SP T3 SD: 0.0813 c. M: 0.1422 c. 463: 101 55 48 55 101 48 55 SP T3 SD: 0.0686 c. M: 0.1223 c. 715: 156 85 74 85 156 74 85 SP T3 SD: 0.0205 c. M:-0.0335 c. 1178: 257 140 122 140 257 122 140 SP T3 SD: 0.0157 c. M: 0.0277 c. 1893: 413 225 196 225 413 196 225 SP T3 SD: 0.0053 c. M: 0.0095 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: 15.3211 cents 3 x x 4 x 5 x 6 S SD: 19.1992 cents 4 x 5 x 6:7 x 8 S SD: 12.6042 cents 5:6 x 7 x x 9:10 SD: 21.4717 cents 6:7 x 8:9:10:11:12 S SD: 10.9876 cents 7:8:9 x 10:12:13:14 S SD: 11.7619 cents 11:13:14:15:16:19:20:22 SD: 6.6595 cents 19:22:24:26:28:33:35:38 SD: 3.9941 cents 25:29:32:34:37:43:46:50 SD: 3.6526 cents 30:35:38:41:44:51:55:60 SD: 3.3121 cents 31:36:39:42:46:53:57:62 SD: 2.2078 cents 42:49:53:57:62:72:77:84 SD: 1.4381 cents 76:88:96:103:112:130:140:152 SD: 1.3128 cents 80:93:101:109:118:137:147:160 SD: 1.2031 cents 84:98:106:114:124:144:155:168 SD: 0.9831 cents 87:101:110:118:128:149:160:174 SD: 0.8284 cents 118:137:149:160:174:202:217:236 SD: 0.7596 cents 129:150:163:175:190:221:238:258 SD: 0.4968 cents 171:199:216:232:252:293:315:342 SD: 0.1787 cents 361:420:456:490:532:619:665:722 SD: 0.0846 cents 532:619:672:722:784:912:980:1064 SD: 0.0675 cents