Scala analysis: xen12-chalmers-tritriadic-dm-17-23-25
Tritriadic D->M scale built from 17:23:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/23 144.353080 2: 529/425 378.965857 3: 23/17 523.318938 4: 25/17 667.672018 5: 625/391 812.025099 6: 46/25 1055.646920 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/23 144.3531 1: 25/23 144.3531 2: 12167/10625 234.6128 3: 25/23 144.3531 4: 25/23 144.3531 5: 25/23 144.3531 6: 17986/15625 243.6218 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 : 144.4 379.0 523.3 667.7 812.0 1055.6 1200.0 144.4 : 234.6 379.0 523.3 667.7 911.3 1055.6 1200.0 379.0 : 144.4 288.7 433.1 676.7 821.0 965.4 1200.0 523.3 : 144.4 288.7 532.3 676.7 821.0 1055.6 1200.0 667.7 : 144.4 388.0 532.3 676.7 911.3 1055.6 1200.0 812.0 : 243.6 388.0 532.3 766.9 911.3 1055.6 1200.0 1055.6: 144.4 288.7 523.3 667.7 812.0 956.4 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 : 170.97812 cents, oct.: 1196.84683 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : SMSSSLS 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 Most common triad is 0.0 144.353 1055.647 cents, amount: 3 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% -- 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 : 0.155907 Specific harmonicity : 0.027118 Fundamental : 1/9775, -13.2549 octaves, 0.0268 Hz. Guide tone : 661250, 19.3348 octaves, 172999905.055 Hz. Exponens Consonantiae : 6.463719E+09, 32.58972 octaves Euler's gradus suavitatis : 108 Sum of Mann's harmonic distance : 1087.0, average 155.28571 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 : 22.08186, average 3.15455 Vogel's harmonic complexity : 50.00000 Wille's k value : 7812 Wilson's harmonic complexity : 116 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 86.68049, average 3.09573 Lattice compactness (without 2's) : 83.60828, average 2.98601 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.28571 2 1 5: -2 .. 4 0.57143 12 17: -1 .. 0 -0.57143 4 1 23: -1 .. 2 0.28571 6 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: 27.2888 c. M:-45.1178 c. Lebeng 9: 1 2 1 1 1 2 1 P M ME I SD: 11.5338 c. M:-21.0341 c. 16: 2 3 2 2 2 3 2 SP M ME I SD: 6.5941 c. M:-12.9749 c. Armodue-7, Antidorian 25: 3 5 3 3 3 5 3 SP M DE I SD: 3.4234 c. M:-5.0341 c. Armodue-7, Antidorian 74: 9 14 9 9 9 15 9 SP T3 SD: 3.1556 c. M: 5.9929 c. 83: 10 16 10 10 10 17 10 SP T3 SD: 2.0717 c. M: 3.0622 c. 92: 11 18 11 11 11 19 11 SP T3 SD: 1.7580 c. M: 3.3294 c. 99: 12 19 12 12 12 20 12 SP T3 SD: 1.6115 c. M: 3.2083 c. 108: 13 21 13 13 13 22 13 SP T3 SD: 0.7997 c. M: 1.1881 c. 133: 16 26 16 16 16 27 16 SP T3 SD: 0.0093 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: 17.1415 cents 3 x x 4 x 5 x 6 S SD: 25.5407 cents 4 x 5 x 6 x 7:8 S SD: 23.4083 cents 5 x 6:7 x 8:9:10 S SD: 18.9362 cents 6 x 7:8:9:10:11:12 S SD: 23.3637 cents 7:8:9 x 10:11:13:14 SD: 19.9552 cents 8:9:10:11:12:13:15:16 SD: 12.3196 cents 11:12:14:15:16:18:20:22 S SD: 9.1958 cents 12:13:15:16:18:19:22:24 SD: 6.7191 cents 20:22:25:27:29:32:37:40 SD: 4.9099 cents 23:25:29:31:34:37:42:46 SD: 4.3278 cents 25:27:31:34:37:40:46:50 SD: 2.7570 cents 32:35:40:43:47:51:59:64 SD: 2.6836 cents 37:40:46:50:54:59:68:74 SD: 2.4372 cents 45:49:56:61:66:72:83:90 SD: 1.1279 cents 57:62:71:77:84:91:105:114 SD: 0.8057 cents 102:111:127:138:150:163:188:204 SD: 0.5220 cents 164:178:204:222:241:262:302:328 SD: 0.5147 cents 172:187:214:233:253:275:316:344 SD: 0.5090 cents 184:200:229:249:271:294:339:368 SD: 0.5085 cents 187:203:233:253:275:299:344:374 SD: 0.4175 cents 204:222:254:276:300:326:375:408 SD: 0.3890 cents 221:240:275:299:325:353:407:442 SD: 0.3696 cents 229:249:285:310:337:366:421:458 SD: 0.3224 cents 266:289:331:360:391:425:489:532 SD: 0.3132 cents 274:298:341:371:403:438:504:548 SD: 0.2612 cents 289:314:360:391:425:462:532:578 SD: 0.2461 cents 323:351:402:437:475:516:594:646 SD: 0.2082 cents 368:400:458:498:541:588:677:736 SD: 0.1497 cents 425:462:529:575:625:679:782:850 SD: 0.1288 cents