Scala analysis: tranh3
Sa Mac Dan Tranh scale
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 17/14 336.129503 supraminor third 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 38/21 1026.732109 5: 51/28 1038.084504 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 56/51 161.9155 1: 17/14 336.1295 supraminor third 2: 56/51 161.9155 3: 9/8 203.9100 major whole tone 4: 76/63 324.7771 5: 153/152 11.3524 Ganassi's comma 6: 56/51 161.9155
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 153/152 11.352 cents Ganassi's comma 1: 2 56/51 161.915 cents 1: 1 9/8 203.910 cents major whole tone 1: 1 76/63 324.777 cents 1: 1 17/14 336.130 cents supraminor third 2: 1 21/19 173.268 cents 2: 1 17/14 336.130 cents supraminor third 2: 1 21/17 365.825 cents submajor third 2: 2 4/3 498.045 cents perfect fourth 2: 1 19/14 528.687 cents 3: 1 4/3 498.045 cents perfect fourth 3: 1 51/38 509.397 cents 3: 1 153/112 540.040 cents 3: 1 224/153 659.960 cents 3: 1 76/51 690.603 cents 3: 1 3/2 701.955 cents perfect fifth 4: 1 28/19 671.313 cents 4: 2 3/2 701.955 cents perfect fifth 4: 1 34/21 834.175 cents supraminor sixth 4: 1 28/17 863.870 cents submajor sixth 4: 1 38/21 1026.732 cents 5: 1 28/17 863.870 cents submajor sixth 5: 1 63/38 875.223 cents 5: 1 16/9 996.090 cents Pythagorean minor seventh 5: 2 51/28 1038.085 cents 5: 1 304/153 1188.648 cents Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 5.20000 = 26/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 336.1 498.0 702.0 1026.7 1038.1 1200.0 336.1 : 161.9 365.8 690.6 702.0 863.9 1200.0 498.0 : 203.9 528.7 540.0 702.0 1038.1 1200.0 702.0 : 324.8 336.1 498.0 834.2 996.1 1200.0 1026.7: 11.4 173.3 509.4 671.3 875.2 1200.0 1038.1: 161.9 498.0 660.0 863.9 1188.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 11.3524 .. 336.1295 cents 76/63, 324.7771 cents 153/152, 11.3524 cents 2: 173.2679 .. 528.6871 cents 361/294, 355.4192 cents 294/323,-162.8616 cents 3: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 56/57,-30.6421 cents 4: 671.3129 .. 1026.7321 cents 361/294, 355.4192 cents 56/57,-30.6421 cents 5: 863.8705 .. 1188.6476 cents 76/63, 324.7771 cents 294/323,-162.8616 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 153/152, 11.3524 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 17/14, 336.1295 cents Average / Smallest step : 17.617428 Largest / Average step : 1.680648 Largest / Smallest step : 29.608686 Median interval of one step : 182.91275 cents, amount: 0 Most common interval of one step : 56/51, 161.9155 cents, amount: 2 Least squares average step : 219.07072 cents, oct.: 1314.42432 cents Scale is not proper Step pattern alph. order: ABCDEB Step pattern size order : EBCDAB Scale is not a Constant Structure Scale diversity : 1.344004 Lumma stability : 0.018921 Lumma impropriety factor : 0.322506 Rothenberg efficiency : 0.427778 redundancy: 0.572222 Efficiency x scale size : 2.566667 Number of different interval sizes : 22 = 4.40000 / class Number of one step interval sizes : 5 Highest interval variety : 6 Mean interval variety : 5.20000 = 26/5 Median interval variety : 5 Lowest interval variety : 5 Smallest interval difference : 153/152, 11.3524 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 3 Number of recognisable fifths : 4, average 699.1169 cents Scale contains a complete diamond : 1 3 Formal octave complements present : 3 = 50.0000% -- Rational properties -- Prime limit : 19 Odd number limit : 153 (O: 153 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.011927 Average absolute harmonicity : 0.259026 Specific harmonicity : 0.068191 Fundamental : 1/84, -6.3923 octaves, 3.1146 Hz. Guide tone : 3876, 11.9204 octaves, 1014060.691 Hz. Exponens Consonantiae : 3.255840E+05, 18.31267 octaves Euler's gradus suavitatis : 49 Sum of Mann's harmonic distance : 92.0, average 15.33333 Mersenne's string divisions : 15171555 Sum of van Prooijen's expressibility: 5.21448, average 0.86908 Sum of Tenney's harmonic distance : 10.59167, average 1.76528 Vogel's harmonic complexity : 17.33333 Wille's k value : 76 Wilson's harmonic complexity : 49 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 50.37545, average 2.39883 Lattice compactness (without 2's) : 32.12968, average 1.52998 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -2 .. 2 0.00000 8 1 3: -1 .. 1 0.00000 4 2 7: -1 .. 0 -0.50000 3 17: 0 .. 1 0.33333 2 2 19: 0 .. 1 0.16667 1 1 Average exponent except 2's : 0 / 6 = 0.00000 Average absolute exponent except 2's: 10 / 6 = 1.66667 Scale is weakly epimorphic with val: <6 10 15 24 24| Scale is weakly epimorphic with val: <6 10 15 26 26| Scale is weakly epimorphic with val: <6 10 16 25 25| Scale is weakly epimorphic with val: <6 10 16 27 27| Scale is weakly epimorphic with val: <6 10 17 24 24| Scale is weakly epimorphic with val: <6 10 17 26 26| Scale is weakly epimorphic with val: <6 10 18 25 25| Scale is weakly epimorphic with val: <6 10 18 27 27| Scale is weakly epimorphic with val: <6 10 19 24 24| Scale is weakly epimorphic with val: <6 10 19 26 26| Scale is weakly epimorphic with val: <6 11 15 24 24| Scale is weakly epimorphic with val: <6 11 16 25 25| Scale is weakly epimorphic with val: <6 11 17 26 26| Scale is weakly epimorphic with val: <6 11 18 27 27| Scale is weakly epimorphic with val: <6 11 19 23 26|
FIT/MODE
6: 2 0 2 1 0 1 N T3 SD: 65.1538 c. M: 98.0450 c. 7: 2 1 1 2 0 1 N D3 SD: 10.5409 c. M:-16.2407 c. 22: 6 3 4 6 0 3 N SD: 6.7825 c. M:-9.6315 c. 29: 8 4 5 8 0 4 N SD: 4.1526 c. M:-7.7506 c. 36: 10 5 6 10 0 5 N SD: 3.6881 c. M:-6.6012 c. 43: 12 6 7 12 0 6 N SD: 4.1369 c. M:-5.8260 c. 53: 15 7 9 14 1 7 N SD: 3.7812 c. M: 7.8642 c. 60: 17 8 10 16 1 8 N SD: 3.4548 c. M: 6.7321 c. 68: 19 9 12 18 1 9 N SD: 2.9258 c. M:-3.9274 c. 75: 21 10 13 20 1 10 N SD: 1.8034 c. M: 2.7321 c. 82: 23 11 14 22 1 11 N SD: 1.0835 c. M: 2.3419 c. 89: 25 12 15 24 1 12 N SD: 1.0287 c. M: 2.0130 c. 96: 27 13 16 26 1 13 N SD: 1.4642 c. M: 1.9550 c. 104: 29 14 18 28 1 14 N SD: 1.2665 c. M:-1.8912 c. 111: 31 15 19 30 1 15 N SD: 0.6130 c. M: 0.9944 c. 118: 33 16 20 32 1 16 N SD: 0.4484 c. M: 0.7964 c. 200: 56 27 34 54 2 27 N SD: 0.3066 c. M: 0.7321 c. 207: 58 28 35 56 2 28 N SD: 0.4284 c. M: 0.6452 c. 229: 64 31 39 62 2 31 N SD: 0.4237 c. M: 0.7583 c. 311: 87 42 53 84 3 42 N SD: 0.2946 c. M: 0.4382 c. 318: 89 43 54 86 3 43 N SD: 0.2273 c. M: 0.3487 c. 735: 206 99 125 199 7 99 N SD: 0.1714 c. M:-0.2828 c. 742: 208 100 126 201 7 100 N SD: 0.1642 c. M:-0.2586 c. 824: 231 111 140 223 8 111 N SD: 0.1576 c. M:-0.2783 c. 846: 237 114 144 229 8 114 N SD: 0.1604 c. M:-0.2182 c. 853: 239 115 145 231 8 115 N SD: 0.1179 c. M:-0.2315 c. 935: 262 126 159 253 9 126 N SD: 0.1079 c. M:-0.2043 c. 942: 264 127 160 255 9 127 N SD: 0.0938 c. M:-0.1762 c. 1046: 293 141 178 283 10 141 N SD: 0.1079 c. M:-0.1564 c. 1053: 295 142 179 285 10 142 N SD: 0.0528 c. M:-0.0921 c. 1171: 328 158 199 317 11 158 N SD: 0.0342 c. M:-0.0826 c. 1253: 351 169 213 339 12 169 N SD: 0.0477 c. M: 0.0761 c. 1260: 353 170 214 341 12 170 N SD: 0.0468 c. M: 0.0654 c. 1371: 384 185 233 371 13 185 N SD: 0.0201 c. M: 0.0363 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x 3 x x 4 S SD: 0.0000 cents 3 x 4 x 5 x 6 S SD: 47.4578 cents 4:5 x 6:7 x 8 S SD: 19.1566 cents 5:6:7:8:9 x 10 S SD: 28.3703 cents 6:7:8:9 x 11:12 SD: 14.0342 cents 7 x 9:11 x 13:14 SD: 26.9031 cents 8:10:11:12:14:15:16 S SD: 17.6604 cents 9:11:12:14:16 x 18 SD: 14.1848 cents 10:12:13:15:18 x 20 SD: 9.8476 cents 11:13:15:17 x 20:22 SD: 15.9947 cents 12:15:16:18 x 22:24 SD: 10.2872 cents 13:16:17:20 x 24:26 SD: 12.8702 cents 14:17:19:21:25:26:28 SD: 8.4900 cents 15:18:20:23:27 x 30 SD: 8.8342 cents 16:19:21:24:29 x 32 SD: 9.4713 cents 17:21:23:26 x 31:34 SD: 10.3048 cents 18:22:24:27 x 33:36 SD: 3.1900 cents 20:24:27:30:36 x 40 S SD: 6.2153 cents 21:26:28:32:38 x 42 SD: 8.6567 cents 22:27:29:33 x 40:44 SD: 5.4414 cents 23:28:31:35 x 42:46 SD: 6.3559 cents 24:29:32:36:43:44:48 SD: 3.7057 cents 26:32:35:39:47 x 52 SD: 5.7356 cents 27:33:36:41:49 x 54 SD: 4.9153 cents 28:34:37:42 x 51:56 SD: 3.1054 cents 31:38:41:47:56 x 62 SD: 5.7106 cents 32:39:43:48:58 x 64 SD: 3.0330 cents 33:40:44:50 x 60:66 SD: 3.5879 cents 34:41:45:51 x 62:68 SD: 3.5314 cents 36:44:48:54:65:66:72 SD: 2.7328 cents 37:45:49:56:67 x 74 SD: 3.9392 cents 38:46:51:57 x 69:76 SD: 2.7314 cents 39:47:52:59 x 71:78 SD: 3.9477 cents 40:49:53:60:72:73:80 SD: 3.5122 cents 41:50:55:62:74:75:82 SD: 3.4867 cents 42:51:56:63:76:77:84 SD: 1.8797 cents 43:52:57:65:78 x 86 SD: 3.7375 cents 44:53:59:66 x 80:88 SD: 3.4650 cents 45:55:60:68:81:82:90 SD: 3.2252 cents 46:56:61:69:83:84:92 SD: 2.0596 cents 48:58:64:72:87 x 96 SD: 1.7941 cents 49:60:65:74 x 89:98 SD: 4.2410 cents 50:61:67:75:90:91:100 SD: 2.5051 cents 51:62:68:77:92:93:102 SD: 2.1343 cents 52:63:69:78:94:95:104 SD: 1.7893 cents 54:66:72:81:98 x 108 SD: 2.4719 cents 55:67:73:83 x 100:110 SD: 2.9116 cents 56:68:75:84:101:102:112 SD: 1.5987 cents 59:72:79:89:107 x 118 SD: 3.0835 cents 60:73:80:90 x 109:120 SD: 1.1321 cents 65:79:87:98:118 x 130 SD: 2.5010 cents 66:80:88:99:119:120:132 SD: 1.2673 cents 74:90:99:111:134:135:148 SD: 1.1871 cents 76:92:101:114 x 138:152 SD: 1.8992 cents 78:95:104:117:141:142:156 SD: 0.9283 cents 84:102:112:126:152:153:168 SD: 0.0000 cents