Scala analysis: xen12-chalmers-tritriadic-mt-7-19-21
Tritriadic M->T scale built from 7:19:21
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 57/56 30.642111 Hendrix comma 2: 21/19 173.267891 3: 19/14 528.687110 4: 28/19 671.312890 5: 3/2 701.955001 perfect fifth 6: 361/196 1057.374219 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 392/361 142.6258 1: 57/56 30.6421 Hendrix comma 2: 392/361 142.6258 3: 361/294 355.4192 4: 392/361 142.6258 5: 57/56 30.6421 Hendrix comma 6: 361/294 355.4192 7: 392/361 142.6258
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 57/56 30.642 cents Hendrix comma 1: 3 392/361 142.626 cents 1: 2 361/294 355.419 cents 2: 3 21/19 173.268 cents 2: 1 6859/5488 386.061 cents 2: 3 4/3 498.045 cents perfect fourth 3: 1 8232/6859 315.894 cents 3: 5 19/14 528.687 cents 3: 1 1568/1083 640.671 cents 4: 1 1083/784 559.329 cents 4: 5 28/19 671.313 cents 4: 1 6859/4116 884.106 cents 5: 3 3/2 701.955 cents perfect fifth 5: 1 10976/6859 813.939 cents 5: 3 38/21 1026.732 cents 6: 2 588/361 844.581 cents 6: 3 361/196 1057.374 cents 6: 2 112/57 1169.358 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 : 30.6 173.3 528.7 671.3 702.0 1057.4 1200.0 30.6 : 142.6 498.0 640.7 671.3 1026.7 1169.4 1200.0 173.3 : 355.4 498.0 528.7 884.1 1026.7 1057.4 1200.0 528.7 : 142.6 173.3 528.7 671.3 702.0 844.6 1200.0 671.3 : 30.6 386.1 528.7 559.3 702.0 1057.4 1200.0 702.0 : 355.4 498.0 528.7 671.3 1026.7 1169.4 1200.0 1057.4: 142.6 173.3 315.9 671.3 813.9 844.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 30.6421 .. 355.4192 cents 76/63, 324.7771 cents 57/56, 30.6421 cents 2: 173.2679 .. 498.0450 cents 76/63, 324.7771 cents 6174/6859,-182.1513 cents 3: 315.8937 .. 640.6708 cents 76/63, 324.7771 cents 6174/6859,-182.1513 cents 4: 559.3292 .. 884.1063 cents 76/63, 324.7771 cents 1172889/1229312,-81.3416 cents 5: 701.9550 .. 1026.7321 cents 76/63, 324.7771 cents 6174/6859,-182.1513 cents 6: 844.5808 .. 1169.3579 cents 76/63, 324.7771 cents 6174/6859,-182.1513 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 57/56, 30.6421 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 361/294, 355.4192 cents Average / Smallest step : 5.594542 Largest / Average step : 2.073279 Largest / Smallest step : 11.599045 Median interval of one step : 392/361, 142.6258 cents, amount: 3 Most common interval of one step : 392/361, 142.6258 cents, amount: 3 Least squares average step : 163.58937 cents, oct.: 1145.12556 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABCBACB Step pattern size order : SMLMSLM Scale is a Constant Structure, by a margin of 30.64211 cents Scale diversity : 1.321817 Lumma stability : 0.051070 Lumma impropriety factor : 0.609080 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 : 57/56, 30.6421 cents Most common intervals : 19/14, 528.6871 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 173.268 671.313 cents Most common triad is 0.0 528.687 671.313 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Scale contains a complete diamond : 7 19 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 3 = 42.8571% -- Rational properties -- Prime limit : 19 Odd number limit : 6859 (O: 6859 U: 6859) Highest odd numerator or denominator: 361 Scale harmonicity : 0.007100 Average absolute harmonicity : 0.195508 Specific harmonicity : 0.039917 Fundamental : 1/7448, -12.8626 octaves, 0.0351 Hz. Guide tone : 30324, 14.8882 octaves, 7933533.642 Hz. Exponens Consonantiae : 2.258532E+08, 27.75081 octaves Euler's gradus suavitatis : 80 Sum of Mann's harmonic distance : 399.0, average 57.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 8.67023, average 1.23860 Sum of Tenney's harmonic distance : 17.18477, average 2.45497 Vogel's harmonic complexity : 40.14286 Wille's k value : 3790 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 7 Triangular lattice diameter : 4 Lattice compactness : 80.76600, average 2.88450 Lattice compactness (without 2's) : 54.93910, average 1.96211 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 2 -0.57143 10 1 3: 0 .. 1 0.42857 3 1 7: -2 .. 1 -0.28571 6 19: -1 .. 2 0.28571 6 5 Average exponent except 2's : 3 / 7 = 0.42857 Average absolute exponent except 2's: 15 / 7 = 2.14286 Scale is weakly epimorphic with val: <7 10 18 31| Scale is weakly epimorphic with val: <7 10 19 32| Scale is weakly epimorphic with val: <7 10 20 33| Scale is weakly epimorphic with val: <7 10 21 27| Scale is weakly epimorphic with val: <7 10 22 28| Scale is weakly epimorphic with val: <7 11 18 33| Scale is weakly epimorphic with val: <7 11 19 27| Scale is weakly epimorphic with val: <7 11 20 28| Scale is weakly epimorphic with val: <7 11 21 29| Scale is weakly epimorphic with val: <7 11 22 30| Scale is JI-epimorphic with val: <7 12 18 28| Scale is JI-epimorphic with val: <7 12 19 29| Scale is JI-epimorphic with val: <7 12 20 30| Scale is JI-epimorphic with val: <7 12 21 31| Scale is JI-epimorphic with val: <7 12 22 32|
FIT/MODE
7: 0 1 2 1 0 2 1 N T3 SD: 18.7101 c. M: 30.6421 c. 16: 0 2 5 2 0 5 2 N T3 SD: 18.0811 c. M: 30.6421 c. 20: 1 2 6 2 1 6 2 N T3 SD: 16.9061 c. M:-29.3579 c. 23: 0 3 7 3 0 7 3 N T3 SD: 17.1981 c. M: 30.6421 c. 24: 1 2 8 2 1 7 3 N SD: 16.4004 c. M: 23.2679 c. 25: 1 3 7 3 1 7 3 N T3 SD: 11.8360 c. M:-18.7321 c. 27: 1 3 8 3 1 8 3 N T3 SD: 7.7846 c. M:-13.8023 c. 34: 1 4 10 4 1 10 4 N T3 SD: 2.6852 c. M:-4.6520 c. 41: 1 5 12 5 1 12 5 N T3 SD: 2.0112 c. M: 3.7157 c. 75: 2 9 22 9 2 22 9 N T3 SD: 1.5270 c. M:-2.7321 c. 77: 2 9 23 9 2 23 9 N T3 SD: 1.3357 c. M:-2.3660 c. 84: 2 10 25 10 2 25 10 N T3 SD: 1.2858 c. M: 2.0707 c. 111: 3 13 33 13 3 33 13 N T3 SD: 1.2174 c. M:-2.0852 c. 118: 3 14 35 14 3 35 14 N T3 SD: 0.2174 c. M: 0.3865 c. 277: 7 33 82 33 7 82 33 N T3 SD: 0.2040 c. M: 0.3345 c. 388: 10 46 115 46 10 115 46 N T3 SD: 0.2036 c. M:-0.3577 c. 395: 10 47 117 47 10 117 47 N T3 SD: 0.1468 c. M: 0.2624 c. 429: 11 51 127 51 11 127 51 N T3 SD: 0.0951 c. M:-0.1587 c. 547: 14 65 162 65 14 162 65 N T3 SD: 0.0400 c. M:-0.0709 c. 665: 17 79 197 79 17 197 79 N T3 SD: 0.0371 c. M:-0.0694 c. 942: 24 112 279 112 24 279 112 N T3 SD: 0.0392 c. M: 0.0689 c. 1212: 31 144 359 144 31 359 144 N T3 SD: 0.0321 c. M:-0.0515 c. 1371: 35 163 406 163 35 406 163 N T3 SD: 0.0252 c. M: 0.0438 c. 1489: 38 177 441 177 38 441 177 N T3 SD: 0.0119 c. M: 0.0203 c. 2036: 52 242 603 242 52 603 242 N T3 SD: 0.0073 c. M:-0.0131 c. 2154: 55 256 638 256 55 638 256 N T3 SD: 0.0052 c. M: 0.0088 c.
FIT/HARMONIC
1 x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x 4 S SD: 0.0000 cents 3 x x 4 x x x 6 S SD: 15.3211 cents 4 x x 5 x 6:7:8 S SD: 41.9158 cents 5 x 6:7 x 8:9:10 S SD: 38.5920 cents 6 x 7:8 x 9:11:12 SD: 19.7632 cents 7 x 8 x 10:11:13:14 SD: 22.7524 cents 8 x 9:11 x 12:15:16 SD: 9.8093 cents 9 x 10:12:13:14:17:18 SD: 14.9976 cents 10 x 11:14 x 15:18:20 SD: 13.4873 cents 11 x 12:15:16:17:20:22 SD: 10.8838 cents 12 x 13:16 x 18:22:24 SD: 9.3955 cents 13 x 14:18:19:20:24:26 SD: 12.2121 cents 14 x 15:19 x 21:26:28 SD: 11.1399 cents 15 x 17:20:22:23:28:30 SD: 11.6401 cents 16 x 18:22 x 24:29:32 SD: 9.4314 cents 18:19:20:24 x 27:33:36 SD: 11.8447 cents 19:20:21:26:28:29:35:38 SD: 9.5771 cents 20:21:22:27:29:30:37:40 SD: 8.9149 cents 22:23:24:30:32:33:41:44 SD: 8.6338 cents 24:25:27:33:35:36:44:48 SD: 8.3865 cents 25:26:28:34:37:38:46:50 SD: 7.1583 cents 26:27:29:35:38:39:48:52 SD: 6.1820 cents 28:29:31:38:41:42:52:56 SD: 5.0370 cents 30:31:33:41:44:45:55:60 SD: 4.5844 cents 34:35:38:46:50:51:63:68 SD: 4.2961 cents 36:37:40:49:53:54:66:72 SD: 3.0577 cents 38:39:42:52:56:57:70:76 SD: 2.8948 cents 40:41:44:54:59:60:74:80 SD: 2.7080 cents 44:45:49:60:65:66:81:88 SD: 2.5785 cents 46:47:51:62:68:69:85:92 SD: 2.3685 cents 48:49:53:65:71:72:88:96 SD: 1.7406 cents 56:57:62:76:83:84:103:112 SD: 1.5158 cents 64:65:71:87:94:96:118:128 SD: 1.4344 cents 68:69:75:92:100:102:125:136 SD: 1.3970 cents 76:77:84:103:112:114:140:152 SD: 1.1952 cents 95:97:105:129:140:143:175:190 SD: 1.1711 cents 103:105:114:140:152:155:190:206 SD: 1.1420 cents 104:106:115:141:153:156:192:208 SD: 0.8383 cents 106:108:117:144:156:159:195:212 SD: 0.6569 cents 112:114:124:152:165:168:206:224 SD: 0.5480 cents 114:116:126:155:168:171:210:228 SD: 0.4640 cents 182:185:201:247:268:273:335:364 SD: 0.4604 cents 216:220:239:293:318:324:398:432 SD: 0.4303 cents 218:222:241:296:321:327:402:436 SD: 0.3996 cents 226:230:250:307:333:339:416:452 SD: 0.3499 cents 230:234:254:312:339:345:424:460 SD: 0.3430 cents 266:271:294:361:392:399:490:532 SD: 0.2311 cents 334:340:369:453:492:501:615:668 SD: 0.2286 cents 342:348:378:464:504:513:630:684 SD: 0.1135 cents 456:464:504:619:672:684:840:912 SD: 0.1018 cents