Scala analysis: xen10-chalmers-tritriadic-23-17-25
Tritriadic scale built from 23:17:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/23 144.353080 2: 625/529 288.706161 3: 34/25 532.327982 4: 34/23 676.681062 5: 850/529 821.034143 6: 46/25 1055.646920 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/23 144.3531 1: 25/23 144.3531 2: 25/23 144.3531 3: 17986/15625 243.6218 4: 25/23 144.3531 5: 25/23 144.3531 6: 12167/10625 234.6128 7: 25/23 144.3531
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 5 25/23 144.353 cents 1: 1 12167/10625 234.613 cents 1: 1 17986/15625 243.622 cents 2: 3 625/529 288.706 cents 2: 2 529/425 378.966 cents 2: 2 782/625 387.975 cents 3: 1 15625/12167 433.059 cents 3: 3 23/17 523.319 cents 3: 3 34/25 532.328 cents 4: 3 25/17 667.672 cents 4: 3 34/23 676.681 cents 4: 1 24334/15625 766.941 cents 5: 2 625/391 812.025 cents 5: 2 850/529 821.034 cents 5: 3 1058/625 911.294 cents 6: 1 15625/8993 956.378 cents 6: 1 21250/12167 965.387 cents 6: 5 46/25 1055.647 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 : 144.4 288.7 532.3 676.7 821.0 1055.6 1200.0 144.4 : 144.4 388.0 532.3 676.7 911.3 1055.6 1200.0 288.7 : 243.6 388.0 532.3 766.9 911.3 1055.6 1200.0 532.3 : 144.4 288.7 523.3 667.7 812.0 956.4 1200.0 676.7 : 144.4 379.0 523.3 667.7 812.0 1055.6 1200.0 821.0 : 234.6 379.0 523.3 667.7 911.3 1055.6 1200.0 1055.6: 144.4 288.7 433.1 676.7 821.0 965.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 144.3531 .. 243.6218 cents 413678/390625, 99.2687 cents 25/23, 144.3531 cents 2: 288.7062 .. 387.9749 cents 413678/390625, 99.2687 cents 9765625/9514594, 45.0843 cents 3: 433.0592 .. 532.3280 cents 413678/390625, 99.2687 cents 9765625/9514594, 45.0843 cents 4: 667.6720 .. 766.9408 cents 413678/390625, 99.2687 cents 625/578, 135.3440 cents 5: 812.0251 .. 911.2938 cents 413678/390625, 99.2687 cents 9765625/9514594, 45.0843 cents 6: 956.3782 .. 1055.6469 cents 413678/390625, 99.2687 cents 9765625/9514594, 45.0843 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 25/23, 144.3531 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 17986/15625, 243.6218 cents Average / Smallest step : 1.187564 Largest / Average step : 1.421127 Largest / Smallest step : 1.687680 Median interval of one step : 25/23, 144.3531 cents, amount: 5 Most common interval of one step : 25/23, 144.3531 cents, amount: 5 Least squares average step : 170.46090 cents, oct.: 1193.22629 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: AABAACA Step pattern size order : SSLSSMS Scale is a Constant Structure, by a margin of 45.08434 cents Scale diversity : 1.287844 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.503656 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 : 578/575, 9.0090 cents Most common intervals : 25/23, 144.3531 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 532.328 1055.647 cents Number of recognisable fifths : 0 Best fifths form a closed circle Scale contains a complete diamond : 23 25 Formal octave complements present : 3 = 42.8571% Limited inverse transpositions with margin 99.2687 cents: 1 -- Rational properties -- Prime limit : 23 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.005108 Average absolute harmonicity : 0.155637 Specific harmonicity : 0.026947 Fundamental : 1/13225, -13.6910 octaves, 0.0198 Hz. Guide tone : 488750, 18.8987 octaves, 127869495.041 Hz. Exponens Consonantiae : 6.463719E+09, 32.58972 octaves Euler's gradus suavitatis : 108 Sum of Mann's harmonic distance : 1385.5, average 197.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.07488, average 1.58213 Sum of Tenney's harmonic distance : 23.11623, average 3.30232 Vogel's harmonic complexity : 50.42857 Wille's k value : 7812 Wilson's harmonic complexity : 116 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 87.30797, average 3.11814 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.71429 5 1 5: -2 .. 4 0.57143 12 17: 0 .. 1 0.42857 3 1 23: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 22 / 7 = 3.14286 Scale is JI-epimorphic with val: <7 15 26 29| Scale is weakly epimorphic with val: <7 15 27 31| Scale is weakly epimorphic with val: <7 15 28 33| Scale is weakly epimorphic with val: <7 15 29 35| Scale is weakly epimorphic with val: <7 15 31 32| Scale is weakly epimorphic with val: <7 15 32 34| Scale is weakly epimorphic with val: <7 16 26 34| Scale is weakly epimorphic with val: <7 16 27 29| Scale is JI-epimorphic with val: <7 16 28 31| Scale is weakly epimorphic with val: <7 16 29 33| Scale is weakly epimorphic with val: <7 16 30 35| Scale is weakly epimorphic with val: <7 17 26 32| Scale is weakly epimorphic with val: <7 17 28 29| Scale is weakly epimorphic with val: <7 17 29 31| Scale is JI-epimorphic with val: <7 17 30 33| Scale is weakly epimorphic with val: <7 17 31 35| Scale is weakly epimorphic with val: <7 18 26 30| Scale is weakly epimorphic with val: <7 18 27 32| Scale is weakly epimorphic with val: <7 18 28 34| Scale is weakly epimorphic with val: <7 18 30 31| Scale is weakly epimorphic with val: <7 18 31 33| Scale is JI-epimorphic with val: <7 18 32 35|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 29.5428 c. M:-54.1510 c. Lebeng 9: 1 1 2 1 1 2 1 P M ME S SD: 13.4820 c. M: 22.0395 c. 16: 2 2 3 2 2 3 2 SP M ME S SD: 6.1363 c. M:-11.2938 c. Antimixolydian 25: 3 3 5 3 3 5 3 SP M DE S SD: 3.0876 c. M: 5.0341 c. Antimixolydian 66: 8 8 13 8 8 13 8 SP M DE S SD: 2.8436 c. M: 5.0553 c. 67: 8 8 14 8 8 13 8 SP T3 SD: 2.8070 c. M:-4.9855 c. 76: 9 9 16 9 9 15 9 SP T3 SD: 2.8241 c. M:-4.5141 c. 83: 10 10 17 10 10 16 10 SP T3 SD: 1.8728 c. M:-3.0622 c. 92: 11 11 19 11 11 18 11 SP T3 SD: 1.3944 c. M:-2.4546 c. 108: 13 13 22 13 13 21 13 SP T3 SD: 0.7246 c. M:-1.1881 c. 133: 16 16 27 16 16 26 16 SP T3 SD: 0.0109 c. M:-0.0185 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: 24.0031 cents 4 x 5 x 6 x 7:8 S SD: 33.2640 cents 5 x 6:7 x 8:9:10 S SD: 13.7779 cents 6 x 7:8:9:10:11:12 S SD: 13.2711 cents 7 x 8 x 10:11:13:14 SD: 18.5008 cents 8:9 x 11:12:13:15:16 SD: 12.8998 cents 10:11:12:14:15:16:18:20 S SD: 10.8900 cents 11:12:13:15:16:18:20:22 SD: 6.8025 cents 20:22:24:27:30:32:37:40 SD: 6.5403 cents 21:23:25:29:31:34:39:42 SD: 5.5000 cents 22:24:26:30:33:35:40:44 SD: 5.3882 cents 23:25:27:31:34:37:42:46 SD: 3.3280 cents 33:36:39:45:49:53:61:66 SD: 1.9402 cents 44:48:52:60:65:71:81:88 SD: 1.5461 cents 56:61:66:76:83:90:103:112 SD: 1.1635 cents 81:88:96:110:120:130:149:162 SD: 1.0594 cents 92:100:109:125:136:148:169:184 SD: 0.8870 cents 94:102:111:128:139:151:173:188 SD: 0.5511 cents 138:150:163:188:204:222:254:276 SD: 0.5220 cents 150:163:177:204:222:241:276:300 SD: 0.4298 cents 186:202:220:253:275:299:342:372 SD: 0.4089 cents 219:238:259:298:324:352:403:438 SD: 0.3553 cents 242:263:286:329:358:389:445:484 SD: 0.2849 cents 264:287:312:359:390:424:486:528 SD: 0.2505 cents 320:348:378:435:473:514:589:640 SD: 0.2128 cents 358:389:423:487:529:575:659:716 SD: 0.2065 cents 381:414:450:518:563:612:701:762 SD: 0.1826 cents 414:450:489:563:612:665:762:828 SD: 0.1314 cents 425:462:502:578:628:683:782:850 SD: 0.1285 cents 506:550:598:688:748:813:931:1012 SD: 0.0936 cents 600:652:709:816:887:964:1104:1200 SD: 0.0811 cents