Scala analysis: xen12-chalmers-tritriadic-mt-13-9-5
Tritriadic M->T scale built from 13:9:5
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 180/169 109.168392 2: 10/9 182.403712 minor whole tone 3: 18/13 563.382340 tridecimal augmented fourth 4: 13/9 636.617660 tridecimal diminished fifth 5: 20/13 745.786052 tridecimal semi-augmented fifth 6: 324/169 1126.764680 two (tridecimal augmented fourth) 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 169/162 73.2353 1: 180/169 109.1684 2: 169/162 73.2353 3: 81/65 380.9786 4: 169/162 73.2353 5: 180/169 109.1684 6: 81/65 380.9786 7: 169/162 73.2353
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 169/162 73.235 cents 1: 2 180/169 109.168 cents 1: 2 81/65 380.979 cents 2: 3 10/9 182.404 cents minor whole tone 2: 3 13/10 454.214 cents tridecimal semi-diminished fourth 2: 1 2916/2197 490.147 cents 3: 1 845/729 255.639 cents 3: 1 2197/1620 527.449 cents 3: 5 18/13 563.382 cents tridecimal augmented fourth 4: 5 13/9 636.618 cents tridecimal diminished fifth 4: 1 3240/2197 672.551 cents 4: 1 1458/845 944.361 cents 5: 1 2197/1458 709.853 cents 5: 3 20/13 745.786 cents tridecimal semi-augmented fifth 5: 3 9/5 1017.596 cents just minor seventh, BP seventh 6: 2 130/81 819.021 cents 6: 2 169/90 1090.832 cents 6: 3 324/169 1126.765 cents two (tridecimal augmented fourth) 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 : 109.2 182.4 563.4 636.6 745.8 1126.8 1200.0 109.2 : 73.2 454.2 527.4 636.6 1017.6 1090.8 1200.0 182.4 : 381.0 454.2 563.4 944.4 1017.6 1126.8 1200.0 563.4 : 73.2 182.4 563.4 636.6 745.8 819.0 1200.0 636.6 : 109.2 490.1 563.4 672.6 745.8 1126.8 1200.0 745.8 : 381.0 454.2 563.4 636.6 1017.6 1090.8 1200.0 1126.8: 73.2 182.4 255.6 636.6 709.9 819.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 73.2353 .. 380.9786 cents 13122/10985, 307.7433 cents 169/162, 73.2353 cents 2: 182.4037 .. 490.1470 cents 13122/10985, 307.7433 cents 650/729,-198.5749 cents 3: 255.6390 .. 563.3823 cents 13122/10985, 307.7433 cents 1856465/2125764,-234.5080 cents 4: 636.6177 .. 944.3610 cents 13122/10985, 307.7433 cents 169/162, 73.2353 cents 5: 709.8530 .. 1017.5963 cents 13122/10985, 307.7433 cents 1856465/2125764,-234.5080 cents 6: 819.0214 .. 1126.7647 cents 13122/10985, 307.7433 cents 650/729,-198.5749 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 169/162, 73.2353 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 81/65, 380.9786 cents Average / Smallest step : 2.340791 Largest / Average step : 2.222375 Largest / Smallest step : 5.202116 Median interval of one step : 180/169, 109.1684 cents, amount: 2 Most common interval of one step : 169/162, 73.2353 cents, amount: 3 Least squares average step : 168.57223 cents, oct.: 1180.00559 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : MSLSMLS Scale is a Constant Structure, by a margin of 37.30225 cents Scale diversity : 1.423570 Lumma stability : 0.183088 Lumma impropriety factor : 0.512906 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 : 29160/28561, 35.9331 cents Most common intervals : 18/13, 563.3823 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 182.404 636.618 cents Most common triad is 0.0 563.382 636.618 cents, amount: 3 Number of recognisable fifths : 1, average 709.8530 cents Scale contains a complete diamond : 9 13 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 13 Odd number limit : 2197 (O: 2197 U: 2197) Highest odd numerator or denominator: 169 Scale harmonicity : 0.011006 Average absolute harmonicity : 0.173932 Specific harmonicity : 0.059274 Fundamental : 1/1521, -10.5708 octaves, 0.1720 Hz. Guide tone : 21060, 14.3622 octaves, 5509834.405 Hz. Exponens Consonantiae : 3.203226E+07, 24.93302 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 475.0, average 67.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.75185, average 1.25026 Sum of Tenney's harmonic distance : 18.32924, average 2.61846 Vogel's harmonic complexity : 27.85714 Wille's k value : 1098 Wilson's harmonic complexity : 62 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 90.98625, average 3.24951 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 1.28571 9 1 3: -2 .. 4 0.57143 12 5: 0 .. 1 0.42857 3 1 13: -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 JI-epimorphic with val: <7 10 15 24| Scale is weakly epimorphic with val: <7 10 16 26| Scale is weakly epimorphic with val: <7 10 17 28| Scale is weakly epimorphic with val: <7 11 16 24| Scale is JI-epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 12 15 27| Scale is weakly epimorphic with val: <7 12 16 29| Scale is weakly epimorphic with val: <7 12 18 26|
FIT/MODE
7: 0 1 2 0 1 2 1 N T3 SD: 78.0698 c. M: 122.3319 c. 8: 1 0 3 0 1 3 0 N T3 SD: 39.2430 c. M:-73.2353 c. 9: 1 0 3 1 1 2 1 N SD: 40.2646 c. M: 60.0980 c. 10: 1 0 3 1 1 3 1 N SD: 46.5324 c. M: 83.3823 c. 11: 1 1 3 1 1 3 1 N M DE S SD: 22.4472 c. M: 35.8556 c. 13: 1 1 4 1 1 4 1 N M DE S SD: 11.2660 c. M: 19.0724 c. 19: 2 1 6 1 2 6 1 N T3 SD: 9.5840 c. M:-17.1474 c. 21: 2 1 7 1 2 7 1 N T3 SD: 8.8129 c. M:-16.0925 c. 32: 3 2 10 2 3 10 2 N T3 SD: 2.9155 c. M:-5.0963 c. 66: 6 4 21 4 6 21 4 N T3 SD: 0.3476 c. M: 0.5855 c. 164: 15 10 52 10 15 52 10 N T3 SD: 0.3652 c. M:-0.5877 c. 230: 21 14 73 14 21 73 14 N T3 SD: 0.2221 c. M:-0.3968 c. 296: 27 18 94 18 27 94 18 N T3 SD: 0.1750 c. M:-0.2911 c. 362: 33 22 115 22 33 115 22 N T3 SD: 0.1705 c. M:-0.3071 c. 441: 40 27 140 27 40 140 27 N T3 SD: 0.1848 c. M: 0.3249 c. 507: 46 31 161 31 46 161 31 N T3 SD: 0.1640 c. M: 0.2927 c. 539: 49 33 171 33 49 171 33 N T3 SD: 0.1278 c. M: 0.2341 c. 605: 55 37 192 37 55 192 37 N T3 SD: 0.0818 c. M: 0.1531 c. 671: 61 41 213 41 61 213 41 N T3 SD: 0.0519 c. M: 0.0881 c. 737: 67 45 234 45 67 234 45 N T3 SD: 0.0435 c. M: 0.0775 c. 901: 82 55 286 55 82 286 55 N T3 SD: 0.0351 c. M:-0.0602 c. 967: 88 59 307 59 88 307 59 N T3 SD: 0.0197 c. M:-0.0353 c. 1638: 149 100 520 100 149 520 100 N T3 SD: 0.0133 c. M: 0.0248 c. 1704: 155 104 541 104 155 541 104 N T3 SD: 0.0078 c. M: 0.0135 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: 21.9155 cents 3 x x 4 x 5 x 6 S SD: 51.0679 cents 4 x x x x 6 x 8 S SD: 21.9155 cents 5 x 6:7 x 8 x 10 S SD: 37.6901 cents 6 x 7:8 x 9 x 12 S SD: 28.8583 cents 7 x 8 x 10:11:13:14 SD: 16.8805 cents 8 x 9:11 x 12:15:16 SD: 12.6668 cents 9 x 10:12:13:14:17:18 SD: 12.1294 cents 10 x 11:14 x 15:19:20 SD: 10.6436 cents 11 x 12:15:16:17:21:22 SD: 7.3942 cents 12:13 x x 17:18:23:24 SD: 12.5157 cents 13:14 x 18:19:20:25:26 SD: 4.7412 cents 26:28:29:36:38:40:50:52 SD: 4.1733 cents 28:30:31:39:40:43:54:56 SD: 3.8613 cents 29:31:32:40:42:45:56:58 SD: 3.5714 cents 34:36:38:47:49:52:65:68 SD: 2.7065 cents 44:47:49:61:64:68:84:88 SD: 2.4987 cents 45:48:50:62:65:69:86:90 SD: 1.7105 cents 47:50:52:65:68:72:90:94 SD: 1.6263 cents 63:67:70:87:91:97:121:126 SD: 0.8978 cents 106:113:118:147:153:163:203:212 SD: 0.7306 cents 135:144:150:187:195:208:259:270 SD: 0.5560 cents 153:163:170:212:221:235:293:306 SD: 0.5245 cents 169:180:188:234:244:260:324:338 SD: 0.3134 cents 216:230:240:299:312:332:414:432 SD: 0.2542 cents 340:362:378:471:491:523:652:680 SD: 0.2284 cents 351:374:390:486:507:540:673:702 SD: 0.1056 cents 522:556:580:723:754:803:1001:1044 SD: 0.1025 cents 567:604:630:785:819:872:1087:1134 SD: 0.0987 cents