Scala analysis: xen12-chalmers-tritriadic-dm-3-7-19
Tritriadic D->M scale built from 3:7:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 361/336 124.245125 2: 7/6 266.870906 septimal minor third 3: 19/14 528.687110 4: 28/19 671.312890 5: 19/12 795.558015 undevicesimal minor sixth 6: 98/57 938.183796 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 57/49 261.8162 1: 361/336 124.2451 2: 392/361 142.6258 3: 57/49 261.8162 4: 392/361 142.6258 5: 361/336 124.2451 6: 392/361 142.6258 7: 57/49 261.8162
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 : 124.2 266.9 528.7 671.3 795.6 938.2 1200.0 124.2 : 142.6 404.4 547.1 671.3 813.9 1075.8 1200.0 266.9 : 261.8 404.4 528.7 671.3 933.1 1057.4 1200.0 528.7 : 142.6 266.9 409.5 671.3 795.6 938.2 1200.0 671.3 : 124.2 266.9 528.7 652.9 795.6 1057.4 1200.0 795.6 : 142.6 404.4 528.7 671.3 933.1 1075.8 1200.0 938.2 : 261.8 386.1 528.7 790.5 933.1 1057.4 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 : 163.82995 cents, oct.: 1146.80963 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : SMLMSML 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 Scale contains two identical disjunct tetrachords 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: 2 -- Rational properties -- Prime limit : 19 Odd number limit : 6859 (O: 6859 U: 6859) Highest odd numerator or denominator: 361 Scale harmonicity : 0.007050 Average absolute harmonicity : 0.167133 Specific harmonicity : 0.039604 Fundamental : 1/6384, -12.6402 octaves, 0.0410 Hz. Guide tone : 70756, 16.1106 octaves, 18511578.498 Hz. Exponens Consonantiae : 4.517063E+08, 28.75081 octaves Euler's gradus suavitatis : 81 Sum of Mann's harmonic distance : 489.5, average 69.92857 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 : 18.26395, average 2.60914 Vogel's harmonic complexity : 38.14286 Wille's k value : 3429 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 88.77291, average 3.17046 Lattice compactness (without 2's) : 56.12138, average 2.00433 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -0.57143 12 1 3: -1 .. 0 -0.57143 4 7: -1 .. 2 0.28571 6 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: 53.9545 c. M:-90.3876 c. Lebeng 8: 1 1 2 0 1 1 2 N T3 SD: 47.0037 c. M:-71.3129 c. 9: 1 1 2 1 1 1 2 P M ME S SD: 4.9146 c. M:-9.0882 c. Pseudo Pelog, Pelogic-7, Antiionian 41: 4 5 9 5 4 5 9 P T3 SD: 3.8000 c. M: 7.1720 c. 50: 5 6 11 6 5 6 11 P T3 SD: 2.5252 c. M: 4.2451 c. 59: 6 7 13 7 6 7 13 P T3 SD: 1.8193 c. M: 2.5906 c. 68: 7 8 15 8 7 8 15 P T3 SD: 1.5434 c. M: 2.8897 c. 125: 13 15 27 15 13 15 27 SP T3 SD: 1.3815 c. M:-2.6162 c. 134: 14 16 29 16 14 16 29 SP T3 SD: 1.2690 c. M:-2.1147 c. 143: 15 17 31 17 15 17 31 SP T3 SD: 1.2494 c. M:-1.6763 c. 166: 17 20 36 20 17 20 36 SP T3 SD: 0.9799 c. M:-1.5752 c. 175: 18 21 38 21 18 21 38 SP T3 SD: 0.7059 c. M:-1.2448 c. 184: 19 22 40 22 19 22 40 SP T3 SD: 0.4854 c. M:-0.9466 c. 193: 20 23 42 23 20 23 42 SP T3 SD: 0.3517 c. M:-0.6763 c. 202: 21 24 44 24 21 24 44 SP T3 SD: 0.3552 c. M:-0.5074 c. 252: 26 30 55 30 26 30 55 SP T3 SD: 0.2294 c. M: 0.4356 c. 261: 27 31 57 31 27 31 57 SP T3 SD: 0.1444 c. M: 0.2528 c. 445: 46 53 97 53 46 53 97 SP T3 SD: 0.1487 c. M:-0.2432 c. 454: 47 54 99 54 47 54 99 SP T3 SD: 0.0711 c. M:-0.1422 c. 715: 74 85 156 85 74 85 156 SP T3 SD: 0.0250 c. M: 0.0493 c. 1178: 122 140 257 140 122 140 257 SP T3 SD: 0.0197 c. M:-0.0333 c. 1439: 149 171 314 171 149 171 314 SP T3 SD: 0.0163 c. M: 0.0323 c. 1893: 196 225 413 225 196 225 413 SP T3 SD: 0.0051 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 x 5:6 S SD: 20.6454 cents 4 x 5 x 6 x 7:8 S SD: 31.7652 cents 5 x 6:7 x 8:9:10 S SD: 21.8272 cents 6 x 7:8:9 x 10:12 S SD: 13.8203 cents 7 x 8 x 10:11:12:14 S SD: 13.2177 cents 8 x 9:11:12:13:14:16 SD: 15.2538 cents 10:11:12:14:15:16:17:20 SD: 13.2376 cents 11:12:13:15:16:17:19:22 SD: 8.5685 cents 12:13:14:16:18:19:21:24 SD: 7.8534 cents 14:15:16:19:21:22:24:28 SD: 7.0458 cents 17:18:20:23:25:27:29:34 SD: 4.7469 cents 25:27:29:34:37:40:43:50 SD: 3.4301 cents 29:31:34:39:43:46:50:58 SD: 3.3354 cents 36:39:42:49:53:57:62:72 SD: 2.2243 cents 42:45:49:57:62:67:72:84 SD: 2.1449 cents 53:57:62:72:78:84:91:106 SD: 0.9200 cents 108:116:126:147:159:171:186:216 SD: 0.8741 cents 118:127:138:160:174:187:203:236 SD: 0.8271 cents 120:129:140:163:177:190:206:240 SD: 0.5080 cents 163:175:190:221:240:258:280:326 SD: 0.4874 cents 199:214:232:270:293:315:342:398 SD: 0.3869 cents 216:232:252:293:318:342:371:432 SD: 0.3753 cents 228:245:266:309:336:361:392:456 SD: 0.3447 cents 257:276:300:349:379:407:442:514 SD: 0.3036 cents 281:302:328:381:414:445:483:562 SD: 0.2920 cents 283:304:330:384:417:448:487:566 SD: 0.2694 cents 336:361:392:456:495:532:578:672 SD: 0.1565 cents 403:433:470:547:594:638:693:806 SD: 0.1170 cents 456:490:532:619:672:722:784:912 SD: 0.0675 cents