Scala analysis: xen12-chalmers-tritriadic-mt-5-17-25
Tritriadic M->T scale built from 5:17:25
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/16 104.955410 17th harmonic 2: 20/17 281.358304 septendecimal augmented second 3: 5/4 386.313714 major third 4: 289/200 637.283391 5: 25/17 667.672018 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: 17/16 104.9554 17th harmonic 2: 320/289 176.4029 3: 17/16 104.9554 17th harmonic 4: 289/250 250.9697 5: 5000/4913 30.3886 6: 289/250 250.9697 7: 20/17 281.3583 septendecimal augmented second
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 5000/4913 30.389 cents 1: 2 17/16 104.955 cents 17th harmonic 1: 1 320/289 176.403 cents 1: 2 289/250 250.970 cents 1: 1 20/17 281.358 cents septendecimal augmented second 2: 4 20/17 281.358 cents septendecimal augmented second 2: 1 4913/4000 355.925 cents 2: 1 5/4 386.314 cents major third 2: 1 34/25 532.328 cents 3: 2 5/4 386.314 cents major third 3: 2 34/25 532.328 cents 3: 2 400/289 562.717 cents two (septendecimal augmented second) 3: 1 289/200 637.283 cents 4: 1 400/289 562.717 cents two (septendecimal augmented second) 4: 2 289/200 637.283 cents 4: 2 25/17 667.672 cents 4: 2 8/5 813.686 cents minor sixth 5: 1 25/17 667.672 cents 5: 1 8/5 813.686 cents minor sixth 5: 1 8000/4913 844.075 cents 5: 4 17/10 918.642 cents septendecimal diminished seventh 6: 1 17/10 918.642 cents septendecimal diminished seventh 6: 2 500/289 949.030 cents 6: 1 289/160 1023.597 cents 6: 2 32/17 1095.045 cents 17th subharmonic 6: 1 4913/2500 1169.611 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.33333 = 13/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 105.0 281.4 386.3 637.3 667.7 918.6 1200.0 105.0 : 176.4 281.4 532.3 562.7 813.7 1095.0 1200.0 281.4 : 105.0 355.9 386.3 637.3 918.6 1023.6 1200.0 386.3 : 251.0 281.4 532.3 813.7 918.6 1095.0 1200.0 637.3 : 30.4 281.4 562.7 667.7 844.1 949.0 1200.0 667.7 : 251.0 532.3 637.3 813.7 918.6 1169.6 1200.0 918.6 : 281.4 386.3 562.7 667.7 918.6 949.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.3886 .. 281.3583 cents 289/250, 250.9697 cents 5000/4913, 30.3886 cents 2: 281.3583 .. 532.3280 cents 289/250, 250.9697 cents 1/1, 0.0000 cents 3: 386.3137 .. 637.2834 cents 289/250, 250.9697 cents 125/136,-146.0143 cents 4: 562.7166 .. 813.6863 cents 289/250, 250.9697 cents 80000/83521,-74.5668 cents 5: 667.6720 .. 918.6417 cents 289/250, 250.9697 cents 125/136,-146.0143 cents 6: 918.6417 .. 1169.6114 cents 289/250, 250.9697 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 5000/4913, 30.3886 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 20/17, 281.3583 cents Average / Smallest step : 5.641208 Largest / Average step : 1.641257 Largest / Smallest step : 9.258671 Median interval of one step : 320/289, 176.4029 cents, amount: 1 Least squares average step : 154.47112 cents, oct.: 1081.29785 cents Scale is not proper Step pattern alph. order: ABACDCE Step pattern size order : BCBDADE Scale is not a Constant Structure Scale diversity : 1.375024 Lumma stability : 0.050648 Lumma impropriety factor : 0.305496 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 : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 5000/4913, 30.3886 cents Most common intervals : 20/17, 281.3583 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 386.314 918.642 cents Most common triad is 0.0 281.358 918.642 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 5 17 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 : 17 Odd number limit : 4913 (O: 4913 U: 4913) Highest odd numerator or denominator: 289 Scale harmonicity : 0.008200 Average absolute harmonicity : 0.176775 Specific harmonicity : 0.047218 Fundamental : 1/6800, -12.7313 octaves, 0.0385 Hz. Guide tone : 28900, 14.8188 octaves, 7560978.837 Hz. Exponens Consonantiae : 1.965200E+08, 27.55010 octaves Euler's gradus suavitatis : 71 Sum of Mann's harmonic distance : 320.0, average 45.71429 Mersenne's string divisions : 25076898 Sum of van Prooijen's expressibility: 8.24915, average 1.17845 Sum of Tenney's harmonic distance : 16.18887, average 2.31270 Vogel's harmonic complexity : 35.57143 Wille's k value : 3612 Wilson's harmonic complexity : 71 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 94.75701, average 3.38418 Lattice compactness (without 2's) : 55.84729, average 1.99455 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 -1.00000 13 1 5: -2 .. 2 0.14286 7 1 17: -1 .. 2 0.28571 6 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 13 / 7 = 1.85714 Scale is weakly epimorphic with val: <7 15 31| Scale is weakly epimorphic with val: <7 16 27| Scale is weakly epimorphic with val: <7 17 30| Scale is weakly epimorphic with val: <7 18 26|
FIT/MODE
7: 1 1 0 2 0 1 2 N T3 SD: 48.6128 c. M:-66.4732 c. 8: 1 1 1 1 0 2 2 N SD: 42.6774 c. M: 67.6720 c. 9: 1 1 1 2 0 2 2 N T3 SD: 18.0819 c. M:-29.3833 c. 13: 1 2 1 3 0 3 3 N SD: 12.1470 c. M: 21.5182 c. 21: 2 3 2 4 1 4 5 N SD: 10.0977 c. M:-18.0423 c. 22: 2 3 2 5 0 5 5 N SD: 9.6849 c. M:-17.2621 c. 25: 2 4 2 5 1 5 6 N SD: 7.2600 c. M: 13.2834 c. 34: 3 5 3 7 1 7 8 N SD: 1.6472 c. M:-2.9162 c. 81: 7 12 7 17 2 17 19 N SD: 0.7504 c. M: 1.2517 c. 115: 10 17 10 24 3 24 27 N SD: 0.4333 c. M: 0.7617 c. 196: 17 29 17 41 5 41 46 N SD: 0.4899 c. M: 0.8738 c. 205: 18 30 18 43 5 43 48 N SD: 0.4095 c. M:-0.7654 c. 239: 21 35 21 50 6 50 56 N SD: 0.2788 c. M:-0.4839 c. 320: 28 47 28 67 8 67 75 N SD: 0.1231 c. M:-0.2166 c. 354: 31 52 31 74 9 74 83 N SD: 0.0832 c. M:-0.1293 c. 435: 38 64 38 91 11 91 102 N SD: 0.0734 c. M: 0.1278 c. 674: 59 99 59 141 17 141 158 N SD: 0.0611 c. M:-0.1053 c. 789: 69 116 69 165 20 165 185 N SD: 0.0113 c. M: 0.0210 c. 2252: 197 331 197 471 57 471 528 N SD: 0.0109 c. M:-0.0179 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 17.1415 cents 3 x x 4 x x 5:6 S SD: 38.9575 cents 4 x x 5 x 6:7:8 S SD: 15.1941 cents 5 x 6 x 7 x 9:10 SD: 29.5457 cents 6 x 7:8 x 9:10:12 S SD: 24.5311 cents 7 x 8:9:10 x 12:14 S SD: 14.8307 cents 8 x 9:10 x 12:14:16 S SD: 19.6896 cents 9:10 x 11:13 x 15:18 SD: 18.6415 cents 10:11:12:13:14:15:17:20 SD: 16.6395 cents 11:12:13:14:16 x 19:22 SD: 10.5550 cents 12:13:14:15:17:18:20:24 SD: 9.9652 cents 13:14:15:16 x 19:22:26 SD: 8.4514 cents 15:16:18:19 x 22:26:30 SD: 8.9730 cents 16:17:19:20:23:24:27:32 SD: 5.8566 cents 17:18:20:21 x 25:29:34 SD: 3.6951 cents 18:19:21:23:26 x 31:36 SD: 7.9801 cents 19:20:22:24:27:28:32:38 SD: 7.0856 cents 20:21:24:25:29 x 34:40 SD: 6.7306 cents 21:22:25:26:30:31:36:42 SD: 6.2850 cents 22:23:26:28:32 x 37:44 SD: 7.9846 cents 23:24:27:29:33:34:39:46 SD: 5.4748 cents 24:26:28:30 x 35:41:48 SD: 6.7114 cents 25:27:29:31:36:37:43:50 SD: 6.6348 cents 26:28:31:33 x 38:44:52 SD: 7.3697 cents 27:29:32:34:39:40:46:54 SD: 4.1801 cents 29:31:34:36:42:43:49:58 SD: 3.5578 cents 32:34:38:40:46:47:54:64 SD: 3.2264 cents 34:36:40:43:49:50:58:68 SD: 3.2034 cents 35:37:41:44:51 x 60:70 SD: 4.2457 cents 36:38:42:45:52:53:61:72 SD: 2.7665 cents 44:47:52:55:64:65:75:88 SD: 2.7099 cents 45:48:53:56:65:66:77:90 SD: 2.2950 cents 47:50:55:59:68:69:80:94 SD: 1.8186 cents 61:65:72:76:88:90:104:122 SD: 1.7768 cents 63:67:74:79:91:93:107:126 SD: 1.3300 cents 79:84:93:99:114:116:134:158 SD: 1.0048 cents 96:102:113:120:139:141:163:192 SD: 0.6730 cents 157:167:185:196:227:231:267:314 SD: 0.6144 cents 159:169:187:199:230:234:270:318 SD: 0.5393 cents 160:170:188:200:231:235:272:320 SD: 0.4870 cents 164:174:193:205:237:241:279:328 SD: 0.4432 cents 176:187:207:220:254:259:299:352 SD: 0.3971 cents 193:205:227:241:279:284:328:386 SD: 0.3395 cents 227:241:267:284:328:334:386:454 SD: 0.3297 cents 272:289:320:340:393:400:462:544 SD: 0.2155 cents 368:391:433:460:532:541:626:736 SD: 0.2123 cents 380:404:447:475:549:559:646:760 SD: 0.1806 cents 436:463:513:545:630:641:741:872 SD: 0.1667 cents 476:506:560:595:688:700:809:952 SD: 0.1512 cents 544:578:640:680:786:800:925:1088 SD: 0.0591 cents