Scala analysis: xen12-chalmers-tritriadic-dm-7-19-21
Tritriadic D->M 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: 21/19 173.267891 2: 361/294 355.419218 3: 19/14 528.687110 4: 3/2 701.955001 perfect fifth 5: 63/38 875.222892 6: 38/21 1026.732109 7: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/19 173.2679 1: 21/19 173.2679 2: 6859/6174 182.1513 3: 21/19 173.2679 4: 21/19 173.2679 5: 21/19 173.2679 6: 1444/1323 151.5092 7: 21/19 173.2679
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 1444/1323 151.509 cents 1: 5 21/19 173.268 cents 1: 1 6859/6174 182.151 cents 2: 2 76/63 324.777 cents 2: 3 441/361 346.536 cents 2: 2 361/294 355.419 cents 3: 3 4/3 498.045 cents perfect fourth 3: 1 9261/6859 519.804 cents 3: 3 19/14 528.687 cents 4: 3 28/19 671.313 cents 4: 1 13718/9261 680.196 cents 4: 3 3/2 701.955 cents perfect fifth 5: 2 588/361 844.581 cents 5: 3 722/441 853.464 cents 5: 2 63/38 875.223 cents 6: 1 12348/6859 1017.849 cents 6: 5 38/21 1026.732 cents 6: 1 1323/722 1048.491 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 : 173.3 355.4 528.7 702.0 875.2 1026.7 1200.0 173.3 : 182.2 355.4 528.7 702.0 853.5 1026.7 1200.0 355.4 : 173.3 346.5 519.8 671.3 844.6 1017.8 1200.0 528.7 : 173.3 346.5 498.0 671.3 844.6 1026.7 1200.0 702.0 : 173.3 324.8 498.0 671.3 853.5 1026.7 1200.0 875.2 : 151.5 324.8 498.0 680.2 853.5 1026.7 1200.0 1026.7: 173.3 346.5 528.7 702.0 875.2 1048.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 151.5092 .. 182.1513 cents 57/56, 30.6421 cents 1444/1323, 151.5092 cents 2: 324.7771 .. 355.4192 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 3: 498.0450 .. 528.6871 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 4: 671.3129 .. 701.9550 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 5: 844.5808 .. 875.2229 cents 57/56, 30.6421 cents 392/361, 142.6258 cents 6: 1017.8487 .. 1048.4908 cents 57/56, 30.6421 cents 392/361, 142.6258 cents
SHOW DATA
Number of notes : 7 -- Interval properties -- Smallest interval : 1444/1323, 151.5092 cents, class 1 Average step (divided formal octave): 171.4286 cents Largest one step interval : 6859/6174, 182.1513 cents Average / Smallest step : 1.131473 Largest / Average step : 1.062549 Largest / Smallest step : 1.202246 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 : 172.96068 cents, oct.: 1210.72474 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 142.62578 cents Scale diversity : 1.159124 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.846789 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 : 130321/129654, 8.8834 cents Most common intervals : 21/19, 173.2679 cents & inv., amount: 5 Scale is a chain of 3 triads 0.0 498.045 1026.732 cents Most common triad is 0.0 173.268 1026.732 cents, amount: 3 Number of recognisable fifths : 3, average 701.9550 cents 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 : 19 21 Formal octave complements present : 3 = 42.8571% Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited transpositions with margin 30.6421 cents: 1 6 Limited inverse transpositions with margin 30.6421 cents: 2 3 4 5 -- Rational properties -- Prime limit : 19 Odd number limit : 9261 (O: 9261 U: 9261) Highest odd numerator or denominator: 361 Scale harmonicity : 0.006985 Average absolute harmonicity : 0.195335 Specific harmonicity : 0.039313 Fundamental : 1/5586, -12.4476 octaves, 0.0468 Hz. Guide tone : 45486, 15.4731 octaves, 11900300.463 Hz. Exponens Consonantiae : 2.540848E+08, 27.92073 octaves Euler's gradus suavitatis : 81 Sum of Mann's harmonic distance : 448.0, average 64.00000 Mersenne's string divisions : 1030430280 Sum of van Prooijen's expressibility: 8.75716, average 1.25102 Sum of Tenney's harmonic distance : 17.41202, average 2.48743 Vogel's harmonic complexity : 41.00000 Wille's k value : 4630 Wilson's harmonic complexity : 87 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 73.33263, average 2.61902 Lattice compactness (without 2's) : 62.53166, average 2.23327 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.28571 6 1 3: -1 .. 2 0.28571 6 1 7: -2 .. 1 -0.28571 6 19: -1 .. 2 0.28571 6 5 Average exponent except 2's : 2 / 7 = 0.28571 Average absolute exponent except 2's: 18 / 7 = 2.57143 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 33| Scale is JI-epimorphic with val: <7 11 18 28| Scale is JI-epimorphic with val: <7 11 19 29| Scale is JI-epimorphic with val: <7 11 20 30| = patent Scale is JI-epimorphic with val: <7 11 21 31| Scale is JI-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: 1 1 1 1 1 1 1 SP B ME I SD: 11.7268 c. M: 18.0800 c. Lebeng 27: 4 4 4 4 4 3 4 SP M ME S SD: 6.8959 c. M:-13.6660 c. 34: 5 5 5 5 5 4 5 SP M ME S SD: 3.6536 c. M:-7.1300 c. 41: 6 6 6 6 6 5 6 SP M ME S SD: 2.3987 c. M: 4.1997 c. 48: 7 7 7 7 7 6 7 SP M ME S SD: 2.7473 c. M: 5.4192 c. 70: 10 11 10 10 10 9 10 SP T3 SD: 2.2977 c. M:-4.5808 c. 77: 11 12 11 11 11 10 11 SP T3 SD: 1.8501 c. M:-3.0223 c. 104: 15 16 15 15 15 13 15 SP T3 SD: 1.5138 c. M:-2.2731 c. 111: 16 17 16 16 16 14 16 SP T3 SD: 0.7382 c. M:-1.3375 c. 118: 17 18 17 17 17 15 17 SP T3 SD: 0.3898 c. M: 0.6466 c. 159: 23 24 23 23 23 20 23 SP T3 SD: 0.3604 c. M: 0.7022 c. 270: 39 41 39 39 39 34 39 SP T3 SD: 0.1890 c. M:-0.3327 c. 277: 40 42 40 40 40 35 40 SP T3 SD: 0.1211 c. M: 0.1846 c. 547: 79 83 79 79 79 69 79 SP T3 SD: 0.0490 c. M:-0.0970 c. 665: 96 101 96 96 96 84 96 SP T3 SD: 0.0372 c. M:-0.0695 c. 942: 136 143 136 136 136 119 136 SP T3 SD: 0.0325 c. M: 0.0637 c. 1212: 175 184 175 175 175 153 175 SP T3 SD: 0.0193 c. M:-0.0263 c. 1489: 215 226 215 215 215 188 215 SP T3 SD: 0.0072 c. M: 0.0129 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: 0.0000 cents 3 x x 4 x 5 x 6 S SD: 10.6583 cents 4 x 5 x 6 x 7:8 S SD: 16.4081 cents 5 x 6:7 x 8:9:10 S SD: 18.2753 cents 6 x 7:8:9:10:11:12 S SD: 16.1377 cents 7:8:9 x 11:12:13:14 SD: 24.4729 cents 8:9:10:11:12:13:14:16 S SD: 11.9202 cents 9:10:11:12:14:15:16:18 S SD: 11.1328 cents 12:13:15:16:18:20:22:24 SD: 8.6812 cents 16:18:20:22:24:27:29:32 SD: 8.2717 cents 17:19:21:23:26:28:31:34 SD: 6.3025 cents 18:20:22:24:27:30:33:36 S SD: 5.8592 cents 20:22:25:27:30:33:36:40 SD: 5.0668 cents 22:24:27:30:33:36:40:44 S SD: 4.8690 cents 26:29:32:35:39:43:47:52 SD: 3.1448 cents 30:33:37:41:45:50:54:60 SD: 2.9980 cents 36:40:44:49:54:60:65:72 SD: 2.3522 cents 47:52:58:64:71:78:85:94 SD: 2.3270 cents 48:53:59:65:72:80:87:96 SD: 1.5131 cents 56:62:69:76:84:93:101:112 SD: 1.3222 cents 58:64:71:79:87:96:105:116 SD: 1.3112 cents 76:84:93:103:114:126:138:152 SD: 1.2525 cents 78:86:96:106:117:129:141:156 SD: 1.1138 cents 84:93:103:114:126:139:152:168 SD: 0.7162 cents 106:117:130:144:159:176:192:212 SD: 0.6762 cents 114:126:140:155:171:189:206:228 SD: 0.5719 cents 132:146:162:179:198:219:239:264 SD: 0.3741 cents 190:210:233:258:285:315:344:380 SD: 0.3719 cents 210:232:258:285:315:348:380:420 SD: 0.2096 cents 246:272:302:334:369:408:445:492 SD: 0.1958 cents 342:378:420:464:513:567:619:684 SD: 0.1018 cents 456:504:560:619:684:756:825:912 SD: 0.0800 cents 588:650:722:798:882:975:1064:1176 SD: 0.0566 cents