Scala analysis: xen12-chalmers-tritriadic-mt-19-25-7
Tritriadic M->T scale built from 19:25:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/25 196.198479 middle second 2: 25/19 475.114412 3: 28/19 671.312890 4: 38/25 724.885588 5: 625/361 950.228823 6: 700/361 1146.427302 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 361/350 53.5727 1: 28/25 196.1985 middle second 2: 625/532 278.9159 3: 28/25 196.1985 middle second 4: 361/350 53.5727 5: 15625/13718 225.3432 6: 28/25 196.1985 middle second 7: 361/350 53.5727
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 361/350 53.573 cents 1: 3 28/25 196.198 cents middle second 1: 1 15625/13718 225.343 cents 1: 1 625/532 278.916 cents 2: 3 722/625 249.771 cents 2: 1 625/532 278.916 cents 2: 1 8750/6859 421.542 cents 2: 2 25/19 475.114 cents 3: 1 20216/15625 445.970 cents 3: 3 25/19 475.114 cents 3: 2 19/14 528.687 cents 3: 1 28/19 671.313 cents 4: 1 19/14 528.687 cents 4: 2 28/19 671.313 cents 4: 3 38/25 724.886 cents 4: 1 15625/10108 754.030 cents 5: 2 38/25 724.886 cents 5: 1 6859/4375 778.458 cents 5: 1 1064/625 921.084 cents 5: 3 625/361 950.229 cents 6: 1 1064/625 921.084 cents 6: 1 27436/15625 974.657 cents 6: 3 25/14 1003.802 cents middle minor seventh 6: 2 700/361 1146.427 cents Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 196.2 475.1 671.3 724.9 950.2 1146.4 1200.0 196.2 : 278.9 475.1 528.7 754.0 950.2 1003.8 1200.0 475.1 : 196.2 249.8 475.1 671.3 724.9 921.1 1200.0 671.3 : 53.6 278.9 475.1 528.7 724.9 1003.8 1200.0 724.9 : 225.3 421.5 475.1 671.3 950.2 1146.4 1200.0 950.2 : 196.2 249.8 446.0 724.9 921.1 974.7 1200.0 1146.4: 53.6 249.8 528.7 724.9 778.5 1003.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 53.5727 .. 278.9159 cents 15625/13718, 225.3432 cents 361/350, 53.5727 cents 2: 249.7712 .. 475.1144 cents 15625/13718, 225.3432 cents 384104/390625,-29.1448 cents 3: 445.9697 .. 671.3129 cents 15625/13718, 225.3432 cents 384104/390625,-29.1448 cents 4: 528.6871 .. 754.0303 cents 15625/13718, 225.3432 cents 361/392,-142.6258 cents 5: 724.8856 .. 950.2288 cents 15625/13718, 225.3432 cents 384104/390625,-29.1448 cents 6: 921.0841 .. 1146.4273 cents 15625/13718, 225.3432 cents 384104/390625,-29.1448 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 361/350, 53.5727 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 625/532, 278.9159 cents Average / Smallest step : 3.199924 Largest / Average step : 1.627010 Largest / Smallest step : 5.206307 Median interval of one step : 28/25, 196.1985 cents, amount: 3 Most common interval of one step : 28/25, 196.1985 cents, amount: 3 Least squares average step : 186.35440 cents, oct.: 1304.48081 cents Scale is not proper Step pattern alph. order: ABACDAC Step pattern size order : BDBACBA Scale is not a Constant Structure Scale diversity : 1.274111 Lumma stability : 0.089288 Lumma impropriety factor : 0.216004 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 : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 9904396/9765625, 24.4279 cents Most common intervals : 25/19, 475.1144 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 196.198 724.886 cents Most common triad is 0.0 475.114 724.886 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 19 25 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 15625 (O: 15625 U: 15625) Highest odd numerator or denominator: 625 Scale harmonicity : 0.006536 Average absolute harmonicity : 0.160713 Specific harmonicity : 0.035297 Fundamental : 1/9025, -13.1397 octaves, 0.0290 Hz. Guide tone : 332500, 18.3430 octaves, 86990500.463 Hz. Exponens Consonantiae : 3.000813E+09, 31.48271 octaves Euler's gradus suavitatis : 87 Sum of Mann's harmonic distance : 1128.5, average 161.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.82596, average 1.54657 Sum of Tenney's harmonic distance : 22.28245, average 3.18321 Vogel's harmonic complexity : 41.42857 Wille's k value : 7812 Wilson's harmonic complexity : 94 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 92.99894, average 3.32139 Lattice compactness (without 2's) : 83.83777, average 2.99421 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.14286 8 1 5: -2 .. 4 0.57143 12 7: 0 .. 1 0.42857 3 1 19: -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 weakly epimorphic with val: <7 15 18 27| Scale is weakly epimorphic with val: <7 15 19 29| Scale is weakly epimorphic with val: <7 15 20 31| Scale is weakly epimorphic with val: <7 15 21 33| Scale is weakly epimorphic with val: <7 15 22 28| Scale is weakly epimorphic with val: <7 16 19 27| Scale is weakly epimorphic with val: <7 16 20 29| Scale is weakly epimorphic with val: <7 16 21 31| Scale is weakly epimorphic with val: <7 16 22 33| Scale is weakly epimorphic with val: <7 17 18 30| Scale is weakly epimorphic with val: <7 17 19 32| Scale is weakly epimorphic with val: <7 17 21 29| Scale is weakly epimorphic with val: <7 17 22 31| Scale is weakly epimorphic with val: <7 18 18 28| Scale is weakly epimorphic with val: <7 18 19 30| Scale is weakly epimorphic with val: <7 18 20 32| Scale is weakly epimorphic with val: <7 18 21 27|
FIT/MODE
7: 1 2 1 0 2 1 0 N T3 SD: 42.9241 c. M:-78.3426 c. 9: 1 3 1 0 2 2 0 N S SD: 44.5742 c. M: 62.8651 c. 10: 2 2 2 0 2 2 0 N M DE S SD: 32.2983 c. M:-53.5727 c. 13: 2 3 2 1 2 2 1 N G T3 S SD: 21.9525 c. M: 38.7350 c. 15: 2 4 2 1 3 2 1 N SD: 21.1540 c. M: 36.1985 c. 16: 3 3 3 1 3 2 1 N SD: 21.3050 c. M:-28.8015 c. 18: 3 4 3 1 3 3 1 N G T3 S SD: 9.5295 c. M: 16.8955 c. 20: 3 5 3 1 4 3 1 N SD: 9.0625 c. M: 16.1985 c. 23: 4 5 4 1 4 4 1 N G T3 S SD: 7.4754 c. M:-12.4972 c. 25: 4 6 4 1 5 4 1 N SD: 5.2422 c. M:-9.7712 c. 38: 6 9 6 2 7 6 2 N SD: 5.5533 c. M: 9.5852 c. 43: 7 10 7 2 8 7 2 N SD: 1.2558 c. M: 2.2413 c. 91: 15 21 15 4 17 15 4 N SD: 0.8974 c. M:-1.6037 c. 134: 22 31 22 6 25 22 6 N SD: 0.5639 c. M: 0.9751 c. 159: 26 37 26 7 30 26 7 N SD: 0.4577 c. M:-0.7425 c. 202: 33 47 33 9 38 33 9 N SD: 0.1433 c. M:-0.2662 c. 336: 55 78 55 15 63 55 15 N SD: 0.1439 c. M:-0.2301 c. 447: 73 104 73 20 84 73 20 N SD: 0.1262 c. M: 0.2253 c. 495: 81 115 81 22 93 81 22 N SD: 0.1382 c. M:-0.2394 c. 538: 88 125 88 24 101 88 24 N SD: 0.0470 c. M:-0.0840 c. 740: 121 172 121 33 139 121 33 N SD: 0.0335 c. M:-0.0592 c. 985: 161 229 161 44 185 161 44 N SD: 0.0317 c. M: 0.0563 c. 1278: 209 297 209 57 240 209 57 N SD: 0.0320 c. M:-0.0516 c. 1321: 216 307 216 59 248 216 59 N SD: 0.0213 c. M: 0.0396 c. 1523: 249 354 249 68 286 249 68 N SD: 0.0041 c. M: 0.0068 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: 11.4653 cents 3 x 4 x x 5 x 6 S SD: 23.2491 cents 4 x 5 x 6:7 x 8 S SD: 23.3950 cents 5:6 x 7:8:9 x 10 S SD: 37.1893 cents 6:7:8 x 9:10 x 12 S SD: 20.3814 cents 7:8:9:10:11:12 x 14 S SD: 16.1019 cents 8:9:11 x 12:14 x 16 SD: 16.4172 cents 9:10:12:13:14:16:17:18 S SD: 12.5235 cents 10:11:13 x 15:17:19:20 SD: 10.7684 cents 12:13:16 x 18:21:23:24 SD: 11.9287 cents 13:15:17:19:20:23:25:26 SD: 10.1276 cents 14:16:18 x 21:24:27:28 S SD: 10.1818 cents 15:17:20:22:23:26:29:30 SD: 5.0966 cents 16:18:21 x 24:28:31:32 SD: 5.1420 cents 18:20:24 x 27:31:35:36 SD: 6.1188 cents 19:21:25:28:29:33:37:38 SD: 3.6777 cents 25:28:33:37:38:43:48:50 SD: 3.2147 cents 32:36:42:47:49:55:62:64 SD: 2.9814 cents 34:38:45:50:52:59:66:68 SD: 2.3180 cents 42:47:55:62:64:73:81:84 SD: 2.1759 cents 44:49:58:65:67:76:85:88 SD: 1.9835 cents 48:54:63:71:73:83:93:96 SD: 1.6098 cents 66:74:87:97:100:114:128:132 SD: 1.2964 cents 67:75:88:99:102:116:130:134 SD: 0.9072 cents 108:121:142:159:164:187:209:216 SD: 0.6355 cents 127:142:167:187:193:220:246:254 SD: 0.5771 cents 133:149:175:196:202:230:258:266 SD: 0.3646 cents 200:224:263:295:304:346:388:400 SD: 0.3461 cents 209:234:275:308:318:362:405:418 SD: 0.3265 cents 234:262:308:345:356:405:454:468 SD: 0.3179 cents 260:291:342:383:395:450:504:520 SD: 0.2689 cents 275:308:362:405:418:476:533:550 SD: 0.2304 cents 298:334:392:439:453:516:578:596 SD: 0.2243 cents 317:355:417:467:482:549:615:634 SD: 0.2030 cents 342:383:450:504:520:592:663:684 SD: 0.1089 cents