Scala analysis: xen12-chalmers-tritriadic-dm-27-21-19
Tritriadic D->M scale built from 27:21:19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/19 173.267891 2: 722/567 418.380122 3: 38/27 591.648014 4: 14/9 764.915905 septimal minor sixth 5: 98/57 938.183796 6: 38/21 1026.732109 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/19 173.2679 1: 21/19 173.2679 2: 13718/11907 245.1122 3: 21/19 173.2679 4: 21/19 173.2679 5: 21/19 173.2679 6: 361/343 88.5483 7: 21/19 173.2679
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 361/343 88.548 cents 1: 5 21/19 173.268 cents 1: 1 13718/11907 245.112 cents 2: 2 57/49 261.816 cents 2: 3 441/361 346.536 cents 2: 2 722/567 418.380 cents 3: 3 9/7 435.084 cents septimal major third, BP third 3: 1 9261/6859 519.804 cents 3: 3 38/27 591.648 cents 4: 3 27/19 608.352 cents 4: 1 13718/9261 680.196 cents 4: 3 14/9 764.916 cents septimal minor sixth 5: 2 567/361 781.620 cents 5: 3 722/441 853.464 cents 5: 2 98/57 938.184 cents 6: 1 11907/6859 954.888 cents 6: 5 38/21 1026.732 cents 6: 1 686/361 1111.452 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 : 173.3 418.4 591.6 764.9 938.2 1026.7 1200.0 173.3 : 245.1 418.4 591.6 764.9 853.5 1026.7 1200.0 418.4 : 173.3 346.5 519.8 608.4 781.6 954.9 1200.0 591.6 : 173.3 346.5 435.1 608.4 781.6 1026.7 1200.0 764.9 : 173.3 261.8 435.1 608.4 853.5 1026.7 1200.0 938.2 : 88.5 261.8 435.1 680.2 853.5 1026.7 1200.0 1026.7: 173.3 346.5 591.6 764.9 938.2 1111.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 88.5483 .. 245.1122 cents 266/243, 156.5639 cents 361/343, 88.5483 cents 2: 261.8162 .. 418.3801 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 3: 435.0841 .. 591.6480 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 4: 608.3520 .. 764.9159 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 5: 781.6199 .. 938.1838 cents 266/243, 156.5639 cents 729/722, 16.7040 cents 6: 954.8878 .. 1111.4517 cents 266/243, 156.5639 cents 729/722, 16.7040 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 361/343, 88.5483 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 13718/11907, 245.1122 cents Average / Smallest step : 1.935989 Largest / Average step : 1.429821 Largest / Smallest step : 2.768119 Median interval of one step : 21/19, 173.2679 cents, amount: 5 Most common interval of one step : 21/19, 173.2679 cents, amount: 5 Least squares average step : 179.25677 cents, oct.: 1254.79737 cents Scale is strictly proper Scale has trivalence property Step pattern alph. order: ABAAACA Step pattern size order : MLMMMSM Scale is a Constant Structure, by a margin of 16.70397 cents Scale diversity : 1.418525 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.217180 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 : 729/722, 16.7040 cents Most common intervals : 21/19, 173.2679 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 435.084 1026.732 cents Most common triad is 0.0 173.268 1026.732 cents, amount: 3 Number of recognisable fifths : 0 Scale contains a complete diamond : 19 21 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 11907 (O: 11907 U: 11907) Highest odd numerator or denominator: 567 Scale harmonicity : 0.006779 Average absolute harmonicity : 0.164808 Specific harmonicity : 0.038309 Fundamental : 1/10773, -13.3951 octaves, 0.0243 Hz. Guide tone : 106134, 16.6955 octaves, 27767367.748 Hz. Exponens Consonantiae : 1.143382E+09, 30.09066 octaves Euler's gradus suavitatis : 84 Sum of Mann's harmonic distance : 817.0, average 116.71429 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 9.53950, average 1.36279 Sum of Tenney's harmonic distance : 20.27474, average 2.89639 Vogel's harmonic complexity : 42.00000 Wille's k value : 5953 Wilson's harmonic complexity : 93 Rectangular lattice diameter : 11 Triangular lattice diameter : 7 Lattice compactness : 83.07777, average 2.96706 Lattice compactness (without 2's) : 80.17236, average 2.86330 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 1 0.85714 6 1 3: -4 .. 1 -1.42857 12 7: -1 .. 2 0.28571 6 1 19: -1 .. 2 0.28571 6 5 Average exponent except 2's :-6 / 7 =-0.85714 Average absolute exponent except 2's: 24 / 7 = 3.42857 Scale is weakly epimorphic with val: <7 10 18 32| Scale is weakly epimorphic with val: <7 10 19 31| Scale is weakly epimorphic with val: <7 10 21 29| Scale is weakly epimorphic with val: <7 10 22 28| Scale is weakly epimorphic with val: <7 11 18 30| Scale is JI-epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 21 27| Scale is weakly epimorphic with val: <7 12 18 28| Scale is weakly epimorphic with val: <7 12 19 27| Scale is weakly epimorphic with val: <7 12 20 33| Scale is JI-epimorphic with val: <7 12 21 32| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
7: 1 1 1 1 1 1 1 SP B ME I SD: 59.2042 c. M: 81.0409 c. Lebeng 8: 1 2 1 1 1 1 1 P M ME S SD: 23.3998 c. M: 38.1838 c. 13: 2 2 2 2 2 1 2 SP M ME S SD: 26.8068 c. M: 49.1494 c. Karakalian 14: 2 3 2 2 2 1 2 P T3 SD: 5.9117 c. M:-10.1913 c. 41: 6 8 6 6 6 3 6 SP T3 SD: 4.5180 c. M: 8.6240 c. 49: 7 10 7 7 7 4 7 SP T3 SD: 4.0765 c. M: 7.5716 c. 55: 8 11 8 8 8 4 8 SP T3 SD: 1.9326 c. M: 3.8347 c. 69: 10 14 10 10 10 5 10 SP T3 SD: 0.6453 c. M: 0.9888 c. 152: 22 31 22 22 22 11 22 SP T3 SD: 0.6529 c. M:-1.2899 c. 201: 29 41 29 29 29 15 29 SP T3 SD: 0.5238 c. M: 0.8704 c. 215: 31 44 31 31 31 16 31 SP T3 SD: 0.2673 c. M: 0.5094 c. 284: 41 58 41 41 41 21 41 SP T3 SD: 0.0900 c. M: 0.1556 c. 582: 84 119 84 84 84 43 84 SP T3 SD: 0.0887 c. M:-0.1766 c. 651: 94 133 94 94 94 48 94 SP T3 SD: 0.0448 c. M:-0.0651 c. 935: 135 191 135 135 135 69 135 SP T3 SD: 0.0078 c. M:-0.0156 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: 31.4805 cents 3 x 4 x x 5 x 6 S SD: 32.0479 cents 4 x 5 x 6:7 x 8 S SD: 19.2537 cents 5 x 6:7:8 x 9:10 S SD: 22.8917 cents 6:7:8 x 9:10:11:12 S SD: 24.9897 cents 7:8:9:10:11:12:13:14 H SD: 11.6554 cents 8:9:10:11:12:14 x 16 S SD: 15.3629 cents 9:10:11:13:14:15:16:18 SD: 14.9686 cents 10:11:13:14:16:17:18:20 SD: 9.3457 cents 11:12:14:15:17:19:20:22 SD: 8.7649 cents 15:17:19:21:23:26:27:30 SD: 7.7647 cents 17:19:22:24:26:29:31:34 SD: 7.0086 cents 18:20:23:25:28:31:33:36 SD: 4.8779 cents 22:24:28:31:34:38:40:44 SD: 3.9818 cents 27:30:34:38:42:46:49:54 SD: 3.8596 cents 29:32:37:41:45:50:52:58 SD: 2.7552 cents 36:40:46:51:56:62:65:72 SD: 2.3528 cents 47:52:60:66:73:81:85:94 SD: 1.1273 cents 74:82:94:104:115:127:134:148 SD: 1.0845 cents 88:97:112:124:137:151:159:176 SD: 0.9835 cents 95:105:121:134:148:163:172:190 SD: 0.8459 cents 103:114:131:145:160:177:186:206 SD: 0.7734 cents 106:117:135:149:165:182:192:212 SD: 0.6377 cents 132:146:168:186:205:227:239:264 SD: 0.5669 cents 135:149:172:190:210:232:244:270 SD: 0.4869 cents 142:157:181:200:221:244:257:284 SD: 0.3741 cents 189:209:241:266:294:325:342:378 SD: 0.3665 cents 209:231:266:294:325:359:378:418 SD: 0.3262 cents 238:263:303:335:370:409:431:476 SD: 0.2793 cents 267:295:340:376:415:459:483:534 SD: 0.2735 cents 285:315:363:401:443:490:516:570 SD: 0.2486 cents 304:336:387:428:473:523:550:608 SD: 0.2045 cents 398:440:507:560:619:684:720:796 SD: 0.1838 cents 410:453:522:577:638:705:742:820 SD: 0.1361 cents 457:505:582:643:711:786:827:914 SD: 0.1346 cents 513:567:653:722:798:882:928:1026 SD: 0.1180 cents 542:599:690:763:843:932:981:1084 SD: 0.1169 cents 560:619:713:788:871:963:1013:1120 SD: 0.1165 cents 589:651:750:829:916:1013:1066:1178 SD: 0.1110 cents 599:662:763:843:932:1030:1084:1198 SD: 0.1108 cents