Scala analysis: xen12-chalmers-tritriadic-dm-9-11-15
Tritriadic D->M scale built from 9:11:15
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 25/22 221.309485 undecimal acute whole tone 2: 11/9 347.407941 undecimal neutral third 3: 15/11 536.950772 undecimal augmented fourth 4: 22/15 663.049228 undecimal diminished fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 242/135 1010.457168 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 135/121 189.5428 1: 25/22 221.3095 undecimal acute whole tone 2: 242/225 126.0985 3: 135/121 189.5428 4: 242/225 126.0985 5: 25/22 221.3095 undecimal acute whole tone 6: 242/225 126.0985 7: 135/121 189.5428
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 : 221.3 347.4 537.0 663.0 884.4 1010.5 1200.0 221.3 : 126.1 315.6 441.7 663.0 789.1 978.7 1200.0 347.4 : 189.5 315.6 537.0 663.0 852.6 1073.9 1200.0 537.0 : 126.1 347.4 473.5 663.0 884.4 1010.5 1200.0 663.0 : 221.3 347.4 537.0 758.3 884.4 1073.9 1200.0 884.4 : 126.1 315.6 537.0 663.0 852.6 978.7 1200.0 1010.5: 189.5 410.9 537.0 726.5 852.6 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 : 171.88365 cents, oct.: 1203.18556 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : LSMSLSM 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 Scale contains two identical disjunct tetrachords 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: 135 Scale harmonicity : 0.011572 Average absolute harmonicity : 0.182215 Specific harmonicity : 0.065994 Fundamental : 1/2970, -11.5362 octaves, 0.0881 Hz. Guide tone : 18150, 14.1477 octaves, 4748504.010 Hz. Exponens Consonantiae : 5.390550E+07, 25.68393 octaves Euler's gradus suavitatis : 53 Sum of Mann's harmonic distance : 259.0, average 37.00000 Mersenne's string divisions : 78672360 Sum of van Prooijen's expressibility: 7.62082, average 1.08869 Sum of Tenney's harmonic distance : 15.46327, average 2.20904 Vogel's harmonic complexity : 28.28571 Wille's k value : 1687 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 10 Triangular lattice diameter : 6 Lattice compactness : 75.32377, average 2.69013 Lattice compactness (without 2's) : 69.37394, average 2.47764 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.28571 4 1 3: -3 .. 1 -0.85714 8 5: -1 .. 2 0.28571 6 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: 25.6489 c. M: 49.8809 c. Lebeng 11: 2 1 2 1 2 1 2 P M ME I SD: 14.7131 c. M: 28.6390 c. Superkleismic-7 18: 3 2 3 2 3 2 3 SP M ME I SD: 12.5398 c. M: 21.3095 c. 20: 4 2 3 2 4 2 3 P T3 SD: 11.0983 c. M:-18.6905 c. 27: 5 3 4 3 5 3 4 SP T3 SD: 6.0039 c. M:-11.7651 c. 31: 6 3 5 3 6 3 5 P T3 SD: 5.6333 c. M:-10.9486 c. 38: 7 4 6 4 7 4 6 SP T3 SD: 0.1298 c. M: 0.2569 c. 677: 125 71 107 71 125 71 107 SP T3 SD: 0.1352 c. M:-0.2562 c. 715: 132 75 113 75 132 75 113 SP T3 SD: 0.1212 c. M:-0.2290 c. 753: 139 79 119 79 139 79 119 SP T3 SD: 0.1087 c. M:-0.2045 c. 791: 146 83 125 83 146 83 125 SP T3 SD: 0.0973 c. M:-0.1823 c. 829: 153 87 131 87 153 87 131 SP T3 SD: 0.0871 c. M:-0.1622 c. 867: 160 91 137 91 160 91 137 SP T3 SD: 0.0777 c. M:-0.1438 c. 905: 167 95 143 95 167 95 143 SP T3 SD: 0.0692 c. M:-0.1270 c. 943: 174 99 149 99 174 99 149 SP T3 SD: 0.0614 c. M:-0.1115 c. 981: 181 103 155 103 181 103 155 SP T3 SD: 0.0542 c. M:-0.0972 c. 1019: 188 107 161 107 188 107 161 SP T3 SD: 0.0476 c. M:-0.0840 c. 1057: 195 111 167 111 195 111 167 SP T3 SD: 0.0415 c. M:-0.0718 c. 1095: 202 115 173 115 202 115 173 SP T3 SD: 0.0359 c. M:-0.0604 c. 1133: 209 119 179 119 209 119 179 SP T3 SD: 0.0308 c. M:-0.0497 c. 1171: 216 123 185 123 216 123 185 SP T3 SD: 0.0262 c. M:-0.0398 c. 1209: 223 127 191 127 223 127 191 SP T3 SD: 0.0220 c. M: 0.0353 c. 1247: 230 131 197 131 230 131 197 SP T3 SD: 0.0184 c. M: 0.0321 c. 1285: 237 135 203 135 237 135 203 SP T3 SD: 0.0154 c. M: 0.0292 c. 1323: 244 139 209 139 244 139 209 SP T3 SD: 0.0132 c. M: 0.0263 c. 1361: 251 143 215 143 251 143 215 SP T3 SD: 0.0121 c. M: 0.0237 c. 1399: 258 147 221 147 258 147 221 SP T3 SD: 0.0120 c. M: 0.0211 c. 1437: 265 151 227 151 265 151 227 SP T3 SD: 0.0129 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: 12.9686 cents 4 x 5 x 6 x 7:8 S SD: 17.2491 cents 5 x 6:7 x 8:9:10 S SD: 18.0339 cents 6:7 x 8:9:10:11:12 S SD: 13.5573 cents 7:8:9 x 10:12:13:14 S SD: 21.0751 cents 8:9:10:11:12:13:14:16 S SD: 12.1141 cents 9:10:11:12:13:15:16:18 SD: 8.9584 cents 11 x 13:15:16:18:20:22 SD: 12.0239 cents 13:15:16:18:19:22:23:26 SD: 7.5511 cents 14:16:17:19:21:23:25:28 SD: 7.1017 cents 19:22:23:26:28:32:34:38 SD: 6.0201 cents 21:24:26:29:31:35:38:42 SD: 5.4660 cents 22:25:27:30:32:37:39:44 SD: 4.2259 cents 28:32:34:38:41:47:50:56 SD: 3.1843 cents 30:34:37:41:44:50:54:60 SD: 2.6052 cents 36:41:44:49:53:60:65:72 SD: 2.1358 cents 45:51:55:61:66:75:81:90 SD: 1.9071 cents 58:66:71:79:85:97:104:116 SD: 1.0557 cents 90:102:110:123:132:150:161:180 SD: 0.9996 cents 96:109:117:131:141:160:172:192 SD: 0.8406 cents 116:132:142:158:170:193:208:232 SD: 0.7562 cents 126:143:154:172:185:210:226:252 SD: 0.5099 cents 154:175:188:210:226:257:276:308 SD: 0.4610 cents 184:209:225:251:270:307:330:368 SD: 0.3695 cents 198:225:242:270:290:330:355:396 SD: 0.3440 cents 212:241:259:289:311:353:380:424 SD: 0.2893 cents 270:307:330:368:396:450:484:540 SD: 0.1908 cents 360:409:440:491:528:600:645:720 SD: 0.1464 cents 396:450:484:540:581:660:710:792 SD: 0.0970 cents 594:675:726:810:871:990:1065:1188 SD: 0.0734 cents