Scala analysis: xen12-chalmers-tritriadic-dm-7-9-5
Tritriadic D->M scale built from 7:9:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 81/70 252.680383 Al-Hwarizmi's lute middle finger 3: 9/7 435.084095 septimal major third, BP third 4: 10/7 617.487807 Euler's tritone 5: 100/63 799.891520 quasi-equal minor sixth 6: 9/5 1017.596288 just minor seventh, BP seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 10/9 182.4037 minor whole tone 2: 729/700 70.2767 3: 10/9 182.4037 minor whole tone 4: 10/9 182.4037 minor whole tone 5: 10/9 182.4037 minor whole tone 6: 567/500 217.7048 7: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 729/700 70.277 cents 1: 5 10/9 182.404 cents minor whole tone 1: 1 567/500 217.705 cents 2: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 2: 3 100/81 364.807 cents grave major third 2: 2 63/50 400.108 cents quasi-equal major third 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 1000/729 547.211 cents 3: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 3 10/7 617.488 cents Euler's tritone 4: 1 729/500 652.789 cents 4: 3 14/9 764.916 cents septimal minor sixth 5: 2 100/63 799.892 cents quasi-equal minor sixth 5: 3 81/50 835.193 cents acute minor sixth 5: 2 140/81 947.320 cents 6: 1 1000/567 982.295 cents 6: 5 9/5 1017.596 cents just minor seventh, BP seventh 6: 1 1400/729 1129.723 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 : 182.4 252.7 435.1 617.5 799.9 1017.6 1200.0 182.4 : 70.3 252.7 435.1 617.5 835.2 1017.6 1200.0 252.7 : 182.4 364.8 547.2 764.9 947.3 1129.7 1200.0 435.1 : 182.4 364.8 582.5 764.9 947.3 1017.6 1200.0 617.5 : 182.4 400.1 582.5 764.9 835.2 1017.6 1200.0 799.9 : 217.7 400.1 582.5 652.8 835.2 1017.6 1200.0 1017.6: 182.4 364.8 435.1 617.5 799.9 982.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 70.2767 .. 217.7048 cents 49/45, 147.4281 cents 729/700, 70.2767 cents 2: 252.6804 .. 400.1085 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 3: 435.0841 .. 582.5122 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 4: 617.4878 .. 764.9159 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 5: 799.8915 .. 947.3196 cents 49/45, 147.4281 cents 50/49, 34.9756 cents 6: 982.2952 .. 1129.7233 cents 49/45, 147.4281 cents 50/49, 34.9756 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 729/700, 70.2767 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 567/500, 217.7048 cents Average / Smallest step : 2.439338 Largest / Average step : 1.269944 Largest / Smallest step : 3.097824 Median interval of one step : 10/9, 182.4037 cents, amount: 5 Most common interval of one step : 10/9, 182.4037 cents, amount: 5 Least squares average step : 164.05717 cents, oct.: 1148.40017 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : MSMMMLM Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.376338 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.262860 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 : 50/49, 34.9756 cents Most common intervals : 10/9, 182.4037 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 582.512 1017.596 cents Most common triad is 0.0 182.404 1017.596 cents, amount: 3 Number of recognisable fifths : 0 Best fifths form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 5 9 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 7 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 81 Scale harmonicity : 0.020625 Average absolute harmonicity : 0.193210 Specific harmonicity : 0.107834 Fundamental : 1/630, -9.2992 octaves, 0.4153 Hz. Guide tone : 8100, 12.9837 octaves, 2119167.079 Hz. Exponens Consonantiae : 5.103000E+06, 22.28291 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 191.5, average 27.35714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.41565, average 1.05938 Sum of Tenney's harmonic distance : 15.10585, average 2.15798 Vogel's harmonic complexity : 18.71429 Wille's k value : 364 Wilson's harmonic complexity : 40 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 90.63598, average 3.23700 Lattice compactness (without 2's) : 83.60828, average 2.98601 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.57143 6 1 3: -2 .. 4 0.57143 12 5: -1 .. 2 0.28571 6 2 7: -1 .. 0 -0.57143 4 4 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 10 15 21| Scale is weakly epimorphic with val: <7 10 16 18| Scale is weakly epimorphic with val: <7 10 17 22| Scale is weakly epimorphic with val: <7 10 18 19| Scale is JI-epimorphic with val: <7 11 16 19| Scale is weakly epimorphic with val: <7 11 18 20| Scale is weakly epimorphic with val: <7 12 16 20| Scale is JI-epimorphic with val: <7 12 18 21|
FIT/MODE
7: 1 0 1 1 1 1 2 N T3 SD: 96.1105 c. M: 160.4534 c. 8: 1 1 1 1 1 2 1 P M ME S SD: 32.4183 c. M: 49.8915 c. 9: 1 1 1 2 1 2 1 N D3 S SD: 35.1748 c. M:-49.1789 c. 12: 2 0 2 2 2 2 2 P M DE S SD: 26.5416 c. M: 52.6804 c. 13: 2 1 2 2 2 2 2 SP M ME S SD: 20.9506 c. M:-30.8777 c. Tamashian 14: 2 1 2 2 2 3 2 P T3 SD: 14.2388 c. M: 28.4629 c. 19: 3 1 3 3 3 3 3 SP M DE S SD: 10.6612 c. M:-21.1611 c. 20: 3 1 3 3 3 4 3 P T3 SD: 12.5435 c. M: 19.8915 c. 24: 4 1 4 3 4 4 4 P SD: 12.8439 c. M: 17.5963 c. 25: 4 1 4 4 4 4 4 SP M DE S SD: 9.6834 c. M:-16.1085 c. 27: 4 2 4 4 4 5 4 SP T3 SD: 7.0555 c. M:-13.9863 c. 33: 5 2 5 5 5 6 5 SP T3 SD: 0.9483 c. M:-1.8651 c. 105: 16 6 16 16 16 19 16 SP T3 SD: 0.6264 c. M: 1.2518 c. 138: 21 8 21 21 21 25 21 SP T3 SD: 0.2543 c. M: 0.5065 c. 171: 26 10 26 26 26 31 26 SP T3 SD: 0.0571 c. M:-0.1085 c. 546: 83 32 83 83 83 99 83 SP T3 SD: 0.0677 c. M:-0.1085 c. 717: 109 42 109 109 109 130 109 SP T3 SD: 0.0604 c. M:-0.1085 c. 888: 135 52 135 135 135 161 135 SP T3 SD: 0.0572 c. M:-0.1085 c. 1059: 161 62 161 161 161 192 161 SP T3 SD: 0.0556 c. M:-0.1085 c. 1230: 187 72 187 187 187 223 187 SP T3 SD: 0.0548 c. M:-0.1085 c. 1401: 213 82 213 213 213 254 213 SP T3 SD: 0.0545 c. M:-0.1085 c. 1572: 239 92 239 239 239 285 239 SP T3 SD: 0.0543 c. M:-0.1085 c. 1605: 244 94 244 244 244 291 244 SP T3 SD: 0.0585 c. M:-0.1085 c. 1743: 265 102 265 265 265 316 265 SP T3 SD: 0.0542 c. M:-0.1085 c. 1862: 283 109 283 283 283 338 283 SP T3 SD: 0.0617 c. M: 0.1063 c. 1895: 288 111 288 288 288 344 288 SP T3 SD: 0.0532 c. M: 0.1026 c. 1928: 293 113 293 293 293 350 293 SP T3 SD: 0.0495 c. M: 0.0990 c. 1961: 298 115 298 298 298 356 298 SP T3 SD: 0.0511 c. M: 0.0955 c. 1994: 303 117 303 303 303 362 303 SP T3 SD: 0.0569 c. M: 0.0921 c. 2000: 304 117 304 304 304 363 304 SP T3 SD: 0.0651 c. M: 0.0915 c. 2019: 307 118 307 307 307 366 307 SP T3 SD: 0.0638 c. M:-0.1085 c. 2033: 309 119 309 309 309 369 309 SP T3 SD: 0.0535 c. M: 0.0883 c. 2066: 314 121 314 314 314 375 314 SP T3 SD: 0.0450 c. M: 0.0851 c. 2099: 319 123 319 319 319 381 319 SP T3 SD: 0.0410 c. M: 0.0821 c. 2132: 324 125 324 324 324 387 324 SP T3 SD: 0.0424 c. M: 0.0791 c. 2165: 329 127 329 329 329 393 329 SP T3 SD: 0.0482 c. M: 0.0763 c. 2204: 335 129 335 335 335 400 335 SP T3 SD: 0.0467 c. M: 0.0730 c. 2237: 340 131 340 340 340 406 340 SP T3 SD: 0.0382 c. M: 0.0703 c. 2270: 345 133 345 345 345 412 345 SP T3 SD: 0.0339 c. M: 0.0677 c. 2303: 350 135 350 350 350 418 350 SP T3 SD: 0.0350 c. M: 0.0652 c. 2336: 355 137 355 355 355 424 355 SP T3 SD: 0.0407 c. M: 0.0628 c. 2375: 361 139 361 361 361 431 361 SP T3 SD: 0.0413 c. M: 0.0599 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: 42.2336 cents 3 x x 4 x 5 x 6 S SD: 35.1169 cents 4 x x 5:6 x 7:8 S SD: 27.2624 cents 5 x 6 x 7:8:9:10 S SD: 14.6665 cents 6 x 7:8:9:10:11:12 S SD: 23.2403 cents 7 x 8:9:10:11:13:14 SD: 10.1279 cents 8:9 x 10:11:13:14:16 SD: 17.6772 cents 9:10 x 12:13:14:16:18 S SD: 12.9270 cents 10:11:12:13:14:16:18:20 S SD: 11.1083 cents 12:13:14:15:17:19:22:24 SD: 10.8222 cents 14 x 16:18:20:22:25:28 SD: 5.1520 cents 15:17 x 19:21:24:27:30 SD: 9.5111 cents 17:19:20:22:24:27:31:34 SD: 6.3552 cents 18:20:21:23:26:29:32:36 SD: 6.0763 cents 19:21:22:24:27:30:34:38 SD: 5.1383 cents 24:27:28:31:34:38:43:48 SD: 4.5648 cents 25:28:29:32:36:40:45:50 SD: 3.6382 cents 36:40:42:46:51:57:65:72 SD: 3.4209 cents 37:41:43:48:53:59:67:74 SD: 3.2308 cents 38:42:44:49:54:60:68:76 SD: 2.7859 cents 39:43:45:50:56:62:70:78 SD: 2.6241 cents 44:49:51:57:63:70:79:88 SD: 2.2347 cents 45:50:52:58:64:71:81:90 SD: 1.9789 cents 46:51:53:59:66:73:83:92 SD: 1.8139 cents 56:62:65:72:80:89:101:112 SD: 1.3037 cents 63:70:73:81:90:100:113:126 SD: 0.9374 cents 70:78:81:90:100:111:126:140 SD: 0.7477 cents 109:121:126:140:156:173:196:218 SD: 0.6697 cents 126:140:146:162:180:200:227:252 SD: 0.4031 cents 189:210:219:243:270:300:340:378 SD: 0.3689 cents 235:261:272:302:336:373:423:470 SD: 0.2708 cents 280:311:324:360:400:444:504:560 SD: 0.2627 cents 305:339:353:392:436:484:549:610 SD: 0.2184 cents 325:361:376:418:464:516:585:650 SD: 0.2050 cents 395:439:457:508:564:627:711:790 SD: 0.1612 cents 441:490:510:567:630:700:794:882 SD: 0.1582 cents 504:560:583:648:720:800:907:1008 SD: 0.1008 cents 560:622:648:720:800:889:1008:1120 SD: 0.0936 cents