Scala analysis: xen09-chalmers-tritriadic-15-18-22
Tritriadic scale built from 15:18:22
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 242/225 126.098455 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: 44/25 978.690515 undecimal grave minor seventh 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 25/22 221.3095 undecimal acute whole tone 1: 242/225 126.0985 2: 135/121 189.5428 3: 25/22 221.3095 undecimal acute whole tone 4: 242/225 126.0985 5: 135/121 189.5428 6: 242/225 126.0985 7: 25/22 221.3095 undecimal acute whole tone
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 : 126.1 315.6 537.0 663.0 852.6 978.7 1200.0 126.1 : 189.5 410.9 537.0 726.5 852.6 1073.9 1200.0 315.6 : 221.3 347.4 537.0 663.0 884.4 1010.5 1200.0 537.0 : 126.1 315.6 441.7 663.0 789.1 978.7 1200.0 663.0 : 189.5 315.6 537.0 663.0 852.6 1073.9 1200.0 852.6 : 126.1 347.4 473.5 663.0 884.4 1010.5 1200.0 978.7 : 221.3 347.4 537.0 758.3 884.4 1073.9 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 : 168.25381 cents, oct.: 1177.77668 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCABAC Step pattern size order : SMLSMSL 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 : 0.011572 Average absolute harmonicity : 0.180081 Specific harmonicity : 0.065944 Fundamental : 1/2475, -11.2732 octaves, 0.1057 Hz. Guide tone : 21780, 14.4107 octaves, 5698204.812 Hz. Exponens Consonantiae : 5.390550E+07, 25.68393 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 321.0, average 45.85714 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 7.84267, average 1.12038 Sum of Tenney's harmonic distance : 16.58820, average 2.36974 Vogel's harmonic complexity : 28.00000 Wille's k value : 1687 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 74.49204, average 2.66043 Lattice compactness (without 2's) : 69.09638, average 2.46773 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 7 1 3: -2 .. 2 0.14286 7 5: -2 .. 1 -0.71429 7 1 11: -1 .. 2 0.28571 6 5 Average exponent except 2's :-2 / 7 =-0.28571 Average absolute exponent except 2's: 20 / 7 = 2.85714 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: 30.0755 c. M:-49.8809 c. Lebeng 11: 1 2 2 1 2 1 2 P M ME S SD: 11.8586 c. M:-20.1352 c. Orgone-7 18: 2 3 3 2 3 2 3 SP M ME S SD: 12.2107 c. M:-21.3095 c. Dicot-7 20: 2 3 4 2 3 2 4 P T3 SD: 10.7460 c. M: 18.6905 c. 27: 3 4 5 3 4 3 5 SP T3 SD: 4.8735 c. M: 8.1476 c. 38: 4 6 7 4 6 4 7 SP T3 SD: 0.1513 c. M:-0.2569 c. 677: 71 107 125 71 107 71 125 SP T3 SD: 0.1586 c. M: 0.2562 c. 715: 75 113 132 75 113 75 132 SP T3 SD: 0.1422 c. M: 0.2290 c. 753: 79 119 139 79 119 79 139 SP T3 SD: 0.1275 c. M: 0.2045 c. 791: 83 125 146 83 125 83 146 SP T3 SD: 0.1141 c. M: 0.1823 c. 829: 87 131 153 87 131 87 153 SP T3 SD: 0.1021 c. M: 0.1636 c. 867: 91 137 160 91 137 91 160 SP T3 SD: 0.0910 c. M: 0.1469 c. 905: 95 143 167 95 143 95 167 SP T3 SD: 0.0809 c. M: 0.1316 c. 943: 99 149 174 99 149 99 174 SP T3 SD: 0.0717 c. M: 0.1175 c. 981: 103 155 181 103 155 103 181 SP T3 SD: 0.0632 c. M: 0.1046 c. 1019: 107 161 188 107 161 107 188 SP T3 SD: 0.0553 c. M: 0.0926 c. 1057: 111 167 195 111 167 111 195 SP T3 SD: 0.0480 c. M: 0.0814 c. 1095: 115 173 202 115 173 115 202 SP T3 SD: 0.0413 c. M: 0.0711 c. 1133: 119 179 209 119 179 119 209 SP T3 SD: 0.0351 c. M: 0.0614 c. 1171: 123 185 216 123 185 123 216 SP T3 SD: 0.0294 c. M: 0.0523 c. 1209: 127 191 223 127 191 127 223 SP T3 SD: 0.0241 c. M: 0.0439 c. 1247: 131 197 230 131 197 131 230 SP T3 SD: 0.0193 c. M: 0.0359 c. 1285: 135 203 237 135 203 135 237 SP T3 SD: 0.0152 c. M: 0.0284 c. 1323: 139 209 244 139 209 139 244 SP T3 SD: 0.0119 c. M: 0.0214 c. 1361: 143 215 251 143 215 143 251 SP T3 SD: 0.0098 c. M:-0.0163 c. 1399: 147 221 258 147 221 147 258 SP T3 SD: 0.0095 c. M:-0.0169 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: 20.3187 cents 5 x 6:7 x 8:9:10 S SD: 14.2873 cents 6 x 7:8:9:10:11:12 S SD: 17.8026 cents 7 x 8 x 10:11:12:14 S SD: 25.4562 cents 8:9:10:11:12:13:14:16 S SD: 16.2958 cents 9:10:11:12:13:15:16:18 SD: 12.5386 cents 11:12:13:15:16:18:19:22 SD: 7.2325 cents 16:17:19:22:23:26:28:32 SD: 7.0483 cents 17:18:20:23:25:28:30:34 SD: 6.8032 cents 21:23:25:29:31:34:37:42 SD: 6.5799 cents 22:24:26:30:32:36:39:44 SD: 5.8253 cents 24:26:29:33:35:39:42:48 SD: 4.1545 cents 25:27:30:34:37:41:44:50 SD: 2.6052 cents 30:32:36:41:44:49:53:60 SD: 2.3661 cents 39:42:47:53:57:64:69:78 SD: 2.2018 cents 41:44:49:56:60:67:72:82 SD: 1.4809 cents 55:59:66:75:81:90:97:110 SD: 1.3133 cents 66:71:79:90:97:108:116:132 SD: 0.8775 cents 80:86:96:109:117:131:141:160 SD: 0.8406 cents 105:113:126:143:154:172:185:210 SD: 0.5099 cents 146:157:175:199:214:239:257:292 SD: 0.3592 cents 184:198:221:251:270:301:324:368 SD: 0.3294 cents 225:242:270:307:330:368:396:450 SD: 0.1908 cents 330:355:396:450:484:540:581:660 SD: 0.0970 cents 555:597:666:757:814:908:977:1110 SD: 0.0965 cents