Scala analysis: xen12-chalmers-tritriadic-mt-11-5-3
Tritriadic M->T scale built from 11:5:3
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 12/11 150.637059 undecimal neutral second, 3/4-tone 2: 11/10 165.004228 Ptolemy's second, 4/5-tone 3: 6/5 315.641287 minor third 4: 200/121 869.991543 5: 20/11 1034.995772 large minor seventh 6: 240/121 1185.632830 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 121/120 14.3672 undecimal seconds comma, biyatisma 1: 12/11 150.6371 undecimal neutral second, 3/4-tone 2: 121/120 14.3672 undecimal seconds comma, biyatisma 3: 12/11 150.6371 undecimal neutral second, 3/4-tone 4: 500/363 554.3503 5: 11/10 165.0042 Ptolemy's second, 4/5-tone 6: 12/11 150.6371 undecimal neutral second, 3/4-tone 7: 121/120 14.3672 undecimal seconds comma, biyatisma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 121/120 14.367 cents undecimal seconds comma, biyatisma 1: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 500/363 554.350 cents 2: 4 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 6/5 315.641 cents minor third 2: 1 2000/1331 704.987 cents 2: 1 50/33 719.354 cents 3 pentatones 3: 1 1331/1200 179.371 cents 3: 2 6/5 315.641 cents minor third 3: 1 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 3: 1 50/33 719.354 cents 3 pentatones 3: 2 200/121 869.992 cents 4: 2 121/100 330.008 cents two (Ptolemy's second, 4/5-tone) 4: 1 33/25 480.646 cents 2 pentatones 4: 1 200/121 869.992 cents 4: 2 5/3 884.359 cents major sixth, BP sixth 4: 1 2400/1331 1020.629 cents 5: 1 33/25 480.646 cents 2 pentatones 5: 1 1331/1000 495.013 cents 5: 1 5/3 884.359 cents major sixth, BP sixth 5: 4 20/11 1034.996 cents large minor seventh 6: 1 363/250 645.650 cents 6: 1 20/11 1034.996 cents large minor seventh 6: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 6: 2 240/121 1185.633 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 : 150.6 165.0 315.6 870.0 1035.0 1185.6 1200.0 150.6 : 14.4 165.0 719.4 884.4 1035.0 1049.4 1200.0 165.0 : 150.6 705.0 870.0 1020.6 1035.0 1185.6 1200.0 315.6 : 554.4 719.4 870.0 884.4 1035.0 1049.4 1200.0 870.0 : 165.0 315.6 330.0 480.6 495.0 645.6 1200.0 1035.0: 150.6 165.0 315.6 330.0 480.6 1035.0 1200.0 1185.6: 14.4 165.0 179.4 330.0 884.4 1049.4 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.3672 .. 554.3503 cents 20000/14641, 539.9831 cents 121/120, 14.3672 cents 2: 165.0042 .. 719.3545 cents 500/363, 554.3503 cents 3993/5000,-389.3460 cents 3: 179.3714 .. 869.9915 cents 240000/161051, 690.6201 cents 14641/20000,-539.9831 cents 4: 330.0085 .. 1020.6286 cents 240000/161051, 690.6201 cents 14641/20000,-539.9831 cents 5: 480.6455 .. 1034.9958 cents 500/363, 554.3503 cents 14641/20000,-539.9831 cents 6: 645.6497 .. 1185.6328 cents 20000/14641, 539.9831 cents 3993/5000,-389.3460 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 121/120, 14.3672 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 500/363, 554.3503 cents Average / Smallest step : 11.931965 Largest / Average step : 3.233710 Largest / Smallest step : 38.584513 Median interval of one step : 12/11, 150.6371 cents, amount: 3 Most common interval of one step : 12/11, 150.6371 cents, amount: 3 Least squares average step : 182.83080 cents, oct.: 1279.81557 cents Scale is not proper Step pattern alph. order: ABACDAB Step pattern size order : BABDCBA Scale is not a Constant Structure Scale diversity : 1.208519 Lumma stability : 0.023945 Lumma impropriety factor : 0.724993 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 : 121/120, 14.3672 cents Most common intervals : 11/10, 165.0042 cents & inv., amount: 5 Most common triad is 0.0 165.004 1034.996 cents, amount: 3 Number of recognisable fifths : 3, average 714.5654 cents Number of appreciable fifths : 1, average 704.9873 cents Scale contains a complete diamond : 5 11 Length of longest harmonic part : 2 at degree 4 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 1331 (O: 1331 U: 1331) Highest odd numerator or denominator: 121 Scale harmonicity : 0.012283 Average absolute harmonicity : 0.179887 Specific harmonicity : 0.067513 Fundamental : 1/1210, -10.2408 octaves, 0.2162 Hz. Guide tone : 13200, 13.6883 octaves, 3453457.462 Hz. Exponens Consonantiae : 1.597200E+07, 23.92904 octaves Euler's gradus suavitatis : 50 Sum of Mann's harmonic distance : 385.5, average 55.07143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.98872, average 1.14125 Sum of Tenney's harmonic distance : 17.12935, average 2.44705 Vogel's harmonic complexity : 24.57143 Wille's k value : 665 Wilson's harmonic complexity : 51 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 80.52962, average 2.87606 Lattice compactness (without 2's) : 56.50032, average 2.01787 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 4 1.71429 14 1 3: 0 .. 1 0.42857 3 5: -1 .. 2 0.28571 6 1 11: -2 .. 1 -0.71429 7 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 10 15 26| Scale is weakly epimorphic with val: <7 10 16 25| Scale is weakly epimorphic with val: <7 10 18 23| Scale is weakly epimorphic with val: <7 11 17 26| Scale is weakly epimorphic with val: <7 12 15 23| Scale is weakly epimorphic with val: <7 12 16 22|
FIT/MODE
7: 1 0 1 3 1 1 0 N SD: 15.2458 c. M:-27.2159 c. 15: 2 0 2 7 2 2 0 N SD: 8.1357 c. M:-14.3672 c. 37: 5 0 5 17 5 5 0 N SD: 8.1337 c. M:-14.3672 c. 42: 5 1 5 19 6 5 1 N SD: 8.5503 c. M: 14.2043 c. 43: 5 1 5 20 6 5 1 N SD: 7.7211 c. M: 13.5398 c. 49: 6 1 6 23 6 6 1 N SD: 6.9861 c. M:-11.6411 c. 50: 6 1 6 23 7 6 1 N SD: 5.3977 c. M: 9.6328 c. 53: 7 0 7 24 8 6 1 N SD: 6.6464 c. M: 9.6142 c. 56: 7 1 7 26 7 7 1 N SD: 5.8544 c. M:-8.5799 c. 57: 7 1 7 26 8 7 1 N SD: 4.2334 c. M: 6.8336 c. 58: 7 1 7 27 8 7 1 N SD: 3.8425 c. M: 6.3225 c. 65: 8 1 8 30 9 8 1 N SD: 2.2862 c. M: 4.0944 c. 72: 9 1 9 33 10 9 1 N SD: 1.8255 c. M: 3.3249 c. 73: 9 1 9 34 10 9 1 N SD: 1.8830 c. M: 3.3125 c. 80: 10 1 10 37 11 10 1 N SD: 0.4171 c. M: 0.6413 c. 167: 21 2 21 77 23 21 2 N SD: 0.3311 c. M: 0.5305 c. 247: 31 3 31 114 34 31 3 N SD: 0.1912 c. M: 0.3559 c. 327: 41 4 41 151 45 41 4 N SD: 0.1843 c. M: 0.3117 c. 342: 43 4 43 158 47 43 4 N SD: 0.1854 c. M:-0.3321 c. 422: 53 5 53 195 58 53 5 N SD: 0.0939 c. M:-0.1506 c. 502: 63 6 63 232 69 63 6 N SD: 0.0731 c. M:-0.1280 c. 589: 74 7 74 272 81 74 7 N SD: 0.0862 c. M:-0.1482 c. 669: 84 8 84 309 92 84 8 N SD: 0.0303 c. M:-0.0538 c. 749: 94 9 94 346 103 94 9 N SD: 0.0291 c. M: 0.0521 c. 1171: 147 14 147 541 161 147 14 N SD: 0.0184 c. M:-0.0341 c. 1418: 178 17 178 655 195 178 17 N SD: 0.0182 c. M: 0.0339 c. 1840: 231 22 231 850 253 231 22 N SD: 0.0109 c. M:-0.0193 c. 1920: 241 23 241 887 264 241 23 N SD: 0.0091 c. M: 0.0163 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: 84.0183 cents 3 x x 4:5 x x 6 S SD: 60.9896 cents 4 x x 5 x 7 x 8 SD: 32.2715 cents 5 x x 6:8:9 x 10 S SD: 14.7331 cents 6 x x 7:10:11 x 12 SD: 13.2084 cents 7 x 8 x 12:13 x 14 S SD: 24.6375 cents 8 x 9:10:13:15 x 16 SD: 20.2132 cents 9 x 10:11:15:16 x 18 SD: 11.0126 cents 10 x 11:12:17:18 x 20 SD: 10.3336 cents 11:12 x 13:18:20 x 22 SD: 6.3289 cents 12:13 x 14:20:22 x 24 SD: 10.8387 cents 13:14 x 16:21:24 x 26 SD: 13.7083 cents 14:15 x 17:23:25 x 28 SD: 9.9541 cents 15:16:17:18:25:27 x 30 SD: 11.4187 cents 16:17:18:19:26:29 x 32 SD: 11.5789 cents 17 x 19:20:28:31 x 34 SD: 8.9394 cents 18 x 20:22:30:33 x 36 SD: 8.3059 cents 19 x 21:23:31:35 x 38 SD: 7.2496 cents 20 x 22:24:33:36 x 40 SD: 3.5323 cents 21:23 x 25:35:38 x 42 SD: 4.5255 cents 22:24 x 26:36:40 x 44 SD: 6.3289 cents 23:25 x 28:38:42 x 46 SD: 5.3553 cents 24:26 x 29:40:44 x 48 SD: 5.2988 cents 25:27:28:30:41:45 x 50 SD: 6.9967 cents 26:28:29:31:43:47 x 52 SD: 6.0150 cents 27:29:30:32:45:49 x 54 SD: 6.8858 cents 28 x 31:34:46:51 x 56 SD: 5.1615 cents 29 x 32:35:48:53 x 58 SD: 2.9207 cents 30 x 33:36:50:55 x 60 SD: 4.0636 cents 31 x 34:37:51:56:61:62 SD: 3.7058 cents 32:35 x 38:53:58:63:64 SD: 3.9333 cents 33:36 x 40:55:60:65:66 SD: 4.2645 cents 34:37 x 41:56:62:67:68 SD: 2.7904 cents 39 x 43:47:64:71:77:78 SD: 2.8617 cents 40 x 44:48:66:73:79:80 SD: 1.7167 cents 41 x 45:49:68:75:81:82 SD: 2.6737 cents 42:46 x 50:69:76:83:84 SD: 3.5640 cents 43:47 x 52:71:78:85:86 SD: 2.6038 cents 44:48 x 53:73:80:87:88 SD: 1.7810 cents 50 x 55:60:83:91:99:100 SD: 1.3680 cents 51 x 56:61:84:93:101:102 SD: 1.7655 cents 52 x 57:62:86:95:103:104 SD: 2.5616 cents 53:58 x 64:88:96:105:106 SD: 2.6643 cents 54:59 x 65:89:98:107:108 SD: 1.4305 cents 61 x 67:73:101:111:121:122 SD: 1.0540 cents 62 x 68:74:102:113:123:124 SD: 2.3360 cents 63:69 x 76:104:115:125:126 SD: 2.2525 cents 64:70 x 77:106:116:127:128 SD: 1.5172 cents 69:75:76:83:114:125:137:138 SD: 1.4662 cents 72 x 79:86:119:131:143:144 SD: 1.5852 cents 73 x 80:88:121:133:145:146 SD: 2.0172 cents 74:81 x 89:122:135:147:148 SD: 1.7487 cents 76:83:84:91:126:138:151:152 SD: 1.6133 cents 77:84:85:92:127:140:153:154 SD: 1.5466 cents 78:85:86:94:129:142:155:156 SD: 1.3594 cents 80:87:88:96:132:145:159:160 SD: 1.2798 cents 83 x 91:100:137:151:165:166 SD: 1.6892 cents 84:92 x 101:139:153:167:168 SD: 1.5671 cents 86:94:95:103:142:156:171:172 SD: 1.5230 cents 87:95:96:104:144:158:173:174 SD: 1.4652 cents 89:97:98:107:147:162:177:178 SD: 0.9358 cents 94 x 103:113:155:171:186:188 SD: 1.5786 cents 96:105:106:115:159:175:190:192 SD: 1.5579 cents 97:106:107:116:160:176:192:194 SD: 1.4727 cents 98:107:108:118:162:178:194:196 SD: 1.1218 cents 99:108:109:119:164:180:196:198 SD: 0.8580 cents 100:109:110:120:165:182:198:200 SD: 0.6920 cents 109:119:120:131:180:198:216:218 SD: 0.6129 cents 110:120:121:132:182:200:218:220 SD: 0.3219 cents 230:251:253:276:380:418:456:460 SD: 0.2067 cents 320:349:352:384:529:582:635:640 SD: 0.1550 cents 429:468:472:515:709:780:851:858 SD: 0.1170 cents 539:588:593:647:891:980:1069:1078 SD: 0.0931 cents 550:600:605:660:909:1000:1091:1100 SD: 0.0322 cents