Scala analysis: xen12-chalmers-tritriadic-dm-23-21-13
Tritriadic D->M scale built from 23:21:13
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 26/23 212.253315 2: 26/21 369.746754 3: 676/483 582.000069 4: 441/299 672.759806 5: 21/13 830.253246 6: 42/23 1042.506560 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 23/21 157.4934 1: 26/23 212.2533 2: 23/21 157.4934 3: 26/23 212.2533 4: 9261/8788 90.7597 5: 23/21 157.4934 6: 26/23 212.2533 7: 23/21 157.4934
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 9261/8788 90.760 cents 1: 3 23/21 157.493 cents 1: 3 26/23 212.253 cents 2: 1 10143/8788 248.253 cents 2: 1 9261/7774 303.013 cents 2: 5 26/21 369.747 cents 3: 3 441/338 460.506 cents 3: 2 598/441 527.240 cents 3: 2 676/483 582.000 cents 4: 2 483/338 618.000 cents 4: 2 441/299 672.760 cents 4: 3 676/441 739.494 cents 5: 5 21/13 830.253 cents 5: 1 15548/9261 896.987 cents 5: 1 17576/10143 951.747 cents 6: 3 23/13 987.747 cents 6: 3 42/23 1042.507 cents 6: 1 17576/9261 1109.240 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 : 212.3 369.7 582.0 672.8 830.3 1042.5 1200.0 212.3 : 157.5 369.7 460.5 618.0 830.3 987.7 1200.0 369.7 : 212.3 303.0 460.5 672.8 830.3 1042.5 1200.0 582.0 : 90.8 248.3 460.5 618.0 830.3 987.7 1200.0 672.8 : 157.5 369.7 527.2 739.5 897.0 1109.2 1200.0 830.3 : 212.3 369.7 582.0 739.5 951.7 1042.5 1200.0 1042.5: 157.5 369.7 527.2 739.5 830.3 987.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 90.7597 .. 212.2533 cents 228488/213003, 121.4936 cents 9261/8788, 90.7597 cents 2: 248.2532 .. 369.7468 cents 228488/213003, 121.4936 cents 233289/228488, 35.9999 cents 3: 460.5065 .. 582.0001 cents 228488/213003, 121.4936 cents 9261/8788, 90.7597 cents 4: 617.9999 .. 739.4935 cents 228488/213003, 121.4936 cents 233289/228488, 35.9999 cents 5: 830.2532 .. 951.7468 cents 228488/213003, 121.4936 cents 9261/8788, 90.7597 cents 6: 987.7467 .. 1109.2403 cents 228488/213003, 121.4936 cents 233289/228488, 35.9999 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 9261/8788, 90.7597 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 26/23, 212.2533 cents Average / Smallest step : 1.888817 Largest / Average step : 1.238144 Largest / Smallest step : 2.338629 Median interval of one step : 23/21, 157.4934 cents, amount: 3 Least squares average step : 172.82208 cents, oct.: 1209.75459 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABACBAB Step pattern size order : LMLSMLM Scale is a Constant Structure, by a margin of 35.99986 cents Scale diversity : 1.475499 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.392532 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 : 233289/228488, 35.9999 cents Most common intervals : 26/21, 369.7468 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 157.493 369.747 cents Most common triad is 0.0 369.747 830.253 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 : 13 21 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 10143 (O: 10143 U: 10143) Highest odd numerator or denominator: 483 Scale harmonicity : 0.006693 Average absolute harmonicity : 0.158616 Specific harmonicity : 0.033880 Fundamental : 1/6279, -12.6163 octaves, 0.0417 Hz. Guide tone : 298116, 18.1855 octaves, 77994767.025 Hz. Exponens Consonantiae : 1.871870E+09, 30.80183 octaves Euler's gradus suavitatis : 85 Sum of Mann's harmonic distance : 1048.5, average 149.78571 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.69628, average 1.52804 Sum of Tenney's harmonic distance : 21.87007, average 3.12430 Vogel's harmonic complexity : 40.28571 Wille's k value : 5071 Wilson's harmonic complexity : 92 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 72.59114, average 2.59254 Lattice compactness (without 2's) : 66.76043, average 2.38430 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.85714 6 1 3: -1 .. 2 0.28571 6 7: -1 .. 2 0.28571 6 13: -1 .. 2 0.28571 6 2 23: -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 18 24 33| Scale is weakly epimorphic with val: <7 10 18 25 30| Scale is weakly epimorphic with val: <7 10 18 26 34| Scale is weakly epimorphic with val: <7 10 18 27 31| Scale is weakly epimorphic with val: <7 10 18 29 32| Scale is JI-epimorphic with val: <7 10 19 24 30| Scale is weakly epimorphic with val: <7 10 19 25 34| Scale is weakly epimorphic with val: <7 10 19 26 31| Scale is weakly epimorphic with val: <7 10 19 27 35| Scale is weakly epimorphic with val: <7 10 19 28 32| Scale is weakly epimorphic with val: <7 10 20 24 34| Scale is JI-epimorphic with val: <7 10 20 25 31| Scale is weakly epimorphic with val: <7 10 20 26 35| Scale is weakly epimorphic with val: <7 10 20 27 32| Scale is weakly epimorphic with val: <7 10 20 28 29| Scale is weakly epimorphic with val: <7 10 20 29 33| Scale is weakly epimorphic with val: <7 10 21 25 35| Scale is JI-epimorphic with val: <7 10 21 26 32| Scale is weakly epimorphic with val: <7 10 21 27 29| Scale is weakly epimorphic with val: <7 10 21 28 33| Scale is weakly epimorphic with val: <7 10 21 29 30| Scale is weakly epimorphic with val: <7 10 22 24 35| Scale is weakly epimorphic with val: <7 10 22 26 29| Scale is JI-epimorphic with val: <7 10 22 27 33| Scale is weakly epimorphic with val: <7 10 22 28 30| Scale is weakly epimorphic with val: <7 10 22 29 34| Scale is JI-epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 25 34| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 35| Scale is weakly epimorphic with val: <7 11 18 28 32| Scale is weakly epimorphic with val: <7 11 19 24 34| Scale is JI-epimorphic with val: <7 11 19 25 31| Scale is weakly epimorphic with val: <7 11 19 26 35| Scale is weakly epimorphic with val: <7 11 19 27 32| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 29 33| Scale is weakly epimorphic with val: <7 11 20 25 35| Scale is JI-epimorphic with val: <7 11 20 26 32| = patent Scale is weakly epimorphic with val: <7 11 20 27 29| Scale is weakly epimorphic with val: <7 11 20 28 33| Scale is weakly epimorphic with val: <7 11 20 29 30| Scale is weakly epimorphic with val: <7 11 21 24 35| Scale is weakly epimorphic with val: <7 11 21 26 29| Scale is JI-epimorphic with val: <7 11 21 27 33| Scale is weakly epimorphic with val: <7 11 21 28 30| Scale is weakly epimorphic with val: <7 11 21 29 34| Scale is weakly epimorphic with val: <7 11 22 24 32| Scale is weakly epimorphic with val: <7 11 22 25 29| Scale is weakly epimorphic with val: <7 11 22 27 30| Scale is JI-epimorphic with val: <7 11 22 28 34| Scale is weakly epimorphic with val: <7 11 22 29 31| Scale is weakly epimorphic with val: <7 12 18 24 34| Scale is JI-epimorphic with val: <7 12 18 25 31| Scale is weakly epimorphic with val: <7 12 18 26 35| Scale is weakly epimorphic with val: <7 12 18 27 32| Scale is weakly epimorphic with val: <7 12 18 28 29| Scale is weakly epimorphic with val: <7 12 18 29 33| Scale is weakly epimorphic with val: <7 12 19 25 35| Scale is JI-epimorphic with val: <7 12 19 26 32| Scale is weakly epimorphic with val: <7 12 19 27 29| Scale is weakly epimorphic with val: <7 12 19 28 33| Scale is weakly epimorphic with val: <7 12 19 29 30| Scale is weakly epimorphic with val: <7 12 20 24 35| Scale is weakly epimorphic with val: <7 12 20 26 29| Scale is JI-epimorphic with val: <7 12 20 27 33| Scale is weakly epimorphic with val: <7 12 20 28 30| Scale is weakly epimorphic with val: <7 12 20 29 34| Scale is weakly epimorphic with val: <7 12 21 24 32| Scale is weakly epimorphic with val: <7 12 21 25 29| Scale is weakly epimorphic with val: <7 12 21 27 30| Scale is JI-epimorphic with val: <7 12 21 28 34| Scale is weakly epimorphic with val: <7 12 21 29 31| Scale is weakly epimorphic with val: <7 12 22 24 29| Scale is weakly epimorphic with val: <7 12 22 25 33| Scale is weakly epimorphic with val: <7 12 22 26 30| Scale is weakly epimorphic with val: <7 12 22 28 31| Scale is JI-epimorphic with val: <7 12 22 29 35|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 33.9327 c. M: 67.7144 c. Lebeng 9: 2 1 1 1 1 2 1 N D3 S SD: 33.3394 c. M:-54.4134 c. 10: 2 1 2 1 1 2 1 P M ME S SD: 26.5149 c. M:-47.2402 c. 12: 2 2 2 1 1 2 2 P D3 S SD: 26.3317 c. M: 42.5066 c. Lydian Minor, Mela Rishabhapriya, Raga Ratipriya, Mixolydian sharp 4 flat 6 13: 2 2 2 1 2 2 2 SP M ME I SD: 20.7037 c. M: 28.1539 c. Horthatian 16: 3 2 3 1 2 3 2 P T3 SD: 9.2801 c. M:-17.9999 c. 23: 4 3 4 2 3 4 3 SP T3 SD: 4.6336 c. M: 8.0870 c. 39: 7 5 7 3 5 7 5 SP T3 SD: 2.6135 c. M:-4.1633 c. 62: 11 8 11 5 8 11 8 SP T3 SD: 2.3621 c. M:-4.6595 c. 68: 12 9 12 5 9 12 9 SP T3 SD: 1.0866 c. M: 2.1716 c. 91: 16 12 16 7 12 16 12 SP T3 SD: 0.9192 c. M: 1.7803 c. 107: 19 14 19 8 14 19 14 SP T3 SD: 0.6060 c. M:-1.1775 c. 130: 23 17 23 10 17 23 17 SP T3 SD: 0.5674 c. M:-1.0863 c. 159: 28 21 28 12 21 28 21 SP T3 SD: 0.7322 c. M: 1.0617 c. 175: 31 23 31 13 23 31 23 SP T3 SD: 0.5402 c. M:-0.8571 c. 198: 35 26 35 15 26 35 26 SP T3 SD: 0.0951 c. M: 0.1819 c. 503: 89 66 89 38 66 89 66 SP T3 SD: 0.0543 c. M:-0.1073 c. 701: 124 92 124 53 92 124 92 SP T3 SD: 0.0129 c. M:-0.0256 c. 899: 159 118 159 68 118 159 118 SP T3 SD: 0.0125 c. M: 0.0201 c. 1600: 283 210 283 121 210 283 210 SP T3 SD: 0.0049 c. M: 0.0098 c. 2301: 407 302 407 174 302 407 302 SP T3 SD: 0.0055 c. M: 0.0088 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: 14.5976 cents 3 x x 4 x 5 x 6 S SD: 33.2931 cents 4 x 5 x 6 x 7:8 S SD: 20.2418 cents 5 x 6:7 x 8:9:10 S SD: 12.3655 cents 6:7 x 8:9:10:11:12 S SD: 19.6202 cents 7:8:9:10 x 11:13:14 SD: 15.8288 cents 8:9:10:11:12:13:15:16 SD: 9.4086 cents 9:10:11 x 13:15:16:18 SD: 14.6990 cents 10:11:12:14:15:16:18:20 S SD: 11.8730 cents 12:14:15:17:18:19:22:24 SD: 10.8813 cents 13:15:16:18:19:21:24:26 SD: 6.8785 cents 17:19:21:24:25:27:31:34 SD: 5.5716 cents 21:24:26:29:31:34:38:42 SD: 4.8715 cents 23:26:28:32:34:37:42:46 SD: 4.5734 cents 25:28:31:35:37:40:46:50 SD: 3.9064 cents 29:33:36:41:43:47:53:58 SD: 3.4292 cents 30:34:37:42:44:48:55:60 SD: 3.1305 cents 38:43:47:53:56:61:69:76 SD: 2.2973 cents 46:52:57:64:68:74:84:92 SD: 1.8879 cents 47:53:58:66:69:76:86:94 SD: 1.8268 cents 55:62:68:77:81:89:100:110 SD: 1.4403 cents 63:71:78:88:93:102:115:126 SD: 1.0855 cents 92:104:114:129:136:149:168:184 SD: 0.9869 cents 93:105:115:130:137:150:170:186 SD: 0.7632 cents 122:138:151:171:180:197:223:244 SD: 0.4860 cents 168:190:208:235:248:271:307:336 SD: 0.4806 cents 177:200:219:248:261:286:323:354 SD: 0.3838 cents 185:209:229:259:273:299:338:370 SD: 0.2836 cents 223:252:276:312:329:360:407:446 SD: 0.2634 cents 315:356:390:441:465:509:575:630 SD: 0.2626 cents 328:371:406:459:484:530:599:656 SD: 0.2111 cents 345:390:427:483:509:557:630:690 SD: 0.1909 cents 390:441:483:546:575:630:712:780 SD: 0.1687 cents 398:450:493:557:587:643:727:796 SD: 0.1523 cents 453:512:561:634:668:732:827:906 SD: 0.1365 cents 575:650:712:805:848:929:1050:1150 SD: 0.0929 cents