Scala analysis: 011_H3
Hyperenharmonic tetrachord 102/101 * 101/99 * 22/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 102/101 17.056631 2: 34/33 51.682466 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/17 446.3625 1: 102/101 17.0566 2: 101/99 34.6258 3: 22/17 446.3625
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 102/101 17.057 cents 1: 1 101/99 34.626 cents 1: 1 22/17 446.363 cents 2: 1 34/33 51.682 cents 2: 1 132/101 463.419 cents 2: 1 202/153 480.988 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 : 17.1 51.7 498.0 17.1 : 34.6 481.0 498.0 51.7 : 446.4 463.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.0566 .. 446.3625 cents 1111/867, 429.3059 cents 102/101, 17.0566 cents 2: 51.6825 .. 480.9884 cents 1111/867, 429.3059 cents 289/363,-394.6801 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 102/101, 17.0566 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/17, 446.3625 cents Average / Smallest step : 9.733165 Largest / Average step : 2.688688 Largest / Smallest step : 26.169443 Median interval of one step : 101/99, 34.6258 cents, amount: 1 Least squares average step : 115.32547 cents, oct.: 345.97641 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1985-tone equal temperament with octave 4/3 degrees: 68 206 1985 Least number of segments generator : 993 of 249.148 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1369 of 343.488 cents and inv. generated superset size: 33 = 30 more = 1100.000% Number of contiguous 1-step segments: 0 Step pattern alph. order: ABC Step pattern size order : SML Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.05663 cents Scale diversity : 0.058954 Lumma stability : 0.068494 Lumma impropriety factor : 0.792459 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 : 102/101, 17.0566 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 480.9884 cents Number of appreciable fourths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 33.3333% 2/1 octave complements present : 0 = 0.0000% Limited inverse transpositions with margin 411.7367 cents: 2 -- Rational properties -- Prime limit : 101 Odd number limit : 153 (O: 101 U: 153) Highest odd numerator or denominator: 101 Scale harmonicity : 0.017975 Fundamental : 1/3333, -11.7026 octaves, 0.0785 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 6.799320E+05, 19.37503 octaves Euler's gradus suavitatis : 133 Sum of Mann's harmonic distance : 138.5, average 46.16667 Mersenne's string divisions : 13601 Sum of van Prooijen's expressibility: 3.99996, average 1.33332 Sum of Tenney's harmonic distance : 8.14210, average 2.71403 Vogel's harmonic complexity : 89.33333 Wille's k value : 858 Wilson's harmonic complexity : 135 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 12.38573, average 2.06429 Lattice compactness (without 2's) : 10.03261, average 1.67210 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: 1 .. 2 1.33333 4 3: -1 .. 1 -0.33333 3 1 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 1 101: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-1 / 3 =-0.33333 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 23 30 48| Scale is weakly epimorphic with val: <6 10 24 31 49| Scale is weakly epimorphic with val: <6 10 25 32 47| Scale is weakly epimorphic with val: <6 10 26 33 48| Scale is weakly epimorphic with val: <6 11 23 31 49| Scale is weakly epimorphic with val: <6 11 23 33 47| Scale is weakly epimorphic with val: <6 11 24 32 47| Scale is weakly epimorphic with val: <6 11 25 33 48| Scale is weakly epimorphic with val: <6 11 26 33 47| Scale is weakly epimorphic with val: <7 10 23 29 47| Scale is weakly epimorphic with val: <7 10 24 30 48| Scale is weakly epimorphic with val: <7 10 25 31 49| Scale is weakly epimorphic with val: <7 10 25 33 47| Scale is weakly epimorphic with val: <7 10 26 32 47| Scale is weakly epimorphic with val: <7 10 27 33 48| Scale is weakly epimorphic with val: <7 11 23 28 47| Scale is weakly epimorphic with val: <7 11 23 29 49| Scale is weakly epimorphic with val: <7 11 23 31 47| Scale is weakly epimorphic with val: <7 11 23 32 49| Scale is weakly epimorphic with val: <7 11 24 27 47| Scale is weakly epimorphic with val: <7 11 24 29 48| Scale is JI-epimorphic with val: <7 11 24 30 47| Scale is weakly epimorphic with val: <7 11 24 32 48| Scale is weakly epimorphic with val: <7 11 24 33 47| Scale is weakly epimorphic with val: <7 11 25 27 49| Scale is weakly epimorphic with val: <7 11 25 28 48| Scale is weakly epimorphic with val: <7 11 25 30 49| Scale is JI-epimorphic with val: <7 11 25 31 48| Scale is weakly epimorphic with val: <7 11 25 33 49| Scale is weakly epimorphic with val: <7 11 26 28 47| Scale is weakly epimorphic with val: <7 11 26 29 49| Scale is weakly epimorphic with val: <7 11 26 31 47| Scale is JI-epimorphic with val: <7 11 26 32 49| Scale is weakly epimorphic with val: <7 11 27 27 47| Scale is weakly epimorphic with val: <7 11 27 29 48| Scale is weakly epimorphic with val: <7 11 27 30 47| Scale is weakly epimorphic with val: <7 11 27 32 48| Scale is weakly epimorphic with val: <7 11 27 33 47| Scale is weakly epimorphic with val: <7 12 23 31 49| Scale is weakly epimorphic with val: <7 12 23 32 48| Scale is weakly epimorphic with val: <7 12 24 32 47| Scale is weakly epimorphic with val: <7 12 24 33 49| Scale is weakly epimorphic with val: <7 12 25 31 47| Scale is weakly epimorphic with val: <7 12 25 33 48| Scale is weakly epimorphic with val: <7 12 26 32 48| Scale is weakly epimorphic with val: <7 12 27 33 49| Scale is weakly epimorphic with val: <8 11 23 29 47| Scale is weakly epimorphic with val: <8 11 23 33 49| Scale is weakly epimorphic with val: <8 11 24 30 48| Scale is weakly epimorphic with val: <8 11 24 31 47| Scale is weakly epimorphic with val: <8 11 25 31 49| Scale is weakly epimorphic with val: <8 11 25 32 48| Scale is weakly epimorphic with val: <8 11 26 32 47| Scale is weakly epimorphic with val: <8 11 26 33 49| Scale is weakly epimorphic with val: <8 11 27 31 47| Scale is weakly epimorphic with val: <8 11 27 33 48| Scale is weakly epimorphic with val: <8 12 23 30 48| Scale is weakly epimorphic with val: <8 12 23 32 49| Scale is weakly epimorphic with val: <8 12 24 30 47| Scale is weakly epimorphic with val: <8 12 24 31 49| Scale is weakly epimorphic with val: <8 12 25 31 48| Scale is weakly epimorphic with val: <8 12 25 32 47| Scale is weakly epimorphic with val: <8 12 26 32 49| Scale is weakly epimorphic with val: <8 12 26 33 48| Scale is weakly epimorphic with val: <8 12 27 30 47|
FIT/MODE
3: 0 0 3 N M DE S SD: 31.4219 c. M: 51.6825 c. 6: 0 1 5 N G T3 SD: 20.5928 c. M:-31.3250 c. 7: 0 1 6 N G T3 SD: 14.9431 c. M:-19.4668 c. 8: 0 1 7 N G T3 SD: 11.5862 c. M: 17.0566 c. 9: 0 1 8 N G T3 SD: 10.0713 c. M: 17.0566 c. 10: 0 1 9 N G T3 SD: 9.9072 c. M: 17.0566 c. 11: 0 1 10 N G T3 SD: 10.5192 c. M: 17.0566 c. 12: 0 1 11 N G T3 SD: 11.4679 c. M: 17.0566 c. 17: 1 1 15 N M DE S SD: 8.1155 c. M:-12.2401 c. 18: 1 1 16 N M DE S SD: 6.4805 c. M:-10.6125 c. 19: 1 1 17 N M DE S SD: 5.3038 c. M:-9.1563 c. 20: 1 1 18 N M DE S SD: 4.6576 c. M:-7.8456 c. 21: 1 1 19 N M DE S SD: 4.5611 c. M:-6.6598 c. 22: 1 1 20 N M DE S SD: 4.9054 c. M: 6.4056 c. 25: 1 2 22 N T3 SD: 4.9512 c. M:-8.0829 c. 26: 1 2 23 N T3 SD: 3.5526 c. M:-5.7843 c. 27: 1 2 24 N T3 SD: 2.2580 c. M:-3.6559 c. 28: 1 2 25 N T3 SD: 1.0575 c. M:-1.6795 c. 29: 1 2 26 N T3 SD: 0.1148 c. M: 0.1606 c. 202: 7 14 181 N T3 SD: 0.1289 c. M:-0.2024 c. 231: 8 16 207 N T3 SD: 0.1164 c. M:-0.1917 c. 260: 9 18 233 N T3 SD: 0.1081 c. M:-0.1834 c. 289: 10 20 259 N T3 SD: 0.1026 c. M:-0.1768 c. 318: 11 22 285 N T3 SD: 0.0989 c. M:-0.1713 c. 347: 12 24 311 N T3 SD: 0.0966 c. M:-0.1668 c. 376: 13 26 337 N T3 SD: 0.0951 c. M:-0.1630 c. 405: 14 28 363 N T3 SD: 0.0942 c. M:-0.1597 c. 434: 15 30 389 N T3 SD: 0.0938 c. M:-0.1569 c. 442: 15 31 396 N T3 SD: 0.1245 c. M: 0.1547 c. 443: 15 31 397 N T3 SD: 0.1130 c. M: 0.1928 c. 463: 16 32 415 N T3 SD: 0.0936 c. M:-0.1544 c. 471: 16 33 422 N T3 SD: 0.1099 c. M: 0.1379 c. 472: 16 33 423 N T3 SD: 0.1011 c. M: 0.1737 c. 492: 17 34 441 N T3 SD: 0.0936 c. M:-0.1522 c. 500: 17 35 448 N T3 SD: 0.0970 c. M: 0.1231 c. 501: 17 35 449 N T3 SD: 0.0908 c. M: 0.1569 c. 529: 18 37 474 N T3 SD: 0.0855 c. M: 0.1099 c. 530: 18 37 475 N T3 SD: 0.0819 c. M: 0.1419 c. 558: 19 39 500 N T3 SD: 0.0752 c. M: 0.0981 c. 559: 19 39 501 N T3 SD: 0.0743 c. M: 0.1284 c. 587: 20 41 526 N T3 SD: 0.0660 c. M: 0.0875 c. 588: 20 41 527 N T3 SD: 0.0677 c. M: 0.1163 c. 616: 21 43 552 N T3 SD: 0.0576 c. M: 0.0778 c. 617: 21 43 553 N T3 SD: 0.0621 c. M: 0.1053 c. 645: 22 45 578 N T3 SD: 0.0501 c. M: 0.0690 c. 646: 22 45 579 N T3 SD: 0.0573 c. M: 0.0953 c. 674: 23 47 604 N T3 SD: 0.0432 c. M: 0.0610 c. 703: 24 49 630 N T3 SD: 0.0370 c. M: 0.0537 c. 732: 25 51 656 N T3 SD: 0.0313 c. M: 0.0469 c. 761: 26 53 682 N T3 SD: 0.0261 c. M: 0.0406 c. 790: 27 55 708 N T3 SD: 0.0215 c. M: 0.0348 c. 819: 28 57 734 N T3 SD: 0.0175 c. M: 0.0295 c. 848: 29 59 760 N T3 SD: 0.0141 c. M: 0.0244 c. 877: 30 61 786 N T3 SD: 0.0116 c. M: 0.0197 c. 906: 31 63 812 N T3 SD: 0.0103 c. M: 0.0154 c. 935: 32 65 838 N T3 SD: 0.0102 c. M: 0.0136 c. 1840: 63 128 1649 N T3 SD: 0.0100 c. M:-0.0168 c. 1841: 63 128 1650 N T3 SD: 0.0101 c. M: 0.0133 c. 1869: 64 130 1675 N T3 SD: 0.0082 c. M:-0.0140 c. 1898: 65 132 1701 N T3 SD: 0.0066 c. M:-0.0114 c. 1927: 66 134 1727 N T3 SD: 0.0051 c. M:-0.0088 c. 1956: 67 136 1753 N T3 SD: 0.0041 c. M:-0.0063 c. 1985: 68 138 1779 N T3 SD: 0.0036 c. M:-0.0049 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: 107.5942 cents 7 x 8:9 S SD: 95.1069 cents 8 x 9:11 SD: 80.6400 cents 9 x 10:12 S SD: 65.3606 cents 10 x 11:13 SD: 60.7515 cents 11 x 12:15 S SD: 53.1641 cents 12 x 13:16 SD: 43.4451 cents 13 x 14:17 SD: 41.8333 cents 14 x 15:19 SD: 37.1833 cents 15 x 16:20 S SD: 30.0244 cents 16 x 17:21 SD: 29.9221 cents 17 x 18:23 SD: 26.8022 cents 18 x 19:24 SD: 20.9603 cents 19 x 20:25 S SD: 21.8150 cents 20 x 21:27 SD: 19.6046 cents 21 x 22:28 SD: 14.4273 cents 22 x 23:29 SD: 16.0487 cents 23 x 24:31 SD: 14.4414 cents 24 x 25:32 SD: 9.4950 cents 25 x 26:33 SD: 11.8928 cents 26 x 27:35 SD: 10.7345 cents 27 x 28:36 SD: 5.6392 cents 28 x 29:37 SD: 8.9906 cents 29 x 30:39 SD: 8.2152 cents 30 x 31:40 SD: 2.5422 cents 31 x 32:41 SD: 7.1986 cents 32 x 33:43 SD: 6.7831 cents 33 x 34:44 SD: 0.0000 cents 34 x 35:45 SD: 6.4321 cents 35 x 36:47 SD: 6.3307 cents 36 x 37:48 SD: 2.1242 cents 37 x 38:49 SD: 6.4838 cents 38 x 39:51 SD: 6.5943 cents 39 x 40:52 SD: 3.9257 cents 40 x 41:53 SD: 7.0290 cents 41 x 42:55 SD: 7.2464 cents 42 x 43:56 SD: 5.4728 cents 43 x 44:57 SD: 7.7957 cents 44 x 45:59 SD: 8.0538 cents 45 x 46:60 SD: 6.8159 cents 46 x 47:61 SD: 8.6287 cents 47 x 48:63 SD: 8.8942 cents 48 x 49:64 SD: 7.9928 cents 49 x 50:65 SD: 9.4543 cents 50:51:52:67 SD: 8.3952 cents 51:52:53:68 SD: 7.4283 cents 53:54:55:71 SD: 7.1138 cents 54:55:56:72 SD: 6.1787 cents 56:57:58:75 SD: 6.0210 cents 57:58:59:76 SD: 5.1067 cents 60:61:62:80 SD: 4.2094 cents 63:64:65:84 SD: 3.4970 cents 66:67:68:88 SD: 2.9925 cents 69:70:71:92 SD: 2.7200 cents 72:73:74:96 SD: 2.6791 cents 87:88:90:116 SD: 2.5072 cents 90:91:93:120 SD: 1.8303 cents 93:94:96:124 SD: 1.1973 cents 96:97:99:128 SD: 0.6065 cents 99:100:102:132 SD: 0.1143 cents