Scala analysis: 010_H3
Hyperenharmonic tetrachord 51/50 * 100/99 * 22/17
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 51/50 34.282983 17th-partial chroma 2: 34/33 51.682466 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 22/17 446.3625 1: 51/50 34.2830 17th-partial chroma 2: 100/99 17.3995 Ptolemy's comma 3: 22/17 446.3625
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 100/99 17.399 cents Ptolemy's comma 1: 1 51/50 34.283 cents 17th-partial chroma 1: 1 22/17 446.363 cents 2: 1 34/33 51.682 cents 2: 1 200/153 463.762 cents 2: 1 33/25 480.646 cents 2 pentatones 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 : 34.3 51.7 498.0 34.3 : 17.4 463.8 498.0 51.7 : 446.4 480.6 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.3995 .. 446.3625 cents 1089/850, 428.9630 cents 100/99, 17.3995 cents 2: 51.6825 .. 480.6455 cents 1089/850, 428.9630 cents 289/363,-394.6801 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 100/99, 17.3995 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 22/17, 446.3625 cents Average / Smallest step : 9.541375 Largest / Average step : 2.688688 Largest / Smallest step : 25.653780 Median interval of one step : 51/50, 34.2830 cents, amount: 1 Least squares average step : 116.55592 cents, oct.: 349.66777 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 17.39948 cents Scale diversity : 0.059736 Lumma stability : 0.069871 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 : 5049/5000, 16.8835 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 480.6455 cents Number of appreciable fourths : 0 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 428.9630 cents: 2 -- Rational properties -- Prime limit : 17 Odd number limit : 153 (O: 51 U: 153) Highest odd numerator or denominator: 51 Scale harmonicity : 0.014402 Average absolute harmonicity : 0.084998 Specific harmonicity : 0.066093 Fundamental : 1/1650, -10.6883 octaves, 0.1586 Hz. Guide tone : 204, 7.6724 octaves, 53371.615 Hz. Exponens Consonantiae : 3.366000E+05, 18.36068 octaves Euler's gradus suavitatis : 42 Sum of Mann's harmonic distance : 87.5, average 29.16667 Mersenne's string divisions : 47369 Sum of van Prooijen's expressibility: 3.70321, average 1.23440 Sum of Tenney's harmonic distance : 7.53571, average 2.51190 Vogel's harmonic complexity : 29.00000 Wille's k value : 841 Wilson's harmonic complexity : 44 Rectangular lattice diameter : 6 Triangular lattice diameter : 3 Lattice compactness : 16.46206, average 2.74368 Lattice compactness (without 2's) : 12.59575, average 2.09929 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 0.66667 4 3: -1 .. 1 -0.33333 3 1 5: -2 .. 0 -0.66667 2 11: -1 .. 0 -0.33333 1 17: 0 .. 1 0.66667 2 2 Average exponent except 2's :-2 / 3 =-0.66667 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 23 30| Scale is weakly epimorphic with val: <6 10 15 24 29| Scale is weakly epimorphic with val: <6 10 15 26 33| Scale is weakly epimorphic with val: <6 10 15 27 29| Scale is weakly epimorphic with val: <6 10 16 23 31| Scale is weakly epimorphic with val: <6 10 16 25 32| Scale is weakly epimorphic with val: <6 10 16 26 31| Scale is weakly epimorphic with val: <6 10 17 24 31| Scale is weakly epimorphic with val: <6 10 17 25 33| Scale is weakly epimorphic with val: <6 10 18 23 30| Scale is weakly epimorphic with val: <6 10 18 26 33| Scale is weakly epimorphic with val: <6 10 19 25 32| Scale is weakly epimorphic with val: <6 11 15 24 28| Scale is weakly epimorphic with val: <6 11 15 25 33| Scale is weakly epimorphic with val: <6 11 15 27 28| Scale is weakly epimorphic with val: <6 11 16 23 30| Scale is weakly epimorphic with val: <6 11 16 24 32| Scale is weakly epimorphic with val: <6 11 16 26 30| Scale is weakly epimorphic with val: <6 11 17 23 31| Scale is weakly epimorphic with val: <6 11 17 25 32| Scale is weakly epimorphic with val: <6 11 18 25 33| Scale is weakly epimorphic with val: <6 11 19 24 32| Scale is weakly epimorphic with val: <7 10 15 23 29| Scale is weakly epimorphic with val: <7 10 15 25 30| Scale is weakly epimorphic with val: <7 10 15 26 32| Scale is weakly epimorphic with val: <7 10 16 24 32| Scale is weakly epimorphic with val: <7 10 16 25 31| Scale is weakly epimorphic with val: <7 10 16 27 32| Scale is weakly epimorphic with val: <7 10 17 24 30| Scale is weakly epimorphic with val: <7 10 17 27 33| Scale is weakly epimorphic with val: <7 10 18 23 29| Scale is weakly epimorphic with val: <7 10 18 26 32| Scale is weakly epimorphic with val: <7 10 19 25 31| Scale is weakly epimorphic with val: <7 11 15 23 28| Scale is weakly epimorphic with val: <7 11 15 23 31| Scale is weakly epimorphic with val: <7 11 15 24 27| Scale is weakly epimorphic with val: <7 11 15 24 30| Scale is weakly epimorphic with val: <7 11 15 24 33| Scale is weakly epimorphic with val: <7 11 15 26 28| Scale is weakly epimorphic with val: <7 11 15 26 31| Scale is weakly epimorphic with val: <7 11 15 27 27| Scale is weakly epimorphic with val: <7 11 15 27 30| Scale is weakly epimorphic with val: <7 11 15 27 33| Scale is JI-epimorphic with val: <7 11 16 23 29| Scale is weakly epimorphic with val: <7 11 16 23 32| Scale is weakly epimorphic with val: <7 11 16 25 27| Scale is weakly epimorphic with val: <7 11 16 25 30| Scale is weakly epimorphic with val: <7 11 16 25 33| Scale is weakly epimorphic with val: <7 11 16 26 29| Scale is weakly epimorphic with val: <7 11 16 26 32| Scale is weakly epimorphic with val: <7 11 17 24 29| Scale is weakly epimorphic with val: <7 11 17 24 32| Scale is weakly epimorphic with val: <7 11 17 25 28| Scale is JI-epimorphic with val: <7 11 17 25 31| 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 18 23 28| Scale is weakly epimorphic with val: <7 11 18 23 31| Scale is weakly epimorphic with val: <7 11 18 24 27| Scale is weakly epimorphic with val: <7 11 18 24 30| Scale is weakly epimorphic with val: <7 11 18 24 33| Scale is weakly epimorphic with val: <7 11 18 26 28| Scale is weakly epimorphic with val: <7 11 18 26 31| Scale is weakly epimorphic with val: <7 11 18 27 27| Scale is weakly epimorphic with val: <7 11 18 27 30| Scale is JI-epimorphic with val: <7 11 18 27 33| Scale is weakly epimorphic with val: <7 11 19 23 29| Scale is weakly epimorphic with val: <7 11 19 23 32| Scale is weakly epimorphic with val: <7 11 19 25 27| Scale is weakly epimorphic with val: <7 11 19 25 30| Scale is weakly epimorphic with val: <7 11 19 25 33| Scale is weakly epimorphic with val: <7 11 19 26 29| Scale is weakly epimorphic with val: <7 11 19 26 32| Scale is weakly epimorphic with val: <7 12 15 24 32| Scale is weakly epimorphic with val: <7 12 15 25 28| Scale is weakly epimorphic with val: <7 12 16 23 31| Scale is weakly epimorphic with val: <7 12 16 24 30| Scale is weakly epimorphic with val: <7 12 16 27 30| Scale is weakly epimorphic with val: <7 12 17 23 32| Scale is weakly epimorphic with val: <7 12 17 25 33| Scale is weakly epimorphic with val: <7 12 17 26 32| Scale is weakly epimorphic with val: <7 12 18 24 32| Scale is weakly epimorphic with val: <7 12 19 23 31| Scale is weakly epimorphic with val: <8 11 15 23 30| Scale is weakly epimorphic with val: <8 11 15 25 31| Scale is weakly epimorphic with val: <8 11 15 26 30| Scale is weakly epimorphic with val: <8 11 16 24 30| Scale is weakly epimorphic with val: <8 11 16 25 32| Scale is weakly epimorphic with val: <8 11 16 27 33| Scale is weakly epimorphic with val: <8 11 17 23 29| Scale is weakly epimorphic with val: <8 11 17 26 32| Scale is weakly epimorphic with val: <8 11 18 25 31| Scale is weakly epimorphic with val: <8 11 19 24 30| Scale is weakly epimorphic with val: <8 11 19 27 33| Scale is weakly epimorphic with val: <8 12 15 23 29| Scale is weakly epimorphic with val: <8 12 15 24 31| Scale is weakly epimorphic with val: <8 12 15 26 29| Scale is weakly epimorphic with val: <8 12 16 23 30| Scale is weakly epimorphic with val: <8 12 16 25 31| Scale is weakly epimorphic with val: <8 12 16 26 33| Scale is weakly epimorphic with val: <8 12 17 24 33| Scale is weakly epimorphic with val: <8 12 17 25 32| Scale is weakly epimorphic with val: <8 12 17 27 33| Scale is weakly epimorphic with val: <8 12 18 24 31| Scale is weakly epimorphic with val: <8 12 19 23 30| Scale is weakly epimorphic with val: <8 12 19 26 33|
FIT/MODE
3: 0 0 3 N M DE S SD: 35.8069 c. M: 51.6825 c. 6: 0 1 5 N G T3 SD: 26.8116 c. M: 34.2830 c. 7: 1 0 6 N G T3 SD: 24.0699 c. M:-36.8663 c. 8: 1 0 7 N G T3 SD: 17.2652 c. M:-27.9726 c. 9: 1 0 8 N G T3 SD: 12.3382 c. M:-21.0554 c. 10: 1 0 9 N G T3 SD: 9.0267 c. M:-15.5215 c. 11: 1 0 10 N G T3 SD: 7.3461 c. M:-10.9938 c. 12: 1 0 11 N G T3 SD: 7.2052 c. M: 10.1787 c. 16: 1 1 14 N M DE S SD: 6.3704 c. M:-10.5732 c. 17: 1 1 15 N M DE S SD: 4.9202 c. M:-6.9111 c. 18: 1 1 16 N M DE S SD: 4.3630 c. M: 6.6138 c. 19: 1 1 17 N M DE S SD: 4.6790 c. M: 8.0701 c. 26: 2 1 23 N T3 SD: 4.0696 c. M:-5.7843 c. 27: 2 1 24 N T3 SD: 2.5932 c. M:-3.6559 c. 28: 2 1 25 N T3 SD: 1.2233 c. M:-1.6795 c. 29: 2 1 26 N T3 SD: 0.1000 c. M: 0.1606 c. 260: 18 9 233 N T3 SD: 0.1158 c. M:-0.1971 c. 289: 20 10 259 N T3 SD: 0.1066 c. M:-0.1838 c. 318: 22 11 285 N T3 SD: 0.0999 c. M:-0.1730 c. 347: 24 12 311 N T3 SD: 0.0949 c. M:-0.1639 c. 376: 26 13 337 N T3 SD: 0.0913 c. M:-0.1563 c. 394: 27 14 353 N T3 SD: 0.1215 c. M: 0.1530 c. 405: 28 14 363 N T3 SD: 0.0886 c. M:-0.1498 c. 423: 29 15 379 N T3 SD: 0.1070 c. M: 0.1381 c. 434: 30 15 389 N T3 SD: 0.0866 c. M:-0.1441 c. 452: 31 16 405 N T3 SD: 0.0944 c. M: 0.1250 c. 463: 32 16 415 N T3 SD: 0.0852 c. M:-0.1391 c. 481: 33 17 431 N T3 SD: 0.0834 c. M: 0.1136 c. 510: 35 18 457 N T3 SD: 0.0738 c. M: 0.1034 c. 539: 37 19 483 N T3 SD: 0.0653 c. M: 0.0944 c. 568: 39 20 509 N T3 SD: 0.0579 c. M: 0.0862 c. 597: 41 21 535 N T3 SD: 0.0513 c. M: 0.0789 c. 626: 43 22 561 N T3 SD: 0.0455 c. M: 0.0722 c. 655: 45 23 587 N T3 SD: 0.0404 c. M: 0.0662 c. 684: 47 24 613 N T3 SD: 0.0361 c. M: 0.0606 c. 713: 49 25 639 N T3 SD: 0.0324 c. M: 0.0555 c. 742: 51 26 665 N T3 SD: 0.0293 c. M: 0.0508 c. 771: 53 27 691 N T3 SD: 0.0269 c. M: 0.0464 c. 800: 55 28 717 N T3 SD: 0.0252 c. M: 0.0424 c. 829: 57 29 743 N T3 SD: 0.0240 c. M: 0.0386 c. 857: 59 30 768 N T3 SD: 0.0232 c. M:-0.0398 c. 858: 59 30 769 N T3 SD: 0.0235 c. M: 0.0351 c. 886: 61 31 794 N T3 SD: 0.0196 c. M:-0.0333 c. 887: 61 31 795 N T3 SD: 0.0234 c. M: 0.0319 c. 915: 63 32 820 N T3 SD: 0.0164 c. M:-0.0271 c. 944: 65 33 846 N T3 SD: 0.0137 c. M:-0.0214 c. 973: 67 34 872 N T3 SD: 0.0115 c. M:-0.0159 c. 1002: 69 35 898 N T3 SD: 0.0100 c. M:-0.0135 c. 1031: 71 36 924 N T3 SD: 0.0093 c. M:-0.0150 c. 1744: 120 61 1563 N T3 SD: 0.0089 c. M: 0.0138 c. 1773: 122 62 1589 N T3 SD: 0.0076 c. M: 0.0125 c. 1802: 124 63 1615 N T3 SD: 0.0066 c. M: 0.0113 c. 1831: 126 64 1641 N T3 SD: 0.0059 c. M: 0.0101 c. 1860: 128 65 1667 N T3 SD: 0.0056 c. M: 0.0089 c. 1889: 130 66 1693 N T3 SD: 0.0057 c. M: 0.0078 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 40:41 x 53 SD: 6.8826 cents 41:42 x 55 SD: 6.4430 cents 42:43 x 56 SD: 3.2269 cents 43:44 x 57 SD: 5.7520 cents 44:45 x 59 SD: 5.4217 cents 45:46 x 60 SD: 1.8838 cents 46:47 x 61 SD: 4.9424 cents 47:48 x 63 SD: 4.7181 cents 48:49 x 64 SD: 0.7069 cents 49:50 x 65 SD: 4.4412 cents 54:55:56:72 SD: 3.8519 cents 57:58:59:76 SD: 3.0140 cents 60:61:62:80 SD: 2.5378 cents 63:64:65:84 SD: 2.4751 cents 75 x 77:100 SD: 3.0605 cents 76 x 78:101 SD: 4.4046 cents 77 x 79:103 SD: 4.5997 cents 78 x 80:104 SD: 3.9257 cents 79 x 81:105 SD: 5.0165 cents 80:82 x 107 SD: 5.0211 cents 81:83 x 108 SD: 3.9722 cents 82:84 x 109 SD: 4.5616 cents 83:85:86:111 SD: 4.3597 cents 84:86:87:112 SD: 3.7103 cents 86:88:89:115 SD: 3.5696 cents 87:89:90:116 SD: 2.8825 cents 89:91:92:119 SD: 2.8629 cents 90:92:93:120 SD: 2.1094 cents 93:95:96:124 SD: 1.3860 cents 96:98:99:128 SD: 0.7093 cents 99:101:102:132 SD: 0.1143 cents 498:508:513:664 SD: 0.1119 cents 597:609:615:796 SD: 0.1025 cents