Scala analysis: xen12-chalmers-tritriadic-dm-27-23-17
Tritriadic D->M scale built from 27:23:17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 529/459 245.728282 2: 34/27 399.090407 septendecimal major third 3: 23/17 523.318938 4: 34/23 676.681062 5: 46/27 922.409345 6: 1156/621 1075.771469 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 621/578 124.2285 1: 529/459 245.7283 2: 578/529 153.3621 3: 621/578 124.2285 4: 578/529 153.3621 5: 529/459 245.7283 6: 578/529 153.3621 7: 621/578 124.2285
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 621/578 124.229 cents 1: 3 578/529 153.362 cents 1: 2 529/459 245.728 cents 2: 3 27/23 277.591 cents vicesimotertial minor third 2: 1 12167/9826 369.957 cents 2: 3 34/27 399.090 cents septendecimal major third 3: 1 15606/12167 430.953 cents 3: 5 23/17 523.319 cents 3: 1 19652/14283 552.453 cents 4: 1 14283/9826 647.547 cents 4: 5 34/23 676.681 cents 4: 1 12167/7803 769.047 cents 5: 3 27/17 800.910 cents septendecimal minor sixth 5: 1 19652/12167 830.043 cents 5: 3 46/27 922.409 cents 6: 2 918/529 954.272 cents 6: 3 529/289 1046.638 cents 6: 2 1156/621 1075.771 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 : 245.7 399.1 523.3 676.7 922.4 1075.8 1200.0 245.7 : 153.4 277.6 431.0 676.7 830.0 954.3 1200.0 399.1 : 124.2 277.6 523.3 676.7 800.9 1046.6 1200.0 523.3 : 153.4 399.1 552.5 676.7 922.4 1075.8 1200.0 676.7 : 245.7 399.1 523.3 769.0 922.4 1046.6 1200.0 922.4 : 153.4 277.6 523.3 676.7 800.9 954.3 1200.0 1075.8: 124.2 370.0 523.3 647.5 800.9 1046.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 124.2285 .. 245.7283 cents 782/729, 121.4998 cents 621/578, 124.2285 cents 2: 277.5907 .. 399.0904 cents 782/729, 121.4998 cents 12393/12167, 31.8624 cents 3: 430.9528 .. 552.4525 cents 782/729, 121.4998 cents 12393/12167, 31.8624 cents 4: 647.5475 .. 769.0472 cents 782/729, 121.4998 cents 204004089/193100552, 95.0949 cents 5: 800.9096 .. 922.4093 cents 782/729, 121.4998 cents 12393/12167, 31.8624 cents 6: 954.2717 .. 1075.7715 cents 782/729, 121.4998 cents 12393/12167, 31.8624 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 621/578, 124.2285 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 529/459, 245.7283 cents Average / Smallest step : 1.379945 Largest / Average step : 1.433415 Largest / Smallest step : 1.978034 Median interval of one step : 578/529, 153.3621 cents, amount: 3 Most common interval of one step : 578/529, 153.3621 cents, amount: 3 Least squares average step : 177.05190 cents, oct.: 1239.36328 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABCBABC Step pattern size order : LMSMLMS Scale is a Constant Structure, by a margin of 31.86237 cents Scale diversity : 1.369396 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.392501 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 : 334084/328509, 29.1336 cents Most common intervals : 23/17, 523.3189 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 277.591 676.681 cents Most common triad is 0.0 523.319 676.681 cents, amount: 3 Number of recognisable fifths : 0 Scale contains two identical disjunct tetrachords Best fifths 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 : 14283 (O: 14283 U: 14283) Highest odd numerator or denominator: 621 Scale harmonicity : 0.004413 Average absolute harmonicity : 0.155675 Specific harmonicity : 0.024568 Fundamental : 1/10557, -13.3659 octaves, 0.0248 Hz. Guide tone : 611524, 19.2220 octaves, 159990312.195 Hz. Exponens Consonantiae : 6.455859E+09, 32.58796 octaves Euler's gradus suavitatis : 123 Sum of Mann's harmonic distance : 1499.5, average 214.21429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 11.10273, average 1.58610 Sum of Tenney's harmonic distance : 23.08470, average 3.29781 Vogel's harmonic complexity : 56.14286 Wille's k value : 7141 Wilson's harmonic complexity : 129 Rectangular lattice diameter : 9 Triangular lattice diameter : 5 Lattice compactness : 85.01663, average 3.03631 Lattice compactness (without 2's) : 79.75641, average 2.84844 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 0.85714 6 1 3: -3 .. 0 -1.71429 12 17: -1 .. 2 0.28571 6 1 23: -1 .. 2 0.28571 6 5 Average exponent except 2's :-8 / 7 =-1.14286 Average absolute exponent except 2's: 24 / 7 = 3.42857 Scale is weakly epimorphic with val: <7 10 26 34| Scale is weakly epimorphic with val: <7 10 27 33| Scale is weakly epimorphic with val: <7 10 28 32| Scale is weakly epimorphic with val: <7 10 29 31| Scale is weakly epimorphic with val: <7 10 32 35| Scale is weakly epimorphic with val: <7 11 27 32| Scale is JI-epimorphic with val: <7 11 28 31| Scale is weakly epimorphic with val: <7 11 29 30| Scale is weakly epimorphic with val: <7 11 31 35| Scale is weakly epimorphic with val: <7 11 32 34| Scale is weakly epimorphic with val: <7 12 26 32| Scale is weakly epimorphic with val: <7 12 27 31| Scale is weakly epimorphic with val: <7 12 28 30| Scale is weakly epimorphic with val: <7 12 30 35| Scale is JI-epimorphic with val: <7 12 31 34| Scale is weakly epimorphic with val: <7 12 32 33|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 46.8026 c. M: 74.2997 c. Lebeng 9: 2 1 1 1 2 1 1 P M ME S SD: 10.9678 c. M:-20.9384 c. 21: 4 3 2 3 4 3 2 SP T3 SD: 9.4358 c. M: 17.1569 c. 25: 5 3 3 3 5 3 3 SP M DE S SD: 10.7146 c. M: 19.7715 c. Antiphrygian 29: 6 4 3 3 6 4 3 P SD: 10.6586 c. M:-14.7027 c. 30: 6 4 3 4 6 4 3 SP T3 SD: 3.3670 c. M: 5.7283 c. 39: 8 5 4 5 8 5 4 SP T3 SD: 0.6434 c. M:-1.1516 c. 250: 51 32 26 32 51 32 26 SP T3 SD: 0.5792 c. M: 0.9283 c. 259: 53 33 27 33 53 33 27 SP T3 SD: 0.4559 c. M: 0.8680 c. 289: 59 37 30 37 59 37 30 SP T3 SD: 0.4317 c. M: 0.7456 c. 298: 61 38 31 38 61 38 31 SP T3 SD: 0.3132 c. M: 0.6037 c. 328: 67 42 34 42 67 42 34 SP T3 SD: 0.3259 c. M: 0.6063 c. 337: 69 43 35 43 69 43 35 SP T3 SD: 0.2044 c. M: 0.4005 c. 376: 77 48 39 48 77 48 39 SP T3 SD: 0.1200 c. M: 0.2396 c. 415: 85 53 43 53 85 53 43 SP T3 SD: 0.0582 c. M: 0.1088 c. 454: 93 58 47 58 93 58 47 SP T3 SD: 0.0437 c. M:-0.0867 c. 869: 178 111 90 111 178 111 90 SP T3 SD: 0.0419 c. M:-0.0715 c. 1275: 261 163 132 163 261 163 132 SP T3 SD: 0.0415 c. M: 0.0812 c. 1284: 263 164 133 164 263 164 133 SP T3 SD: 0.0456 c. M: 0.0705 c. 1314: 269 168 136 168 269 168 136 SP T3 SD: 0.0345 c. M: 0.0662 c. 1353: 277 173 140 173 277 173 140 SP T3 SD: 0.0375 c. M:-0.0600 c. 1651: 338 211 171 211 338 211 171 SP T3 SD: 0.0449 c. M: 0.0598 c. 1690: 346 216 175 216 346 216 175 SP T3 SD: 0.0306 c. M: 0.0478 c. 1729: 354 221 179 221 354 221 179 SP T3 SD: 0.0192 c. M: 0.0371 c. 1768: 362 226 183 226 362 226 183 SP T3 SD: 0.0160 c. M: 0.0269 c. 2144: 439 274 222 274 439 274 222 SP T3 SD: 0.0169 c. M: 0.0252 c. 2183: 447 279 226 279 447 279 226 SP T3 SD: 0.0064 c. M: 0.0114 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: 15.2265 cents 4 x 5 x 6:7 x 8 S SD: 13.5935 cents 5:6 x 7 x x 9:10 SD: 27.1293 cents 6:7 x 8:9:10:11:12 S SD: 10.3680 cents 7:8:9 x 10:12:13:14 S SD: 11.9521 cents 8:9:10:11:12:14:15:16 S SD: 10.7337 cents 11:13:14:15:16:19:20:22 SD: 10.5250 cents 12:14:15:16:18:20:22:24 S SD: 9.0723 cents 13:15:16:18:19:22:24:26 SD: 8.9299 cents 14:16:18:19:21:24:26:28 SD: 6.8608 cents 19:22:24:26:28:32:35:38 SD: 5.0239 cents 20:23:25:27:30:34:37:40 SD: 4.4262 cents 27:31:34:37:40:46:50:54 SD: 3.5841 cents 31:36:39:42:46:53:58:62 SD: 2.6266 cents 34:39:43:46:50:58:63:68 SD: 2.3604 cents 46:53:58:62:68:78:86:92 SD: 1.8694 cents 51:59:64:69:75:87:95:102 SD: 1.8409 cents 54:62:68:73:80:92:101:108 SD: 1.6078 cents 65:75:82:88:96:111:121:130 SD: 0.8335 cents 105:121:132:142:155:179:195:210 SD: 0.8161 cents 111:128:140:150:164:189:207:222 SD: 0.7031 cents 124:143:156:168:183:211:231:248 SD: 0.7031 cents 131:151:165:177:194:223:244:262 SD: 0.6100 cents 138:159:174:187:204:235:257:276 SD: 0.5307 cents 159:183:200:215:235:271:296:318 SD: 0.4679 cents 165:190:208:223:244:281:307:330 SD: 0.4637 cents 182:210:229:246:269:310:339:364 SD: 0.4538 cents 190:219:239:257:281:324:354:380 SD: 0.4335 cents 196:226:247:265:290:334:365:392 SD: 0.3711 cents 209:241:263:283:309:356:389:418 SD: 0.3076 cents 243:280:306:329:359:414:452:486 SD: 0.3043 cents 274:316:345:371:405:467:510:548 SD: 0.2796 cents 289:333:364:391:427:492:538:578 SD: 0.2370 cents 301:347:379:407:445:513:560:602 SD: 0.2316 cents 320:369:403:433:473:545:596:640 SD: 0.2099 cents 354:408:446:479:523:603:659:708 SD: 0.1976 cents 374:431:471:506:553:637:696:748 SD: 0.1215 cents 439:506:553:594:649:748:817:878 SD: 0.1130 cents 544:627:685:736:804:927:1013:1088 SD: 0.1116 cents 598:689:753:809:884:1019:1113:1196 SD: 0.0962 cents