Scala analysis: 014_H4
Hyperenharmonic tetrachord 99/98 * 49/48 * 128/99
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 99/98 17.576131 small undecimal comma 2: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 128/99 444.7721 1: 99/98 17.5761 small undecimal comma 2: 49/48 35.6968 slendro diesis, septimal 1/6-tone 3: 128/99 444.7721
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 99/98 17.576 cents small undecimal comma 1: 1 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 1 128/99 444.772 cents 2: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 2: 1 64/49 462.348 cents 2 septatones or septatonic major third 2: 1 392/297 480.469 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 : 17.6 53.3 498.0 17.6 : 35.7 480.5 498.0 53.3 : 444.8 462.3 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 17.5761 .. 444.7721 cents 12544/9801, 427.1959 cents 99/98, 17.5761 cents 2: 53.2729 .. 480.4689 cents 12544/9801, 427.1959 cents 3267/4096,-391.4991 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 99/98, 17.5761 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 128/99, 444.7721 cents Average / Smallest step : 9.445480 Largest / Average step : 2.679108 Largest / Smallest step : 25.305458 Median interval of one step : 49/48, 35.6968 cents, amount: 1 Least squares average step : 115.58979 cents, oct.: 346.76936 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1898-tone equal temperament with octave 4/3 degrees: 67 203 1898 Least number of segments generator : 951 of 249.547 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1559 of 409.090 cents and inv. generated superset size: 12 = 9 more = 400.000% 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 17.57613 cents Scale diversity : 0.069555 Lumma stability : 0.070580 Lumma impropriety factor : 0.786072 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 : 99/98, 17.5761 cents Number of recognisable fifths : 0 Number of recognisable fourths : 1, average 480.4689 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% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 409.0752 cents: 2 -- Rational properties -- Prime limit : 11 Odd number limit : 297 (O: 99 U: 297) Highest odd numerator or denominator: 99 Scale harmonicity : 0.018604 Average absolute harmonicity : 0.091717 Specific harmonicity : 0.087380 Fundamental : 1/4704, -12.1997 octaves, 0.0556 Hz. Guide tone : 396, 8.6294 octaves, 103603.724 Hz. Exponens Consonantiae : 1.862784E+06, 20.82903 octaves Euler's gradus suavitatis : 36 Sum of Mann's harmonic distance : 134.5, average 44.83333 Mersenne's string divisions : 89635 Sum of van Prooijen's expressibility: 3.99127, average 1.33042 Sum of Tenney's harmonic distance : 8.08971, average 2.69657 Vogel's harmonic complexity : 25.33333 Wille's k value : 2425 Wilson's harmonic complexity : 34 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 27.32137, average 4.55356 Lattice compactness (without 2's) : 13.62801, average 2.27133 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 2 -1.33333 8 3: -1 .. 2 0.66667 4 1 7: -2 .. 0 -0.66667 2 11: 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 18 23| Scale is weakly epimorphic with val: <6 10 19 27| Scale is weakly epimorphic with val: <6 10 21 23| Scale is weakly epimorphic with val: <6 11 20 27| Scale is weakly epimorphic with val: <7 11 19 25| Scale is weakly epimorphic with val: <7 11 20 23| Scale is JI-epimorphic with val: <7 11 20 26| Scale is weakly epimorphic with val: <7 11 22 25| Scale is weakly epimorphic with val: <7 12 18 26| Scale is weakly epimorphic with val: <7 12 19 24| Scale is weakly epimorphic with val: <7 12 21 26| Scale is weakly epimorphic with val: <8 11 19 27| Scale is weakly epimorphic with val: <8 12 20 27|
FIT/MODE
3: 0 0 3 N M DE S SD: 32.3879 c. M: 53.2729 c. 6: 0 1 5 N G T3 SD: 19.9421 c. M:-29.7346 c. 7: 0 1 6 N G T3 SD: 14.4739 c. M:-17.8763 c. 8: 0 1 7 N G T3 SD: 11.3960 c. M: 17.5761 c. 9: 0 1 8 N G T3 SD: 10.2174 c. M: 17.5761 c. 10: 0 1 9 N G T3 SD: 10.3433 c. M: 17.5761 c. 11: 0 1 10 N G T3 SD: 11.1484 c. M: 17.5761 c. 16: 1 1 14 N M DE S SD: 9.3868 c. M:-13.5517 c. 17: 1 1 15 N M DE S SD: 7.4315 c. M:-11.7206 c. 18: 1 1 16 N M DE S SD: 5.9480 c. M:-10.0930 c. 19: 1 1 17 N M DE S SD: 5.0104 c. M:-8.6368 c. 20: 1 1 18 N M DE S SD: 4.6798 c. M:-7.3261 c. 21: 1 1 19 N M DE S SD: 4.8925 c. M:-6.1403 c. 24: 1 2 21 N T3 SD: 5.5007 c. M:-8.9827 c. 25: 1 2 22 N T3 SD: 3.9856 c. M:-6.4925 c. 26: 1 2 23 N T3 SD: 2.5873 c. M:-4.1938 c. 27: 1 2 24 N T3 SD: 1.2939 c. M:-2.0654 c. 28: 1 2 25 N T3 SD: 0.1323 c. M:-0.2112 c. 197: 7 14 176 N T3 SD: 0.1261 c. M: 0.1819 c. 225: 8 16 201 N T3 SD: 0.1146 c. M: 0.1481 c. 253: 9 18 226 N T3 SD: 0.1076 c. M:-0.1409 c. 281: 10 20 251 N T3 SD: 0.1034 c. M:-0.1479 c. 309: 11 22 276 N T3 SD: 0.1010 c. M:-0.1536 c. 337: 12 24 301 N T3 SD: 0.0998 c. M:-0.1584 c. 365: 13 26 326 N T3 SD: 0.0994 c. M:-0.1625 c. 457: 16 33 408 N T3 SD: 0.1091 c. M: 0.1391 c. 458: 16 33 409 N T3 SD: 0.1025 c. M: 0.1772 c. 477: 17 34 426 N T3 SD: 0.1013 c. M:-0.1739 c. 478: 17 34 427 N T3 SD: 0.1106 c. M:-0.1368 c. 485: 17 35 433 N T3 SD: 0.0999 c. M:-0.1257 c. 486: 17 35 434 N T3 SD: 0.0898 c. M: 0.1548 c. 513: 18 37 458 N T3 SD: 0.0921 c. M:-0.1237 c. 514: 18 37 459 N T3 SD: 0.0787 c. M: 0.1349 c. 541: 19 39 483 N T3 SD: 0.0857 c. M:-0.1219 c. 542: 19 39 484 N T3 SD: 0.0689 c. M: 0.1170 c. 570: 20 41 509 N T3 SD: 0.0602 c. M: 0.1009 c. 598: 21 43 534 N T3 SD: 0.0526 c. M: 0.0863 c. 626: 22 45 559 N T3 SD: 0.0460 c. M: 0.0730 c. 654: 23 47 584 N T3 SD: 0.0404 c. M: 0.0608 c. 682: 24 49 609 N T3 SD: 0.0357 c. M: 0.0496 c. 710: 25 51 634 N T3 SD: 0.0319 c. M: 0.0393 c. 738: 26 53 659 N T3 SD: 0.0292 c. M:-0.0408 c. 766: 27 55 684 N T3 SD: 0.0274 c. M:-0.0426 c. 767: 27 55 685 N T3 SD: 0.0297 c. M: 0.0439 c. 794: 28 57 709 N T3 SD: 0.0266 c. M:-0.0442 c. 795: 28 57 710 N T3 SD: 0.0241 c. M: 0.0349 c. 823: 29 59 735 N T3 SD: 0.0189 c. M: 0.0266 c. 851: 30 61 760 N T3 SD: 0.0140 c. M: 0.0187 c. 879: 31 63 785 N T3 SD: 0.0096 c. M: 0.0122 c. 907: 32 65 810 N T3 SD: 0.0058 c. M: 0.0090 c. 935: 33 67 835 N T3 SD: 0.0037 c. M: 0.0061 c. 1842: 65 132 1645 N T3 SD: 0.0044 c. M: 0.0075 c. 1898: 67 136 1695 N T3 SD: 0.0040 c. M:-0.0050 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: 106.7990 cents 7 x 8:9 S SD: 94.3569 cents 8 x 9:11 SD: 79.8898 cents 9 x 10:12 S SD: 64.5654 cents 10 x 11:13 SD: 60.0105 cents 11 x 12:15 S SD: 52.4248 cents 12 x 13:16 SD: 42.6499 cents 13 x 14:17 SD: 41.1063 cents 14 x 15:19 SD: 36.4602 cents 15 x 16:20 S SD: 29.2292 cents 16 x 17:21 SD: 29.2165 cents 17 x 18:23 SD: 26.1036 cents 18 x 19:24 SD: 20.1650 cents 19 x 20:25 S SD: 21.1426 cents 20 x 21:27 SD: 18.9447 cents 21 x 22:28 SD: 13.6320 cents 22 x 23:29 SD: 15.4303 cents 23 x 24:31 SD: 13.8453 cents 24 x 25:32 SD: 8.6997 cents 25 x 26:33 SD: 11.3655 cents 26 x 27:35 SD: 10.2471 cents 27 x 28:36 SD: 4.8440 cents 28 x 29:37 SD: 8.6170 cents 29 x 30:39 SD: 7.9088 cents 30 x 31:40 SD: 1.7470 cents 31 x 32:41 SD: 7.0599 cents 32 x 33:43 SD: 6.7364 cents 33 x 34:44 SD: 0.7952 cents 34 x 35:45 SD: 6.5724 cents 35 x 36:47 SD: 6.5594 cents 36 x 37:48 SD: 2.9195 cents 37 x 38:49 SD: 6.8598 cents 38 x 39:51 SD: 7.0325 cents 39 x 40:52 SD: 4.7209 cents 40 x 41:53 SD: 7.5593 cents 41 x 42:55 SD: 7.8145 cents 42 x 43:56 SD: 6.2681 cents 43 x 44:57 SD: 8.4175 cents 44 x 45:59 SD: 8.6981 cents 45 x 46:60 SD: 7.6112 cents 46 x 47:61 SD: 9.3048 cents 47 x 48:63 SD: 9.5841 cents 48 x 50:64 SD: 8.6997 cents 49:50:51:65 SD: 8.4110 cents 50:51:52:67 SD: 7.9417 cents 51:52:53:68 SD: 6.9504 cents 53:54:55:71 SD: 6.6897 cents 54:55:56:72 SD: 5.7274 cents 56:57:58:75 SD: 5.6383 cents 57:58:59:76 SD: 4.6955 cents 60:61:62:80 SD: 3.8599 cents 63:64:65:84 SD: 3.2412 cents 66:67:68:88 SD: 2.8687 cents 69:70:71:92 SD: 2.7543 cents 84:85:87:112 SD: 2.6751 cents 87:88:90:116 SD: 1.9506 cents 90:91:93:120 SD: 1.2746 cents 93:94:96:124 SD: 0.6450 cents 96:97:99:128 SD: 0.1214 cents