Scala analysis: xen12-chalmers-tritriadic-dm-7-17-23
Tritriadic D->M scale built from 7:17:23
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 529/476 182.767379 2: 17/14 336.129503 supraminor third 3: 23/17 523.318938 4: 34/23 676.681062 5: 23/14 859.448441 6: 289/161 1012.810565 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 322/289 187.1894 1: 529/476 182.7674 2: 578/529 153.3621 3: 322/289 187.1894 4: 578/529 153.3621 5: 529/476 182.7674 6: 578/529 153.3621 7: 322/289 187.1894
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 578/529 153.362 cents 1: 2 529/476 182.767 cents 1: 2 322/289 187.189 cents 2: 3 17/14 336.130 cents supraminor third 2: 3 28/23 340.552 cents 2: 1 12167/9826 369.957 cents 3: 1 4913/3703 489.492 cents 3: 1 16184/12167 493.914 cents 3: 5 23/17 523.319 cents 4: 5 34/23 676.681 cents 4: 1 12167/8092 706.086 cents 4: 1 7406/4913 710.508 cents 5: 1 19652/12167 830.043 cents 5: 3 23/14 859.448 cents 5: 3 28/17 863.870 cents submajor sixth 6: 2 289/161 1012.811 cents 6: 2 952/529 1017.233 cents 6: 3 529/289 1046.638 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 : 182.8 336.1 523.3 676.7 859.4 1012.8 1200.0 182.8 : 153.4 340.6 493.9 676.7 830.0 1017.2 1200.0 336.1 : 187.2 340.6 523.3 676.7 863.9 1046.6 1200.0 523.3 : 153.4 336.1 489.5 676.7 859.4 1012.8 1200.0 676.7 : 182.8 336.1 523.3 706.1 859.4 1046.6 1200.0 859.4 : 153.4 340.6 523.3 676.7 863.9 1017.2 1200.0 1012.8: 187.2 370.0 523.3 710.5 863.9 1046.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 153.3621 .. 187.1894 cents 85169/83521, 33.8273 cents 578/529, 153.3621 cents 2: 336.1295 .. 369.9568 cents 85169/83521, 33.8273 cents 4913/4508, 148.9401 cents 3: 489.4916 .. 523.3189 cents 85169/83521, 33.8273 cents 48275138/45054401, 119.5348 cents 4: 676.6811 .. 710.5084 cents 85169/83521, 33.8273 cents 578/529, 153.3621 cents 5: 830.0432 .. 863.8705 cents 85169/83521, 33.8273 cents 48275138/45054401, 119.5348 cents 6: 1012.8106 .. 1046.6379 cents 85169/83521, 33.8273 cents 4913/4508, 148.9401 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 578/529, 153.3621 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 322/289, 187.1894 cents Average / Smallest step : 1.117803 Largest / Average step : 1.091938 Largest / Smallest step : 1.220571 Median interval of one step : 529/476, 182.7674 cents, amount: 2 Most common interval of one step : 578/529, 153.3621 cents, amount: 3 Least squares average step : 170.75581 cents, oct.: 1195.29065 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : MSLSMSL Scale is a Constant Structure, by a margin of 119.53481 cents Scale diversity : 1.166414 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.830863 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 : 392/391, 4.4221 cents Most common intervals : 23/17, 523.3189 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 340.552 676.681 cents Most common triad is 0.0 523.319 676.681 cents, amount: 3 Number of recognisable fifths : 2, average 708.2973 cents Scale contains two identical disjunct tetrachords Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 17 23 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 23 Odd number limit : 12167 (O: 12167 U: 12167) Highest odd numerator or denominator: 529 Scale harmonicity : 0.004350 Average absolute harmonicity : 0.155311 Specific harmonicity : 0.024118 Fundamental : 1/10948, -13.4184 octaves, 0.0239 Hz. Guide tone : 305762, 18.2220 octaves, 79995156.098 Hz. Exponens Consonantiae : 3.347482E+09, 31.64043 octaves Euler's gradus suavitatis : 124 Sum of Mann's harmonic distance : 811.5, average 115.92857 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 10.49999, average 1.50000 Sum of Tenney's harmonic distance : 20.73963, average 2.96280 Vogel's harmonic complexity : 56.14286 Wille's k value : 6083 Wilson's harmonic complexity : 127 Rectangular lattice diameter : 7 Triangular lattice diameter : 3 Lattice compactness : 69.06344, average 2.46655 Lattice compactness (without 2's) : 56.12138, average 2.00433 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.28571 6 1 7: -1 .. 0 -0.57143 4 17: -1 .. 2 0.28571 6 1 23: -1 .. 2 0.28571 6 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 18 26 31| Scale is JI-epimorphic with val: <7 18 27 30| Scale is weakly epimorphic with val: <7 18 28 29| Scale is weakly epimorphic with val: <7 18 29 35| Scale is weakly epimorphic with val: <7 18 30 34| Scale is weakly epimorphic with val: <7 18 31 33| Scale is weakly epimorphic with val: <7 19 27 32| Scale is JI-epimorphic with val: <7 19 28 31| Scale is weakly epimorphic with val: <7 19 29 30| Scale is weakly epimorphic with val: <7 19 31 35| Scale is weakly epimorphic with val: <7 19 32 34| Scale is weakly epimorphic with val: <7 20 26 35| Scale is weakly epimorphic with val: <7 20 28 33| Scale is JI-epimorphic with val: <7 20 29 32| = patent Scale is weakly epimorphic with val: <7 20 30 31| Scale is weakly epimorphic with val: <7 21 26 30| Scale is weakly epimorphic with val: <7 21 27 29| Scale is weakly epimorphic with val: <7 21 29 34| Scale is JI-epimorphic with val: <7 21 30 33| Scale is weakly epimorphic with val: <7 21 31 32| Scale is weakly epimorphic with val: <7 22 26 32| Scale is weakly epimorphic with val: <7 22 27 31| Scale is weakly epimorphic with val: <7 22 28 30| Scale is weakly epimorphic with val: <7 22 30 35| Scale is JI-epimorphic with val: <7 22 31 34| Scale is weakly epimorphic with val: <7 22 32 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 9.1865 c. M:-15.7609 c. Lebeng 25: 4 3 4 3 4 3 4 SP M ME I SD: 4.9705 c. M:-9.2326 c. 32: 5 4 5 4 5 4 5 SP M ME I SD: 2.3705 c. M:-4.7326 c. 39: 6 5 6 5 6 5 6 SP M ME I SD: 1.6888 c. M:-2.5741 c. 133: 20 17 21 17 20 17 21 SP T3 SD: 1.7389 c. M: 2.3163 c. 140: 21 18 22 18 21 18 22 SP T3 SD: 1.6349 c. M: 2.7674 c. 149: 23 19 23 19 23 19 23 SP M DE I SD: 1.6801 c. M:-2.4675 c. 158: 24 20 25 20 24 20 25 SP T3 SD: 1.4048 c. M: 2.6840 c. 165: 25 21 26 21 25 21 26 SP T3 SD: 1.1232 c. M: 1.9015 c. 172: 26 22 27 22 26 22 27 SP T3 SD: 0.9676 c. M: 1.3720 c. 179: 27 23 28 23 27 23 28 SP T3 SD: 0.9566 c. M: 1.7618 c. 197: 30 25 31 25 30 25 31 SP T3 SD: 0.8298 c. M: 1.6431 c. 204: 31 26 32 26 31 26 32 SP T3 SD: 0.5907 c. M: 1.0459 c. 211: 32 27 33 27 32 27 33 SP T3 SD: 0.4878 c. M: 0.7769 c. 236: 36 30 37 30 36 30 37 SP T3 SD: 0.4803 c. M: 0.9462 c. 243: 37 31 38 31 37 31 38 SP T3 SD: 0.2389 c. M: 0.4649 c. 250: 38 32 39 32 38 32 39 SP T3 SD: 0.1859 c. M: 0.3674 c. 282: 43 36 44 36 43 36 44 SP T3 SD: 0.1061 c. M:-0.2113 c. 532: 81 68 83 68 81 68 83 SP T3 SD: 0.0354 c. M: 0.0606 c. 814: 124 104 127 104 124 104 127 SP T3 SD: 0.0226 c. M: 0.0342 c. 1346: 205 172 210 172 205 172 210 SP T3 SD: 0.0164 c. M: 0.0320 c. 1878: 286 240 293 240 286 240 293 SP T3 SD: 0.0196 c. M: 0.0310 c. 1917: 292 245 299 245 292 245 299 SP T3 SD: 0.0152 c. M:-0.0220 c. 2167: 330 277 338 277 330 277 338 SP T3 SD: 0.0151 c. M: 0.0263 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: 12.6370 cents 3 x x 4 x 5 x 6 S SD: 11.8288 cents 4 x 5 x 6 x 7:8 S SD: 17.8393 cents 5 x 6:7 x 8:9:10 S SD: 15.5444 cents 6 x 7:8:9:10:11:12 S SD: 14.9359 cents 7:8 x 9:10:12:13:14 S SD: 25.0164 cents 8:9:10:11:12:13:14:16 S SD: 11.6766 cents 9:10:11:12:13:15:16:18 SD: 8.1707 cents 14:16:17:19:21:23:25:28 SD: 7.9436 cents 15:17:18:20:22:25:27:30 SD: 7.8744 cents 17:19:21:23:25:28:31:34 SD: 6.0979 cents 19:21:23:26:28:31:34:38 SD: 3.7981 cents 28:31:34:38:41:46:50:56 SD: 2.9396 cents 34:38:41:46:50:56:61:68 SD: 2.6414 cents 37:41:45:50:55:61:66:74 SD: 2.4118 cents 42:47:51:57:62:69:75:84 SD: 2.2985 cents 46:51:56:62:68:76:83:92 SD: 2.2848 cents 48:53:58:65:71:79:86:96 SD: 2.1293 cents 53:59:64:72:78:87:95:106 SD: 2.1140 cents 54:60:66:73:80:89:97:108 SD: 1.8950 cents 56:62:68:76:83:92:101:112 SD: 1.8068 cents 62:69:75:84:92:102:111:124 SD: 1.5951 cents 65:72:79:88:96:107:117:130 SD: 1.2262 cents 79:88:96:107:117:130:142:158 SD: 0.9630 cents 98:109:119:133:145:161:176:196 SD: 0.8323 cents 107:119:130:145:158:176:192:214 SD: 0.6200 cents 117:130:142:158:173:192:210:234 SD: 0.5569 cents 182:202:221:246:269:299:327:364 SD: 0.4642 cents 190:211:231:257:281:312:341:380 SD: 0.3971 cents 196:218:238:265:290:322:352:392 SD: 0.3629 cents 215:239:261:291:318:353:386:430 SD: 0.2476 cents 224:249:272:303:331:368:402:448 SD: 0.1344 cents 439:488:533:594:649:721:788:878 SD: 0.1053 cents