Scala analysis: xen12-chalmers-tritriadic-mt-13-23-7
Tritriadic M->T scale built from 13:23:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 14/13 128.298245 2/3-tone 2: 26/23 212.253315 3: 28/23 340.551559 4: 529/338 775.493371 5: 23/13 987.746685 6: 322/169 1116.044930 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 169/161 83.9551 1: 14/13 128.2982 2/3-tone 2: 169/161 83.9551 3: 14/13 128.2982 2/3-tone 4: 12167/9464 434.9418 5: 26/23 212.2533 6: 14/13 128.2982 2/3-tone 7: 169/161 83.9551
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 169/161 83.955 cents 1: 3 14/13 128.298 cents 2/3-tone 1: 1 26/23 212.253 cents 1: 1 12167/9464 434.942 cents 2: 4 26/23 212.253 cents 2: 1 28/23 340.552 cents 2: 1 12167/8788 563.240 cents 2: 1 529/364 647.195 cents 3: 1 4394/3703 296.208 cents 3: 2 28/23 340.552 cents 3: 1 676/529 424.507 cents 3: 1 529/364 647.195 cents 3: 2 529/338 775.493 cents 4: 2 676/529 424.507 cents 4: 1 728/529 552.805 cents 4: 1 529/338 775.493 cents 4: 2 23/14 859.448 cents 4: 1 3703/2197 903.792 cents 5: 1 728/529 552.805 cents 5: 1 17576/12167 636.760 cents 5: 1 23/14 859.448 cents 5: 4 23/13 987.747 cents 6: 1 18928/12167 765.058 cents 6: 1 23/13 987.747 cents 6: 3 13/7 1071.702 cents 16/3-tone 6: 2 322/169 1116.045 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 : 128.3 212.3 340.6 775.5 987.7 1116.0 1200.0 128.3 : 84.0 212.3 647.2 859.4 987.7 1071.7 1200.0 212.3 : 128.3 563.2 775.5 903.8 987.7 1116.0 1200.0 340.6 : 434.9 647.2 775.5 859.4 987.7 1071.7 1200.0 775.5 : 212.3 340.6 424.5 552.8 636.8 765.1 1200.0 987.7 : 128.3 212.3 340.6 424.5 552.8 987.7 1200.0 1116.0: 84.0 212.3 296.2 424.5 859.4 1071.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 83.9551 .. 434.9418 cents 279841/228488, 350.9867 cents 169/161, 83.9551 cents 2: 212.2533 .. 647.1951 cents 12167/9464, 434.9418 cents 246064/279841,-222.6885 cents 3: 296.2084 .. 775.4934 cents 1958887/1485172, 479.2850 cents 228488/279841,-350.9867 cents 4: 424.5066 .. 903.7916 cents 1958887/1485172, 479.2850 cents 228488/279841,-350.9867 cents 5: 552.8049 .. 987.7467 cents 12167/9464, 434.9418 cents 228488/279841,-350.9867 cents 6: 765.0582 .. 1116.0449 cents 279841/228488, 350.9867 cents 246064/279841,-222.6885 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 169/161, 83.9551 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 12167/9464, 434.9418 cents Average / Smallest step : 2.041909 Largest / Average step : 2.537161 Largest / Smallest step : 5.180650 Median interval of one step : 14/13, 128.2982 cents, amount: 3 Most common interval of one step : 14/13, 128.2982 cents, amount: 3 Least squares average step : 176.51026 cents, oct.: 1235.57180 cents Scale is not proper Step pattern alph. order: ABACDAB Step pattern size order : BABDCBA Scale is not a Constant Structure Scale diversity : 1.381711 Lumma stability : 0.139925 Lumma impropriety factor : 0.646244 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 : 5 Mean interval variety : 4.33333 = 13/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 6436343/6397664, 10.4352 cents Most common intervals : 26/23, 212.2533 cents & inv., amount: 5 Most common triad is 0.0 212.253 987.747 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 13 23 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 : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.004854 Average absolute harmonicity : 0.156735 Specific harmonicity : 0.026782 Fundamental : 1/7774, -12.9244 octaves, 0.0337 Hz. Guide tone : 192556, 17.5549 octaves, 50377572.352 Hz. Exponens Consonantiae : 1.496930E+09, 30.47936 octaves Euler's gradus suavitatis : 112 Sum of Mann's harmonic distance : 762.0, average 108.85714 Mersenne's string divisions : 750929508 Sum of van Prooijen's expressibility: 10.15047, average 1.45007 Sum of Tenney's harmonic distance : 20.61047, average 2.94435 Vogel's harmonic complexity : 51.00000 Wille's k value : 6083 Wilson's harmonic complexity : 115 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 66.70558, average 2.38234 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.71429 7 1 7: 0 .. 1 0.42857 3 13: -2 .. 1 -0.71429 7 1 23: -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 18 24 33| Scale is weakly epimorphic with val: <7 18 26 31| Scale is weakly epimorphic with val: <7 18 27 30| Scale is weakly epimorphic with val: <7 18 28 29| Scale is weakly epimorphic with val: <7 18 29 35| Scale is weakly epimorphic with val: <7 19 24 35| Scale is weakly epimorphic with val: <7 19 25 34| Scale is weakly epimorphic with val: <7 19 27 32| Scale is weakly epimorphic with val: <7 19 28 31| Scale is weakly epimorphic with val: <7 19 29 30| Scale is weakly epimorphic with val: <7 20 24 30| Scale is weakly epimorphic with val: <7 20 25 29| Scale is weakly epimorphic with val: <7 20 26 35| Scale is weakly epimorphic with val: <7 20 28 33| Scale is weakly epimorphic with val: <7 20 29 32| Scale is weakly epimorphic with val: <7 21 24 32| Scale is weakly epimorphic with val: <7 21 25 31| Scale is weakly epimorphic with val: <7 21 26 30| Scale is weakly epimorphic with val: <7 21 27 29| Scale is weakly epimorphic with val: <7 21 29 34| Scale is weakly epimorphic with val: <7 22 24 34| Scale is weakly epimorphic with val: <7 22 25 33| Scale is weakly epimorphic with val: <7 22 26 32| Scale is weakly epimorphic with val: <7 22 27 31| Scale is weakly epimorphic with val: <7 22 28 30|
FIT/MODE
7: 1 0 1 3 1 1 0 N SD: 51.9807 c. M:-83.9551 c. 8: 1 0 1 3 1 1 1 N SD: 51.6889 c. M: 87.7467 c. 10: 1 1 1 3 2 1 1 N SD: 30.1558 c. M: 55.4934 c. 11: 1 1 1 4 2 1 1 N SD: 14.0811 c. M: 25.1358 c. 17: 2 1 2 6 3 2 1 N SD: 8.4469 c. M:-13.3668 c. 28: 3 2 3 10 5 3 2 N SD: 2.1801 c. M: 4.0648 c. 57: 6 4 6 21 10 6 4 N SD: 2.2568 c. M: 3.7095 c. 74: 8 5 8 27 13 8 5 N SD: 1.8045 c. M:-2.8850 c. 85: 9 6 9 31 15 9 6 N SD: 0.9650 c. M: 1.7280 c. 102: 11 7 11 37 18 11 7 N SD: 0.8968 c. M:-1.6021 c. 113: 12 8 12 41 20 12 8 N SD: 0.5844 c. M: 1.0007 c. 130: 14 9 14 47 23 14 9 N SD: 0.6132 c. M:-0.9869 c. 187: 20 13 20 68 33 20 13 N SD: 0.5231 c. M:-0.9772 c. 215: 23 15 23 78 38 23 15 N SD: 0.1780 c. M:-0.3206 c. 243: 26 17 26 88 43 26 17 N SD: 0.1173 c. M:-0.1892 c. 458: 49 32 49 166 81 49 32 N SD: 0.0629 c. M:-0.1123 c. 571: 61 40 61 207 101 61 40 N SD: 0.0671 c. M: 0.1080 c. 701: 75 49 75 254 124 75 49 N SD: 0.0609 c. M:-0.1046 c. 786: 84 55 84 285 139 84 55 N SD: 0.0551 c. M: 0.0935 c. 814: 87 57 87 295 144 87 57 N SD: 0.0439 c. M: 0.0744 c. 1029: 110 72 110 373 182 110 72 N SD: 0.0150 c. M: 0.0268 c. 1272: 136 89 136 461 225 136 89 N SD: 0.0118 c. M: 0.0217 c. 2301: 246 161 246 834 407 246 161 N SD: 0.0047 c. M: 0.0084 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: 36.7692 cents 3 x x 4 x 5 x 6 S SD: 62.7988 cents 4 x x 5:6:7 x 8 S SD: 22.1642 cents 5 x x 6:8:9 x 10 S SD: 13.6249 cents 6 x 7 x 9:11 x 12 SD: 27.5993 cents 7 x 8:9:11:12:13:14 SD: 19.9254 cents 8 x 9:10:13:14:15:16 SD: 14.4556 cents 9 x 10:11:14:16:17:18 SD: 6.1112 cents 10:11 x 12:16:18:19:20 S SD: 10.9811 cents 11:12 x 13:17:19:21:22 SD: 12.1916 cents 12:13:14:15:19:21:23:24 SD: 11.1107 cents 13:14:15:16:20:23:25:26 SD: 7.5019 cents 14:15:16:17:22:25:27:28 SD: 4.9559 cents 23:25:26:28:36:41:44:46 SD: 3.1195 cents 37:40:42:45:58:65:70:74 SD: 2.8803 cents 39:42:44:47:61:69:74:78 SD: 2.7542 cents 40:43:45:49:63:71:76:80 SD: 2.7487 cents 41:44:46:50:64:73:78:82 SD: 2.7251 cents 51:55:58:62:80:90:97:102 SD: 1.8323 cents 55:59:62:67:86:97:105:110 SD: 1.5305 cents 64:69:72:78:100:113:122:128 SD: 1.4175 cents 69:74:78:84:108:122:131:138 SD: 1.3616 cents 78:84:88:95:122:138:149:156 SD: 0.8271 cents 92:99:104:112:144:163:175:184 SD: 0.5725 cents 129:139:146:157:202:228:246:258 SD: 0.4847 cents 170:183:192:207:266:301:324:340 SD: 0.3294 cents 207:223:234:252:324:366:394:414 SD: 0.3094 cents 221:238:250:269:346:391:421:442 SD: 0.2002 cents 285:307:322:347:446:504:543:570 SD: 0.1905 cents 299:322:338:364:468:529:570:598 SD: 0.1351 cents 391:421:442:476:612:692:745:782 SD: 0.0964 cents 506:545:572:616:792:895:964:1012 SD: 0.0793 cents