Scala analysis: xen12-chalmers-tritriadic-mt-17-21-7
Tritriadic M->T scale built from 17:21:7
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 294/289 29.695995 2: 21/17 365.825498 submajor third 3: 4/3 498.044999 perfect fourth 4: 441/289 731.650996 two (submajor third) 5: 34/21 834.174502 supraminor sixth 6: 28/17 863.870497 submajor sixth 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 17/14 336.1295 supraminor third 1: 294/289 29.6960 2: 17/14 336.1295 supraminor third 3: 68/63 132.2195 supraminor second 4: 1323/1156 233.6060 5: 9826/9261 102.5235 6: 294/289 29.6960 7: 17/14 336.1295 supraminor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 294/289 29.696 cents 1: 1 9826/9261 102.524 cents 1: 1 68/63 132.220 cents supraminor second 1: 1 1323/1156 233.606 cents 1: 2 17/14 336.130 cents supraminor third 2: 1 68/63 132.220 cents supraminor second 2: 1 17/14 336.130 cents supraminor third 2: 4 21/17 365.825 cents submajor third 2: 1 578/441 468.349 cents 3: 1 21/17 365.825 cents submajor third 3: 1 6174/4913 395.521 cents 3: 2 578/441 468.349 cents 3: 1 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 4: 2 4/3 498.045 cents perfect fourth 4: 1 3/2 701.955 cents perfect fifth 4: 2 441/289 731.651 cents two (submajor third) 4: 1 4913/3087 804.479 cents 4: 1 34/21 834.175 cents supraminor sixth 5: 1 441/289 731.651 cents two (submajor third) 5: 4 34/21 834.175 cents supraminor sixth 5: 1 28/17 863.870 cents submajor sixth 5: 1 63/34 1067.780 cents submajor seventh 6: 2 28/17 863.870 cents submajor sixth 6: 1 2312/1323 966.394 cents 6: 1 63/34 1067.780 cents submajor seventh 6: 1 9261/4913 1097.476 cents 6: 2 289/147 1170.304 cents Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 0.0 : 29.7 365.8 498.0 731.7 834.2 863.9 1200.0 29.7 : 336.1 468.3 702.0 804.5 834.2 1170.3 1200.0 365.8 : 132.2 365.8 468.3 498.0 834.2 863.9 1200.0 498.0 : 233.6 336.1 365.8 702.0 731.7 1067.8 1200.0 731.7 : 102.5 132.2 468.3 498.0 834.2 966.4 1200.0 834.2 : 29.7 365.8 395.5 731.7 863.9 1097.5 1200.0 863.9 : 336.1 365.8 702.0 834.2 1067.8 1170.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 29.6960 .. 336.1295 cents 4913/4116, 306.4335 cents 294/289, 29.6960 cents 2: 132.2195 .. 468.3490 cents 17/14, 336.1295 cents 8/9,-203.9100 cents 3: 365.8255 .. 701.9550 cents 17/14, 336.1295 cents 9261/9826,-102.5235 cents 4: 498.0450 .. 834.1745 cents 17/14, 336.1295 cents 8/9,-203.9100 cents 5: 731.6510 .. 1067.7805 cents 17/14, 336.1295 cents 9261/9826,-102.5235 cents 6: 863.8705 .. 1170.3040 cents 4913/4116, 306.4335 cents 8/9,-203.9100 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 294/289, 29.6960 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 5.772784 Largest / Average step : 1.960755 Largest / Smallest step : 11.319018 Median interval of one step : 68/63, 132.2195 cents, amount: 1 Least squares average step : 163.82987 cents, oct.: 1146.80907 cents Scale is not proper Scale is a mode of a 2142-tone equal temperament with octave 2/1 degrees: 53 653 889 1306 1489 1542 2142 Least number of segments generator : 1073 of 601.120 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1403 of 785.994 cents and inv. generated superset size: 94 = 87 more = 1342.857% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABCDEAB Step pattern size order : AECDBAE Scale is not a Constant Structure Scale diversity : 1.306996 Lumma stability : 0.049493 Lumma impropriety factor : 0.680648 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 : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 294/289, 29.6960 cents Most common intervals : 21/17, 365.8255 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 834.175 cents Most common triad is 0.0 365.825 834.175 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents Scale contains a complete diamond : 17 21 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 17 Odd number limit : 9261 (O: 9261 U: 9261) Highest odd numerator or denominator: 441 Scale harmonicity : 0.007621 Average absolute harmonicity : 0.186746 Specific harmonicity : 0.041781 Fundamental : 1/6069, -12.5672 octaves, 0.0431 Hz. Guide tone : 29988, 14.8721 octaves, 7845627.452 Hz. Exponens Consonantiae : 1.819972E+08, 27.43934 octaves Euler's gradus suavitatis : 75 Sum of Mann's harmonic distance : 730.5, average 104.35714 Mersenne's string divisions : 509431230 Sum of van Prooijen's expressibility: 9.45735, average 1.35105 Sum of Tenney's harmonic distance : 19.49877, average 2.78554 Vogel's harmonic complexity : 38.71429 Wille's k value : 4630 Wilson's harmonic complexity : 81 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 73.36877, average 2.62031 Lattice compactness (without 2's) : 63.54627, average 2.26951 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 0 .. 2 1.00000 7 1 3: -1 .. 2 0.28571 6 1 7: -1 .. 2 0.71429 7 17: -2 .. 1 -0.71429 7 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 20 / 7 = 2.85714 Scale is weakly epimorphic with val: <7 10 18 29| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 10 20 31| Scale is weakly epimorphic with val: <7 10 21 32| Scale is weakly epimorphic with val: <7 10 22 26| Scale is weakly epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 11 19 29| Scale is weakly epimorphic with val: <7 11 20 30| Scale is weakly epimorphic with val: <7 11 21 31| Scale is weakly epimorphic with val: <7 11 22 32| Scale is weakly epimorphic with val: <7 12 18 27| Scale is weakly epimorphic with val: <7 12 19 28| Scale is weakly epimorphic with val: <7 12 20 29| Scale is weakly epimorphic with val: <7 12 21 30| Scale is weakly epimorphic with val: <7 12 22 31|
FIT/MODE
7: 0 2 1 1 1 0 2 N T3 SD: 24.9461 c. M: 45.9367 c. 10: 0 3 1 2 1 0 3 N SD: 16.8222 c. M: 29.6960 c. 23: 1 6 3 4 2 1 6 N SD: 15.1273 c. M:-23.6941 c. 26: 1 7 3 5 2 1 7 N SD: 9.2881 c. M:-16.4579 c. 29: 1 8 3 6 2 1 8 N SD: 7.7931 c. M:-13.1766 c. 33: 1 9 4 6 3 1 9 N SD: 6.2526 c. M:-11.0459 c. 36: 1 10 4 7 3 1 10 N SD: 2.0395 c. M:-3.6373 c. 46: 1 13 5 9 4 1 13 N SD: 2.0693 c. M: 3.6090 c. 79: 2 22 9 15 7 2 22 N SD: 1.8635 c. M:-3.2208 c. 82: 2 23 9 16 7 2 23 N SD: 0.2999 c. M: 0.4840 c. 200: 5 56 22 39 17 5 56 N SD: 0.2049 c. M:-0.3490 c. 282: 7 79 31 55 24 7 79 N SD: 0.1436 c. M:-0.2639 c. 364: 9 102 40 71 31 9 102 N SD: 0.1456 c. M: 0.2428 c. 525: 13 147 58 102 45 13 147 N SD: 0.1460 c. M:-0.2407 c. 607: 15 170 67 118 52 15 170 N SD: 0.1041 c. M: 0.1848 c. 689: 17 193 76 134 59 17 193 N SD: 0.0837 c. M: 0.1561 c. 725: 18 203 80 141 62 18 203 N SD: 0.0916 c. M:-0.1619 c. 771: 19 216 85 150 66 19 216 N SD: 0.0806 c. M: 0.1335 c. 807: 20 226 89 157 69 20 226 N SD: 0.0537 c. M:-0.0963 c. 889: 22 249 98 173 76 22 249 N SD: 0.0267 c. M:-0.0427 c. 971: 24 272 107 189 83 24 272 N SD: 0.0220 c. M: 0.0359 c. 1171: 29 328 129 228 100 29 328 N SD: 0.0173 c. M:-0.0313 c. 2060: 51 577 227 401 176 51 577 N SD: 0.0085 c. M:-0.0133 c. 2142: 53 600 236 417 183 53 600 N SD: 0.0034 c. M: 0.0058 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: 14.8480 cents 3 x x 4 x x 5:6 S SD: 6.8294 cents 4 x 5 x 6 x 7:8 S SD: 27.7458 cents 5 x 6:7 x 8 x 10 S SD: 25.0910 cents 6 x 7:8:9 x 10:12 S SD: 21.0653 cents 7 x x 9:11 x 12:14 SD: 26.6290 cents 8 x 10:11:12:13 x 16 SD: 12.9306 cents 9:10:11:12:14 x 15:18 S SD: 26.4497 cents 10:11:12:13:15:16 x 20 SD: 25.8465 cents 11:12:14:15:17 x 18:22 SD: 23.2272 cents 12:13:15:16:18:19:20:24 SD: 17.5352 cents 13:14:16:17:20:21 x 26 SD: 17.5658 cents 14:15:17:19:21 x 23:28 SD: 17.3018 cents 15:16:19:20:23:24:25:30 SD: 13.9418 cents 16:17:20:21:24:26 x 32 SD: 14.6717 cents 17:18:21:23:26 x 28:34 SD: 12.3050 cents 18:19:22:24:27:29:30:36 SD: 10.8771 cents 19:20:23:25:29:31 x 38 SD: 12.2780 cents 20:21:25:27:31:32:33:40 SD: 10.1462 cents 21:22:26:28:32:34:35:42 SD: 7.8583 cents 22:23:27:29:34 x 36:44 SD: 9.6650 cents 23:24:28:31:35:37:38:46 SD: 7.9524 cents 24:25:30:32:37:39:40:48 SD: 7.6580 cents 25:26:31:33:38:40:41:50 SD: 6.8905 cents 26:27:32:35:40:42:43:52 SD: 6.1462 cents 27:28:33:36:41:44 x 54 SD: 6.7586 cents 28:29:35:37:43:45:46:56 SD: 6.2759 cents 29:30:36:39:44:47:48:58 SD: 5.1659 cents 30:31:37:40:46 x 49:60 SD: 5.3231 cents 31:32:38:41:47:50:51:62 SD: 4.9187 cents 33:34:41:44:50:53:54:66 SD: 4.6412 cents 34:35:42:45:52:55:56:68 SD: 3.5011 cents 39:40:48:52:60:63:64:78 SD: 3.1806 cents 42:43:52:56:64:68:69:84 SD: 1.8224 cents 51:52:63:68:78:83:84:102 SD: 1.5056 cents 60:61:74:80:92:97:99:120 SD: 1.3892 cents 63:64:78:84:96:102:104:126 SD: 0.9322 cents 102:104:126:136:156:165:168:204 SD: 0.8206 cents 105:107:130:140:160:170:173:210 SD: 0.7884 cents 110:112:136:147:168:178:181:220 SD: 0.7268 cents 114:116:141:152:174:185:188:228 SD: 0.7265 cents 123:125:152:164:188:199:203:246 SD: 0.7220 cents 158:161:195:211:241:256:260:316 SD: 0.6821 cents 162:165:200:216:247:262:267:324 SD: 0.4998 cents 165:168:204:220:252:267:272:330 SD: 0.4480 cents 171:174:211:228:261:277:282:342 SD: 0.4418 cents 213:217:263:284:325:345:351:426 SD: 0.4094 cents 221:225:273:295:337:358:364:442 SD: 0.4037 cents 226:230:279:301:345:366:372:452 SD: 0.3830 cents 234:238:289:312:357:379:385:468 SD: 0.2936 cents 289:294:357:385:441:468:476:578 SD: 0.2199 cents 297:302:367:396:453:481:489:594 SD: 0.2129 cents 357:363:441:476:545:578:588:714 SD: 0.1608 cents 399:406:493:532:609:646:657:798 SD: 0.1219 cents 519:528:641:692:792:840:855:1038 SD: 0.1092 cents