Scala analysis: xen10-chalmers-tritriadic-17-7-23
Tritriadic scale built from 17:7:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 322/289 187.189435 2: 28/23 340.551559 3: 23/17 523.318938 4: 34/23 676.681062 5: 28/17 863.870497 submajor sixth 6: 529/289 1046.637876 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 578/529 153.3621 1: 322/289 187.1894 2: 578/529 153.3621 3: 529/476 182.7674 4: 578/529 153.3621 5: 322/289 187.1894 6: 529/476 182.7674 7: 578/529 153.3621
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 578/529 153.362 cents 1: 2 529/476 182.767 cents 1: 2 322/289 187.189 cents 2: 3 17/14 336.130 cents supraminor third 2: 3 28/23 340.552 cents 2: 1 12167/9826 369.957 cents 3: 1 4913/3703 489.492 cents 3: 1 16184/12167 493.914 cents 3: 5 23/17 523.319 cents 4: 5 34/23 676.681 cents 4: 1 12167/8092 706.086 cents 4: 1 7406/4913 710.508 cents 5: 1 19652/12167 830.043 cents 5: 3 23/14 859.448 cents 5: 3 28/17 863.870 cents submajor sixth 6: 2 289/161 1012.811 cents 6: 2 952/529 1017.233 cents 6: 3 529/289 1046.638 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 : 187.2 340.6 523.3 676.7 863.9 1046.6 1200.0 187.2 : 153.4 336.1 489.5 676.7 859.4 1012.8 1200.0 340.6 : 182.8 336.1 523.3 706.1 859.4 1046.6 1200.0 523.3 : 153.4 340.6 523.3 676.7 863.9 1017.2 1200.0 676.7 : 187.2 370.0 523.3 710.5 863.9 1046.6 1200.0 863.9 : 182.8 336.1 523.3 676.7 859.4 1012.8 1200.0 1046.6: 153.4 340.6 493.9 676.7 830.0 1017.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 153.3621 .. 187.1894 cents 85169/83521, 33.8273 cents 578/529, 153.3621 cents 2: 336.1295 .. 369.9568 cents 85169/83521, 33.8273 cents 4913/4508, 148.9401 cents 3: 489.4916 .. 523.3189 cents 85169/83521, 33.8273 cents 48275138/45054401, 119.5348 cents 4: 676.6811 .. 710.5084 cents 85169/83521, 33.8273 cents 578/529, 153.3621 cents 5: 830.0432 .. 863.8705 cents 85169/83521, 33.8273 cents 48275138/45054401, 119.5348 cents 6: 1012.8106 .. 1046.6379 cents 85169/83521, 33.8273 cents 4913/4508, 148.9401 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 578/529, 153.3621 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 322/289, 187.1894 cents Average / Smallest step : 1.117803 Largest / Average step : 1.091938 Largest / Smallest step : 1.220571 Median interval of one step : 529/476, 182.7674 cents, amount: 2 Most common interval of one step : 578/529, 153.3621 cents, amount: 3 Least squares average step : 172.45824 cents, oct.: 1207.20767 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : LSMSLMS Scale is a Constant Structure, by a margin of 119.53481 cents Scale diversity : 1.166414 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.830863 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 : 392/391, 4.4221 cents Most common intervals : 23/17, 523.3189 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 340.552 676.681 cents Most common triad is 0.0 523.319 676.681 cents, amount: 3 Number of recognisable fifths : 2, average 708.2973 cents 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 : 17 23 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 33.8273 cents: 3 -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.004369 Average absolute harmonicity : 0.155030 Specific harmonicity : 0.024002 Fundamental : 1/6647, -12.6985 octaves, 0.0394 Hz. Guide tone : 251804, 17.9419 octaves, 65878363.845 Hz. Exponens Consonantiae : 1.673741E+09, 30.64043 octaves Euler's gradus suavitatis : 123 Sum of Mann's harmonic distance : 812.5, average 116.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.49999, average 1.50000 Sum of Tenney's harmonic distance : 21.42601, average 3.06086 Vogel's harmonic complexity : 55.42857 Wille's k value : 6083 Wilson's harmonic complexity : 127 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 66.09890, average 2.36068 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 7 1 7: 0 .. 1 0.42857 3 17: -2 .. 1 -0.71429 7 1 23: -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 18 26 31| Scale is JI-epimorphic with val: <7 18 27 30| Scale is weakly epimorphic with val: <7 18 28 29| Scale is weakly epimorphic with val: <7 18 29 35| Scale is weakly epimorphic with val: <7 18 30 34| Scale is weakly epimorphic with val: <7 18 31 33| Scale is weakly epimorphic with val: <7 19 27 32| Scale is JI-epimorphic with val: <7 19 28 31| Scale is weakly epimorphic with val: <7 19 29 30| Scale is weakly epimorphic with val: <7 19 31 35| Scale is weakly epimorphic with val: <7 19 32 34| Scale is weakly epimorphic with val: <7 20 26 35| Scale is weakly epimorphic with val: <7 20 28 33| Scale is JI-epimorphic with val: <7 20 29 32| = patent Scale is weakly epimorphic with val: <7 20 30 31| Scale is weakly epimorphic with val: <7 21 26 30| Scale is weakly epimorphic with val: <7 21 27 29| Scale is weakly epimorphic with val: <7 21 29 34| Scale is JI-epimorphic with val: <7 21 30 33| Scale is weakly epimorphic with val: <7 21 31 32| Scale is weakly epimorphic with val: <7 22 26 32| Scale is weakly epimorphic with val: <7 22 27 31| Scale is weakly epimorphic with val: <7 22 28 30| Scale is weakly epimorphic with val: <7 22 30 35| Scale is JI-epimorphic with val: <7 22 31 34| Scale is weakly epimorphic with val: <7 22 32 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 10.6138 c. M: 18.0664 c. Lebeng 25: 4 3 4 3 4 4 3 SP M ME S SD: 5.0050 c. M:-9.3621 c. 32: 5 4 5 4 5 5 4 SP M ME S SD: 2.0086 c. M:-3.3621 c. 39: 6 5 6 5 6 6 5 SP M ME S SD: 1.5484 c. M: 2.5741 c. Amity-7 71: 11 9 11 9 11 11 9 SP M DE S SD: 1.4110 c. M: 2.5234 c. 110: 17 14 17 14 17 17 14 SP M DE S SD: 1.3857 c. M: 2.3697 c. 133: 21 17 20 17 21 20 17 SP T3 SD: 1.5024 c. M:-2.3056 c. 140: 22 18 21 18 22 21 18 SP T3 SD: 1.3041 c. M:-2.3056 c. 149: 23 19 23 19 23 23 19 SP M DE S SD: 1.4034 c. M: 2.2965 c. 158: 25 20 24 20 25 24 20 SP T3 SD: 1.4984 c. M:-2.6840 c. 165: 26 21 25 21 26 25 21 SP T3 SD: 1.0911 c. M:-1.9015 c. 172: 27 22 26 22 27 26 22 SP T3 SD: 0.8183 c. M:-1.3089 c. 179: 28 23 27 23 28 27 23 SP T3 SD: 0.7547 c. M:-1.3479 c. 204: 32 26 31 26 32 31 26 SP T3 SD: 0.5914 c. M:-1.0459 c. 211: 33 27 32 27 33 32 27 SP T3 SD: 0.3962 c. M:-0.6807 c. 243: 38 31 37 31 38 37 31 SP T3 SD: 0.2599 c. M:-0.4649 c. 250: 39 32 38 32 39 38 32 SP T3 SD: 0.1528 c. M:-0.2484 c. 282: 44 36 43 36 44 43 36 SP T3 SD: 0.0950 c. M:-0.1706 c. 532: 83 68 81 68 83 81 68 SP T3 SD: 0.0281 c. M:-0.0499 c. 814: 127 104 124 104 127 124 104 SP T3 SD: 0.0253 c. M:-0.0452 c. 1346: 210 172 205 172 210 205 172 SP T3 SD: 0.0179 c. M:-0.0320 c. 1878: 293 240 286 240 293 286 240 SP T3 SD: 0.0183 c. M:-0.0310 c. 1917: 299 245 292 245 299 292 245 SP T3 SD: 0.0136 c. M: 0.0220 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: 12.6370 cents 3 x x 4 x 5 x 6 S SD: 10.8451 cents 4 x 5 x 6 x 7:8 S SD: 23.4356 cents 5 x 6:7 x 8:9:10 S SD: 17.3046 cents 6 x 7:8:9:10:11:12 S SD: 14.0767 cents 7:8 x 9:10:12:13:14 S SD: 22.7601 cents 8:9:10:11:12:13:15:16 SD: 11.1341 cents 9:10:11:12:13:15:16:18 SD: 10.3890 cents 11:12:13:15:16:18:20:22 SD: 10.3061 cents 14:16:17:19:21:23:26:28 SD: 8.1686 cents 17:19:21:23:25:28:31:34 SD: 4.0197 cents 23:26:28:31:34:38:42:46 SD: 3.8255 cents 28:31:34:38:41:46:51:56 SD: 3.2952 cents 34:38:41:46:50:56:62:68 SD: 2.9396 cents 36:40:44:49:53:59:66:72 SD: 2.5165 cents 37:41:45:50:55:61:68:74 SD: 2.2147 cents 42:47:51:57:62:69:77:84 SD: 1.6784 cents 54:60:66:73:80:89:99:108 SD: 1.3909 cents 60:67:73:81:89:99:110:120 SD: 1.2953 cents 77:86:94:104:114:127:141:154 SD: 1.1295 cents 79:88:96:107:117:130:145:158 SD: 0.9967 cents 88:98:107:119:130:145:161:176 SD: 0.4160 cents 184:205:224:249:272:303:337:368 SD: 0.1638 cents 272:303:331:368:402:448:498:544 SD: 0.1344 cents 456:508:555:617:674:751:835:912 SD: 0.1231 cents 561:625:683:759:829:924:1027:1122 SD: 0.0992 cents