Scala analysis: xen12-chalmers-tritriadic-dm-5-17-7
Tritriadic D->M scale built from 5:17:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 289/280 54.771199 2: 98/85 246.382690 3: 17/14 336.129503 supraminor third 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 28/17 863.870497 submajor sixth 6: 17/10 918.641696 septendecimal diminished seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 20/17 281.3583 septendecimal augmented second 1: 289/280 54.7712 2: 5488/4913 191.6115 3: 1445/1372 89.7468 4: 98/85 246.3827 5: 20/17 281.3583 septendecimal augmented second 6: 289/280 54.7712 7: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 289/280 54.771 cents 1: 1 1445/1372 89.747 cents 1: 1 5488/4913 191.611 cents 1: 1 98/85 246.383 cents 1: 2 20/17 281.358 cents septendecimal augmented second 2: 1 98/85 246.383 cents 2: 1 20/17 281.358 cents septendecimal augmented second 2: 4 17/14 336.130 cents supraminor third 2: 1 392/289 527.741 cents 3: 1 17/14 336.130 cents supraminor third 3: 1 4913/3920 390.901 cents 3: 2 392/289 527.741 cents 3: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 3: 2 10/7 617.488 cents Euler's tritone 4: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 1 10/7 617.488 cents Euler's tritone 4: 2 289/196 672.259 cents two (supraminor third) 4: 1 7840/4913 809.099 cents 4: 1 28/17 863.870 cents submajor sixth 5: 1 289/196 672.259 cents two (supraminor third) 5: 4 28/17 863.870 cents submajor sixth 5: 1 17/10 918.642 cents septendecimal diminished seventh 5: 1 85/49 953.617 cents 6: 2 17/10 918.642 cents septendecimal diminished seventh 6: 1 85/49 953.617 cents 6: 1 4913/2744 1008.389 cents 6: 1 2744/1445 1110.253 cents 6: 2 560/289 1145.229 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 54.8 246.4 336.1 582.5 863.9 918.6 1200.0 54.8 : 191.6 281.4 527.7 809.1 863.9 1145.2 1200.0 246.4 : 89.7 336.1 617.5 672.3 953.6 1008.4 1200.0 336.1 : 246.4 527.7 582.5 863.9 918.6 1110.3 1200.0 582.5 : 281.4 336.1 617.5 672.3 863.9 953.6 1200.0 863.9 : 54.8 336.1 390.9 582.5 672.3 918.6 1200.0 918.6 : 281.4 336.1 527.7 617.5 863.9 1145.2 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 54.7712 .. 281.3583 cents 5600/4913, 226.5871 cents 289/280, 54.7712 cents 2: 246.3827 .. 527.7410 cents 20/17, 281.3583 cents 49/50,-34.9756 cents 3: 336.1295 .. 617.4878 cents 20/17, 281.3583 cents 4913/5488,-191.6115 cents 4: 582.5122 .. 863.8705 cents 20/17, 281.3583 cents 49/50,-34.9756 cents 5: 672.2590 .. 953.6173 cents 20/17, 281.3583 cents 4913/5488,-191.6115 cents 6: 918.6417 .. 1145.2288 cents 5600/4913, 226.5871 cents 49/50,-34.9756 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 289/280, 54.7712 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 3.129904 Largest / Average step : 1.641257 Largest / Smallest step : 5.136975 Median interval of one step : 5488/4913, 191.6115 cents, amount: 1 Least squares average step : 157.97983 cents, oct.: 1105.85883 cents Scale is not proper Step pattern alph. order: ABCDEAE Step pattern size order : ACBDEAE Scale is not a Constant Structure Scale diversity : 1.400743 Lumma stability : 0.091285 Lumma impropriety factor : 0.406792 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 : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 50/49, 34.9756 cents Most common intervals : 17/14, 336.1295 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 281.358 863.870 cents Most common triad is 0.0 336.130 863.870 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 7 17 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 17 Odd number limit : 4913 (O: 4913 U: 4913) Highest odd numerator or denominator: 289 Scale harmonicity : 0.007541 Average absolute harmonicity : 0.166292 Specific harmonicity : 0.041909 Fundamental : 1/4760, -12.2167 octaves, 0.0550 Hz. Guide tone : 56644, 15.7896 octaves, 14819518.521 Hz. Exponens Consonantiae : 2.696254E+08, 28.00638 octaves Euler's gradus suavitatis : 76 Sum of Mann's harmonic distance : 435.0, average 62.14286 Mersenne's string divisions : 581028660 Sum of van Prooijen's expressibility: 8.92676, average 1.27525 Sum of Tenney's harmonic distance : 17.95843, average 2.56549 Vogel's harmonic complexity : 35.85714 Wille's k value : 2456 Wilson's harmonic complexity : 77 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 78.85600, average 2.81629 Lattice compactness (without 2's) : 56.12138, average 2.00433 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.14286 9 1 5: -1 .. 0 -0.57143 4 7: -1 .. 2 0.28571 6 1 17: -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 15 18 26| Scale is weakly epimorphic with val: <7 15 19 32| Scale is weakly epimorphic with val: <7 15 20 31| Scale is weakly epimorphic with val: <7 15 21 30| Scale is weakly epimorphic with val: <7 16 18 28| Scale is weakly epimorphic with val: <7 16 19 27| Scale is weakly epimorphic with val: <7 16 20 26| Scale is weakly epimorphic with val: <7 16 21 32| Scale is weakly epimorphic with val: <7 16 22 31| Scale is weakly epimorphic with val: <7 17 18 30| Scale is weakly epimorphic with val: <7 17 19 29| Scale is weakly epimorphic with val: <7 17 20 28| Scale is weakly epimorphic with val: <7 17 21 27| Scale is weakly epimorphic with val: <7 17 22 26| Scale is weakly epimorphic with val: <7 18 19 31| Scale is weakly epimorphic with val: <7 18 20 30| Scale is weakly epimorphic with val: <7 18 21 29| Scale is weakly epimorphic with val: <7 18 22 28|
FIT/MODE
7: 0 1 1 1 2 0 2 N T3 SD: 49.4910 c. M: 74.9541 c. 8: 0 2 0 2 2 0 2 N M DE S SD: 36.1321 c. M: 54.7712 c. 10: 0 2 1 2 2 1 2 N T3 S SD: 29.7527 c. M: 54.7712 c. 11: 0 2 1 2 3 0 3 N SD: 32.5872 c. M: 54.7712 c. 12: 1 1 1 3 3 0 3 N SD: 32.6475 c. M: 46.3827 c. 14: 1 2 1 3 3 1 3 N SD: 17.1381 c. M:-30.9431 c. 18: 1 3 1 4 4 1 4 N SD: 12.4800 c. M:-20.2840 c. 21: 1 3 2 4 5 1 5 N SD: 8.9059 c. M: 17.8113 c. 25: 1 4 2 5 6 1 6 N SD: 4.9734 c. M: 6.7712 c. 39: 2 6 3 8 9 2 9 N SD: 3.3979 c. M:-6.7673 c. 43: 2 7 3 9 10 2 10 N SD: 2.5290 c. M:-4.7801 c. 64: 3 10 5 13 15 3 15 N SD: 1.4382 c. M: 2.6327 c. 68: 3 11 5 14 16 3 16 N SD: 0.9424 c. M: 1.8300 c. 107: 5 17 8 22 25 5 25 N SD: 0.7005 c. M:-1.3036 c. 132: 6 21 10 27 31 6 31 N SD: 0.4950 c. M: 0.9281 c. 175: 8 28 13 36 41 8 41 N SD: 0.2483 c. M:-0.4745 c. 239: 11 38 18 49 56 11 56 N SD: 0.2749 c. M:-0.4589 c. 307: 14 49 23 63 72 14 72 N SD: 0.0720 c. M: 0.1286 c. 482: 22 77 36 99 113 22 113 N SD: 0.0456 c. M:-0.0903 c. 789: 36 126 59 162 185 36 185 N SD: 0.0093 c. M: 0.0183 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: 59.7214 cents 3 x x x 4:5 x 6 S SD: 28.9722 cents 4 x x 5:6 x 7:8 S SD: 34.7343 cents 5 x x 6:7:8:9:10 S SD: 22.5657 cents 6 x 7 x 8:10 x 12 S SD: 22.3247 cents 7 x 8:9:10 x 12:14 S SD: 21.4070 cents 8 x 9:10:11:13:14:16 SD: 15.2378 cents 9 x 10:11:13:15 x 18 SD: 17.3985 cents 10 x x 12:14:16:17:20 SD: 10.8411 cents 11 x 13 x 15:18:19:22 SD: 13.8512 cents 12:13:14:15:17:20 x 24 SD: 17.3209 cents 13:14:15:16:18:21:22:26 SD: 12.3806 cents 14:15:16:17:20:23:24:28 SD: 10.9418 cents 17:18:20:21:24:28:29:34 SD: 9.3710 cents 18:19:21:22:25:30:31:36 SD: 8.0438 cents 19:20:22:23:27:31:32:38 SD: 7.0535 cents 20:21:23:24:28:33:34:40 SD: 5.2113 cents 25:26:29:30:35:41:43:50 SD: 4.8846 cents 26:27:30:32:36:43:44:52 SD: 4.8163 cents 27:28:31:33:38:44:46:54 SD: 3.7339 cents 28:29:32:34:39:46:48:56 SD: 3.4254 cents 32:33:37:39:45:53:54:64 SD: 2.7949 cents 33:34:38:40:46:54:56:66 SD: 2.1036 cents 57:59:66:69:80:94:97:114 SD: 1.6593 cents 60:62:69:73:84:99:102:120 SD: 0.9538 cents 93:96:107:113:130:153:158:186 SD: 0.7362 cents 117:121:135:142:164:193:199:234 SD: 0.7359 cents 125:129:144:152:175:206:213:250 SD: 0.7222 cents 130:134:150:158:182:214:221:260 SD: 0.4633 cents 150:155:173:182:210:247:255:300 SD: 0.3598 cents 190:196:219:231:266:313:323:380 SD: 0.3443 cents 210:217:242:255:294:346:357:420 SD: 0.3206 cents 247:255:285:300:346:407:420:494 SD: 0.2829 cents 280:289:323:340:392:461:476:560 SD: 0.1650 cents 340:351:392:413:476:560:578:680 SD: 0.0993 cents