Scala analysis: xen09-chalmers-tritriadic-11-18-15
Tritriadic scale built from 11:18:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 135/121 189.542832 2: 6/5 315.641287 minor third 3: 15/11 536.950772 undecimal augmented fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 18/11 852.592059 undecimal neutral sixth 6: 225/121 1073.901545 two (undecimal augmented fourth) 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 242/225 126.0985 1: 135/121 189.5428 2: 242/225 126.0985 3: 25/22 221.3095 undecimal acute whole tone 4: 242/225 126.0985 5: 135/121 189.5428 6: 25/22 221.3095 undecimal acute whole tone 7: 242/225 126.0985
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 242/225 126.098 cents 1: 2 135/121 189.543 cents 1: 2 25/22 221.309 cents undecimal acute whole tone 2: 3 6/5 315.641 cents minor third 2: 3 11/9 347.408 cents undecimal neutral third 2: 1 3375/2662 410.852 cents 3: 1 484/375 441.740 cents 3: 1 2662/2025 473.506 cents 3: 5 15/11 536.951 cents undecimal augmented fourth 4: 5 22/15 663.049 cents undecimal diminished fifth 4: 1 2025/1331 726.494 cents 4: 1 375/242 758.260 cents 5: 1 5324/3375 789.148 cents 5: 3 18/11 852.592 cents undecimal neutral sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 6: 2 44/25 978.691 cents undecimal grave minor seventh 6: 2 242/135 1010.457 cents 6: 3 225/121 1073.902 cents two (undecimal 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 : 189.5 315.6 537.0 663.0 852.6 1073.9 1200.0 189.5 : 126.1 347.4 473.5 663.0 884.4 1010.5 1200.0 315.6 : 221.3 347.4 537.0 758.3 884.4 1073.9 1200.0 537.0 : 126.1 315.6 537.0 663.0 852.6 978.7 1200.0 663.0 : 189.5 410.9 537.0 726.5 852.6 1073.9 1200.0 852.6 : 221.3 347.4 537.0 663.0 884.4 1010.5 1200.0 1073.9: 126.1 315.6 441.7 663.0 789.1 978.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 126.0985 .. 221.3095 cents 5625/5324, 95.2110 cents 242/225, 126.0985 cents 2: 315.6413 .. 410.8523 cents 5625/5324, 95.2110 cents 132/125, 94.3318 cents 3: 441.7397 .. 536.9508 cents 5625/5324, 95.2110 cents 1288408/1265625, 30.8874 cents 4: 663.0492 .. 758.2603 cents 5625/5324, 95.2110 cents 242/225, 126.0985 cents 5: 789.1477 .. 884.3587 cents 5625/5324, 95.2110 cents 1288408/1265625, 30.8874 cents 6: 978.6905 .. 1073.9015 cents 5625/5324, 95.2110 cents 132/125, 94.3318 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 242/225, 126.0985 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 25/22, 221.3095 cents Average / Smallest step : 1.359482 Largest / Average step : 1.290972 Largest / Smallest step : 1.755053 Median interval of one step : 135/121, 189.5428 cents, amount: 2 Most common interval of one step : 242/225, 126.0985 cents, amount: 3 Least squares average step : 172.78746 cents, oct.: 1209.51221 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : MSLSMLS Scale is a Constant Structure, by a margin of 30.88743 cents Scale diversity : 1.383098 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.523945 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 : 1288408/1265625, 30.8874 cents Most common intervals : 15/11, 536.9508 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 315.641 663.049 cents Most common triad is 0.0 536.951 663.049 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 : 11 15 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 11 Odd number limit : 3375 (O: 3375 U: 3375) Highest odd numerator or denominator: 225 Scale harmonicity : 0.011708 Average absolute harmonicity : 0.178611 Specific harmonicity : 0.064823 Fundamental : 1/1815, -10.8258 octaves, 0.1441 Hz. Guide tone : 14850, 13.8582 octaves, 3885139.645 Hz. Exponens Consonantiae : 2.695275E+07, 24.68393 octaves Euler's gradus suavitatis : 52 Sum of Mann's harmonic distance : 354.0, average 50.57143 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.57506, average 1.22501 Sum of Tenney's harmonic distance : 17.45890, average 2.49413 Vogel's harmonic complexity : 27.57143 Wille's k value : 1687 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 74.55617, average 2.66272 Lattice compactness (without 2's) : 70.60197, average 2.52150 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.57143 4 1 3: -1 .. 3 1.14286 10 5: -1 .. 2 0.28571 6 1 11: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 5 / 7 = 0.71429 Average absolute exponent except 2's: 23 / 7 = 3.28571 Scale is JI-epimorphic with val: <7 10 15 22| Scale is weakly epimorphic with val: <7 10 18 26| Scale is weakly epimorphic with val: <7 11 15 25| Scale is JI-epimorphic with val: <7 11 16 24| = patent Scale is weakly epimorphic with val: <7 11 17 23| Scale is JI-epimorphic with val: <7 12 17 26| Scale is weakly epimorphic with val: <7 12 18 25|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 24.4124 c. M: 45.3301 c. Lebeng 11: 2 1 2 1 2 2 1 P M ME S SD: 16.0125 c. M:-28.6390 c. 18: 3 2 3 2 3 3 2 SP M ME S SD: 9.9926 c. M:-17.6920 c. 20: 3 2 4 2 3 4 2 P T3 SD: 8.8646 c. M: 15.6413 c. 27: 4 3 5 3 4 5 3 SP T3 SD: 6.5883 c. M: 11.7651 c. 31: 5 3 6 3 5 6 3 P T3 SD: 5.3673 c. M:-9.9694 c. 38: 6 4 7 4 6 7 4 SP T3 SD: 0.1190 c. M: 0.2173 c. 715: 113 75 132 75 113 132 75 SP T3 SD: 0.1199 c. M:-0.2243 c. 753: 119 79 139 79 119 139 79 SP T3 SD: 0.1080 c. M:-0.2020 c. 791: 125 83 146 83 125 146 83 SP T3 SD: 0.0972 c. M:-0.1819 c. 829: 131 87 153 87 131 153 87 SP T3 SD: 0.0874 c. M:-0.1636 c. 867: 137 91 160 91 137 160 91 SP T3 SD: 0.0785 c. M:-0.1469 c. 905: 143 95 167 95 143 167 95 SP T3 SD: 0.0704 c. M:-0.1316 c. 943: 149 99 174 99 149 174 99 SP T3 SD: 0.0630 c. M:-0.1175 c. 981: 155 103 181 103 155 181 103 SP T3 SD: 0.0561 c. M:-0.1046 c. 1019: 161 107 188 107 161 188 107 SP T3 SD: 0.0498 c. M:-0.0926 c. 1057: 167 111 195 111 167 195 111 SP T3 SD: 0.0440 c. M:-0.0814 c. 1095: 173 115 202 115 173 202 115 SP T3 SD: 0.0386 c. M:-0.0711 c. 1133: 179 119 209 119 179 209 119 SP T3 SD: 0.0337 c. M:-0.0614 c. 1171: 185 123 216 123 185 216 123 SP T3 SD: 0.0292 c. M:-0.0523 c. 1209: 191 127 223 127 191 223 127 SP T3 SD: 0.0250 c. M:-0.0439 c. 1247: 197 131 230 131 197 230 131 SP T3 SD: 0.0213 c. M:-0.0359 c. 1285: 203 135 237 135 203 237 135 SP T3 SD: 0.0181 c. M:-0.0292 c. 1323: 209 139 244 139 209 244 139 SP T3 SD: 0.0153 c. M:-0.0263 c. 1361: 215 143 251 143 215 251 143 SP T3 SD: 0.0133 c. M:-0.0237 c. 1399: 221 147 258 147 221 258 147 SP T3 SD: 0.0120 c. M:-0.0211 c. 1437: 227 151 265 151 227 265 151 SP T3 SD: 0.0116 c. M:-0.0188 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: 19.4529 cents 3 x x 4 x 5 x 6 S SD: 16.7424 cents 4 x 5 x 6 x 7:8 S SD: 33.1183 cents 5 x 6:7 x 8:9:10 S SD: 16.4436 cents 6 x 7:8:9:10:11:12 S SD: 13.9614 cents 7:8 x x 10:11:13:14 SD: 18.6846 cents 8:9:10:11:12:13:15:16 SD: 12.1832 cents 9:10:11:12:13:15:17:18 SD: 10.1200 cents 11:12:13:15:16:18:20:22 SD: 8.9584 cents 14:16:17:19:21:23:26:28 SD: 8.7909 cents 15:17:18:20:22:25:28:30 SD: 8.2113 cents 16:18:19:22:23:26:30:32 SD: 6.8552 cents 17:19:20:23:25:28:32:34 SD: 6.3340 cents 19:21:23:26:28:31:35:38 SD: 4.2597 cents 25:28:30:34:37:41:46:50 SD: 3.6677 cents 34:38:41:46:50:56:63:68 SD: 3.0393 cents 35:39:42:48:51:57:65:70 SD: 2.4846 cents 36:40:43:49:53:59:67:72 SD: 1.9060 cents 50:56:60:68:73:82:93:100 SD: 1.7075 cents 60:67:72:82:88:98:112:120 SD: 1.2088 cents 69:77:83:94:101:113:128:138 SD: 1.0214 cents 85:95:102:116:125:139:158:170 SD: 0.8328 cents 94:105:113:128:138:154:175:188 SD: 0.7927 cents 105:117:126:143:154:172:195:210 SD: 0.6039 cents 129:144:155:176:189:211:240:258 SD: 0.4803 cents 165:184:198:225:242:270:307:330 SD: 0.1908 cents 319:356:383:435:468:522:593:638 SD: 0.1772 cents 371:414:445:506:544:607:690:742 SD: 0.1527 cents 390:435:468:532:572:638:725:780 SD: 0.1485 cents 440:491:528:600:645:720:818:880 SD: 0.1464 cents 465:519:558:634:682:761:865:930 SD: 0.1414 cents 476:531:571:649:698:779:885:952 SD: 0.1190 cents 484:540:581:660:710:792:900:968 SD: 0.0970 cents