Scala analysis: 101_E12
Enharmonic tetrachord 68/65 * 65/64 * 64/51
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 68/65 78.114034 Valentine semitone 2: 17/16 104.955410 17th harmonic 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 64/51 393.0896 1: 68/65 78.1140 Valentine semitone 2: 65/64 26.8414 13th-partial chroma 3: 64/51 393.0896
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 65/64 26.841 cents 13th-partial chroma 1: 1 68/65 78.114 cents Valentine semitone 1: 1 64/51 393.090 cents 2: 1 17/16 104.955 cents 17th harmonic 2: 1 65/51 419.931 cents 2: 1 256/195 471.204 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 0.0 : 78.1 105.0 498.0 78.1 : 26.8 419.9 498.0 105.0: 393.1 471.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.8414 .. 393.0896 cents 4096/3315, 366.2482 cents 65/64, 26.8414 cents 2: 104.9554 .. 471.2036 cents 4096/3315, 366.2482 cents 867/1024,-288.1342 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 65/64, 26.8414 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 64/51, 393.0896 cents Average / Smallest step : 6.185041 Largest / Average step : 2.367796 Largest / Smallest step : 14.644912 Median interval of one step : 68/65, 78.1140 cents, amount: 1 Least squares average step : 127.29713 cents, oct.: 381.89140 cents Scale is not proper Scale has trivalence property Step pattern alph. order: ABC Step pattern size order : MSL Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 26.84138 cents Scale diversity : 0.396830 Lumma stability : 0.107787 Lumma impropriety factor : 0.578530 Rothenberg efficiency : 0.666667 redundancy: 0.333333 Efficiency x scale size : 2.000000 Number of different interval sizes : 6 = 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 : 65/64, 26.8414 cents Number of recognisable fifths : 0 Number of recognisable fourths : 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 17 Odd number limit : 195 (O: 65 U: 195) Highest odd numerator or denominator: 65 Scale harmonicity : 0.014850 Average absolute harmonicity : 0.086692 Specific harmonicity : 0.068337 Fundamental : 1/3120, -11.6073 octaves, 0.0839 Hz. Guide tone : 68, 6.0875 octaves, 17790.538 Hz. Exponens Consonantiae : 2.121600E+05, 17.69479 octaves Euler's gradus suavitatis : 41 Sum of Mann's harmonic distance : 86.5, average 28.83333 Mersenne's string divisions : 4389 Sum of van Prooijen's expressibility: 3.52048, average 1.17349 Sum of Tenney's harmonic distance : 7.15917, average 2.38639 Vogel's harmonic complexity : 29.33333 Wille's k value : 1657 Wilson's harmonic complexity : 38 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 23.33375, average 3.88896 Lattice compactness (without 2's) : 8.56048, average 1.42675 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 2 0.00000 8 3: -1 .. 0 -0.33333 1 1 5: -1 .. 0 -0.33333 1 13: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <6 10 15 25 31| Scale is weakly epimorphic with val: <6 10 15 26 27| Scale is weakly epimorphic with val: <6 10 16 25 27| Scale is weakly epimorphic with val: <6 10 17 27 27| Scale is weakly epimorphic with val: <6 10 18 26 27| Scale is weakly epimorphic with val: <6 10 19 25 27| Scale is weakly epimorphic with val: <6 11 15 25 27| Scale is weakly epimorphic with val: <6 11 15 26 32| Scale is weakly epimorphic with val: <6 11 16 25 32| Scale is weakly epimorphic with val: <6 11 16 27 27| Scale is weakly epimorphic with val: <6 11 17 26 27| Scale is weakly epimorphic with val: <6 11 18 25 27| Scale is weakly epimorphic with val: <6 11 19 27 27| Scale is weakly epimorphic with val: <7 10 15 25 31| Scale is weakly epimorphic with val: <7 10 15 26 30| Scale is weakly epimorphic with val: <7 10 15 28 31| Scale is weakly epimorphic with val: <7 10 15 29 33| Scale is weakly epimorphic with val: <7 10 16 25 30| Scale is weakly epimorphic with val: <7 10 16 27 31| Scale is weakly epimorphic with val: <7 10 16 28 33| Scale is weakly epimorphic with val: <7 10 16 30 31| Scale is weakly epimorphic with val: <7 10 17 26 31| Scale is weakly epimorphic with val: <7 10 17 27 33| Scale is weakly epimorphic with val: <7 10 17 29 31| Scale is weakly epimorphic with val: <7 10 18 25 31| Scale is weakly epimorphic with val: <7 10 18 26 33| Scale is weakly epimorphic with val: <7 10 18 28 31| Scale is weakly epimorphic with val: <7 10 19 25 33| Scale is weakly epimorphic with val: <7 10 19 27 31| Scale is weakly epimorphic with val: <7 10 19 30 31| Scale is weakly epimorphic with val: <7 11 15 25 27| Scale is weakly epimorphic with val: <7 11 15 25 30| Scale is weakly epimorphic with val: <7 11 15 25 33| Scale is weakly epimorphic with val: <7 11 15 26 29| Scale is weakly epimorphic with val: <7 11 15 26 32| Scale is JI-epimorphic with val: <7 11 15 28 30| Scale is weakly epimorphic with val: <7 11 15 28 33| Scale is weakly epimorphic with val: <7 11 15 29 29| Scale is weakly epimorphic with val: <7 11 15 29 32| Scale is weakly epimorphic with val: <7 11 16 25 29| Scale is weakly epimorphic with val: <7 11 16 25 32| Scale is weakly epimorphic with val: <7 11 16 27 27| Scale is JI-epimorphic with val: <7 11 16 27 30| Scale is weakly epimorphic with val: <7 11 16 27 33| Scale is weakly epimorphic with val: <7 11 16 28 29| Scale is weakly epimorphic with val: <7 11 16 28 32| Scale is weakly epimorphic with val: <7 11 16 30 30| Scale is weakly epimorphic with val: <7 11 16 30 33| Scale is weakly epimorphic with val: <7 11 17 26 27| Scale is JI-epimorphic with val: <7 11 17 26 30| Scale is weakly epimorphic with val: <7 11 17 26 33| Scale is weakly epimorphic with val: <7 11 17 27 29| Scale is weakly epimorphic with val: <7 11 17 27 32| Scale is weakly epimorphic with val: <7 11 17 29 30| Scale is weakly epimorphic with val: <7 11 17 29 33| Scale is weakly epimorphic with val: <7 11 17 30 32| Scale is weakly epimorphic with val: <7 11 18 25 27| Scale is JI-epimorphic with val: <7 11 18 25 30| Scale is weakly epimorphic with val: <7 11 18 25 33| Scale is weakly epimorphic with val: <7 11 18 26 29| Scale is weakly epimorphic with val: <7 11 18 26 32| Scale is weakly epimorphic with val: <7 11 18 28 30| Scale is weakly epimorphic with val: <7 11 18 28 33| Scale is weakly epimorphic with val: <7 11 18 29 29| Scale is weakly epimorphic with val: <7 11 18 29 32| Scale is weakly epimorphic with val: <7 11 19 25 29| Scale is weakly epimorphic with val: <7 11 19 25 32| Scale is weakly epimorphic with val: <7 11 19 27 27| Scale is weakly epimorphic with val: <7 11 19 27 30| Scale is weakly epimorphic with val: <7 11 19 27 33| Scale is weakly epimorphic with val: <7 11 19 28 29| Scale is weakly epimorphic with val: <7 11 19 28 32| Scale is weakly epimorphic with val: <7 11 19 30 30| Scale is weakly epimorphic with val: <7 11 19 30 33| Scale is weakly epimorphic with val: <7 12 15 25 29| Scale is weakly epimorphic with val: <7 12 15 26 31| Scale is weakly epimorphic with val: <7 12 15 28 32| Scale is weakly epimorphic with val: <7 12 15 29 31| Scale is weakly epimorphic with val: <7 12 16 25 31| Scale is weakly epimorphic with val: <7 12 16 27 32| Scale is weakly epimorphic with val: <7 12 16 28 31| Scale is weakly epimorphic with val: <7 12 17 26 32| Scale is weakly epimorphic with val: <7 12 17 27 31| Scale is weakly epimorphic with val: <7 12 17 30 31| Scale is weakly epimorphic with val: <7 12 18 25 32| Scale is weakly epimorphic with val: <7 12 18 26 31| Scale is weakly epimorphic with val: <7 12 18 29 31| Scale is weakly epimorphic with val: <7 12 19 25 31| Scale is weakly epimorphic with val: <7 12 19 28 31| Scale is weakly epimorphic with val: <8 11 15 25 27| Scale is weakly epimorphic with val: <8 11 15 28 30| Scale is weakly epimorphic with val: <8 11 16 27 30| Scale is weakly epimorphic with val: <8 11 16 30 33| Scale is weakly epimorphic with val: <8 11 17 26 30| Scale is weakly epimorphic with val: <8 11 17 29 33| Scale is weakly epimorphic with val: <8 11 18 25 30| Scale is weakly epimorphic with val: <8 11 18 28 33| Scale is weakly epimorphic with val: <8 11 19 27 33| Scale is weakly epimorphic with val: <8 12 15 26 28| Scale is weakly epimorphic with val: <8 12 15 29 31| Scale is weakly epimorphic with val: <8 12 16 25 28| Scale is weakly epimorphic with val: <8 12 16 28 31| Scale is weakly epimorphic with val: <8 12 17 27 31| Scale is weakly epimorphic with val: <8 12 18 26 31| Scale is weakly epimorphic with val: <8 12 19 25 31|
FIT/MODE
3: 0 0 3 N M DE S SD: 75.5368 c. M: 104.9554 c. 4: 1 0 3 N G T3 SD: 29.0696 c. M:-46.3972 c. 5: 1 0 4 N G T3 SD: 12.7882 c. M:-21.4950 c. 8: 1 1 6 N M DE S SD: 14.5364 c. M:-19.5558 c. 9: 1 1 7 N M DE S SD: 13.5581 c. M: 22.7757 c. 11: 2 0 9 N G T3 SD: 10.9872 c. M: 14.4018 c. 12: 2 1 9 N T3 SD: 11.6387 c. M:-19.5558 c. 13: 2 1 10 N T3 SD: 5.8249 c. M:-9.9781 c. 14: 2 1 11 N T3 SD: 4.1487 c. M: 6.9647 c. 18: 3 1 14 N T3 SD: 4.3466 c. M:-5.7213 c. 19: 3 1 15 N T3 SD: 0.3088 c. M:-0.5247 c. 109: 17 6 86 N T3 SD: 0.2645 c. M: 0.4373 c. 128: 20 7 101 N T3 SD: 0.1797 c. M: 0.2945 c. 147: 23 8 116 N T3 SD: 0.1171 c. M: 0.1886 c. 166: 26 9 131 N T3 SD: 0.0692 c. M: 0.1070 c. 185: 29 10 146 N T3 SD: 0.0327 c. M: 0.0421 c. 204: 32 11 161 N T3 SD: 0.0155 c. M:-0.0247 c. 835: 131 45 659 N T3 SD: 0.0180 c. M:-0.0224 c. 982: 154 53 775 N T3 SD: 0.0179 c. M:-0.0296 c. 1001: 157 54 790 N T3 SD: 0.0157 c. M:-0.0271 c. 1039: 163 56 820 N T3 SD: 0.0173 c. M:-0.0223 c. 1205: 189 65 951 N T3 SD: 0.0155 c. M:-0.0267 c. 1243: 195 67 981 N T3 SD: 0.0169 c. M:-0.0227 c. 1390: 218 75 1097 N T3 SD: 0.0164 c. M:-0.0282 c. 1409: 221 76 1112 N T3 SD: 0.0154 c. M:-0.0264 c. 1447: 227 78 1142 N T3 SD: 0.0166 c. M:-0.0230 c. 1613: 253 87 1273 N T3 SD: 0.0153 c. M:-0.0262 c. 1651: 259 89 1303 N T3 SD: 0.0165 c. M:-0.0232 c. 1798: 282 97 1419 N T3 SD: 0.0158 c. M:-0.0274 c. 1817: 285 98 1434 N T3 SD: 0.0153 c. M:-0.0260 c. 1855: 291 100 1464 N T3 SD: 0.0163 c. M:-0.0233 c. 1874: 294 101 1479 N T3 SD: 0.0176 c. M:-0.0221 c. 1983: 311 107 1565 N T3 SD: 0.0165 c. M:-0.0284 c. 2021: 317 109 1595 N T3 SD: 0.0153 c. M:-0.0259 c. 2059: 323 111 1625 N T3 SD: 0.0162 c. M:-0.0235 c. 2206: 346 119 1741 N T3 SD: 0.0156 c. M:-0.0269 c. 2225: 349 120 1756 N T3 SD: 0.0153 c. M:-0.0258 c. 2283: 358 123 1802 N T3 SD: 0.0161 c. M: 0.0235 c. 2302: 361 124 1817 N T3 SD: 0.0152 c. M: 0.0241 c. 2321: 364 125 1832 N T3 SD: 0.0147 c. M: 0.0248 c. 2340: 367 126 1847 N T3 SD: 0.0147 c. M: 0.0254 c.
FIT/HARMONIC
1 x x 2 S SD: 701.9550 cents 2 x x 3 S SD: 203.9100 cents 3 x x 4 S SD: 0.0000 cents 4 x x 5 S SD: 111.7313 cents 5 x x 7 SD: 84.4672 cents 6 x 7:8 S SD: 80.9577 cents 7 x 8:9 S SD: 70.5252 cents 8 x 9:11 SD: 56.1917 cents 9 x 10:12 S SD: 38.7242 cents 10 x 11:13 SD: 37.1720 cents 11 x 12:15 S SD: 30.0020 cents 12 x 13:16 SD: 16.8086 cents 13 x 14:17 SD: 20.4634 cents 14 x 15:19 SD: 16.9472 cents 15 x 16:20 S SD: 3.3879 cents 16 x 17:21 SD: 13.6320 cents 17 x 18:23 SD: 12.9883 cents 18 x 19:24 SD: 5.6762 cents 19:20 x 25 S SD: 12.6493 cents 20:21 x 27 SD: 11.2125 cents 21:22 x 28 SD: 1.2115 cents 22:23 x 29 SD: 9.9098 cents 23:24 x 31 SD: 9.6171 cents 27:28:29:36 SD: 8.0376 cents 30:31:32:40 S SD: 7.4656 cents 33 x 35:44 SD: 1.5444 cents 34 x 36:45 S SD: 7.0579 cents 35 x 37:47 SD: 7.5566 cents 36 x 38:48 SD: 5.6762 cents 37:39 x 49 SD: 8.7664 cents 38:40 x 51 SD: 7.7955 cents 39:41 x 52 SD: 4.2329 cents 45:47:48:60 SD: 2.4479 cents 55 x 58:73 SD: 7.6070 cents 56:59:60:75 SD: 6.8229 cents 57:60:61:76 SD: 5.4721 cents 58:61:62:77 SD: 5.2785 cents 59:62:63:79 SD: 4.5675 cents 60:63:64:80 S SD: 3.0961 cents 62:65:66:83 SD: 2.8468 cents 63:66:67:84 SD: 0.9708 cents 111:116:118:148 SD: 0.6841 cents 129:135:137:172 SD: 0.3290 cents 240:251:255:320 SD: 0.1768 cents 303:317:322:404 SD: 0.1155 cents 369:386:392:492 SD: 0.1029 cents 432:452:459:576 SD: 0.0786 cents