Scala analysis: 086_E9
Enharmonic tetrachord 76/75 * 25/24 * 24/19
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76/75 22.930588 2: 19/18 93.603014 undevicesimal semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 24/19 404.4420 smaller undevicesimal major third 1: 76/75 22.9306 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 24/19 404.4420 smaller undevicesimal major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 76/75 22.931 cents 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 19/18 93.603 cents undevicesimal semitone 2: 1 32/25 427.373 cents classic diminished fourth 2: 1 25/19 475.114 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 : 22.9 93.6 498.0 22.9 : 70.7 475.1 498.0 93.6 : 404.4 427.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.9306 .. 404.4420 cents 450/361, 381.5114 cents 76/75, 22.9306 cents 2: 93.6030 .. 475.1144 cents 450/361, 381.5114 cents 361/432,-310.8390 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 76/75, 22.9306 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 24/19, 404.4420 cents Average / Smallest step : 7.239893 Largest / Average step : 2.436177 Largest / Smallest step : 17.637663 Median interval of one step : 25/24, 70.6724 cents, amount: 1 Least squares average step : 121.73369 cents, oct.: 365.20106 cents Scale is not proper Scale has trivalence property Scale is a mode of a 2107-tone equal temperament with octave 4/3 degrees: 97 396 2107 Least number of segments generator : 1054 of 249.141 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1711 of 404.440 cents and inv. generated superset size: 39 = 36 more = 1300.000% 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 22.93059 cents Scale diversity : 0.318572 Lumma stability : 0.092082 Lumma impropriety factor : 0.624118 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 : 76/75, 22.9306 cents Number of recognisable fifths : 0 Number of recognisable 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 -- Rational properties -- Prime limit : 19 Odd number limit : 75 (O: 25 U: 75) Highest odd numerator or denominator: 75 Scale harmonicity : 0.018103 Average absolute harmonicity : 0.086135 Specific harmonicity : 0.079278 Fundamental : 1/450, -8.8138 octaves, 0.5814 Hz. Guide tone : 76, 6.2479 octaves, 19883.543 Hz. Exponens Consonantiae : 3.420000E+04, 15.06171 octaves Euler's gradus suavitatis : 34 Sum of Mann's harmonic distance : 97.5, average 32.50000 Mersenne's string divisions : 39109 Sum of van Prooijen's expressibility: 3.63094, average 1.21031 Sum of Tenney's harmonic distance : 7.36908, average 2.45636 Vogel's harmonic complexity : 23.33333 Wille's k value : 237 Wilson's harmonic complexity : 35 Rectangular lattice diameter : 5 Triangular lattice diameter : 2 Lattice compactness : 17.14219, average 2.85703 Lattice compactness (without 2's) : 11.57191, average 1.92865 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 2 1.00000 5 3: -2 ..-1 -1.33333 4 1 5: -2 .. 0 -0.66667 2 19: 0 .. 1 0.66667 2 2 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 8 / 3 = 2.66667 Scale is weakly epimorphic with val: <6 10 15 29| Scale is weakly epimorphic with val: <6 10 16 33| Scale is weakly epimorphic with val: <6 10 18 29| Scale is weakly epimorphic with val: <6 11 15 31| Scale is weakly epimorphic with val: <6 11 18 31| Scale is weakly epimorphic with val: <7 10 15 29| Scale is weakly epimorphic with val: <7 10 16 30| Scale is weakly epimorphic with val: <7 10 19 30| Scale is weakly epimorphic with val: <7 11 15 28| Scale is weakly epimorphic with val: <7 11 15 31| Scale is weakly epimorphic with val: <7 11 15 34| Scale is weakly epimorphic with val: <7 11 17 30| Scale is weakly epimorphic with val: <7 11 17 33| Scale is weakly epimorphic with val: <7 11 18 28| Scale is weakly epimorphic with val: <7 11 18 31| Scale is weakly epimorphic with val: <7 11 18 34| Scale is weakly epimorphic with val: <7 12 16 34| Scale is weakly epimorphic with val: <7 12 19 34| Scale is weakly epimorphic with val: <8 11 15 28| Scale is weakly epimorphic with val: <8 11 17 33| Scale is weakly epimorphic with val: <8 11 18 34| Scale is weakly epimorphic with val: <8 12 16 31|
FIT/MODE
3: 0 0 3 N M DE S SD: 55.6397 c. M: 93.6030 c. 4: 0 1 3 N G T3 SD: 22.2196 c. M:-30.9082 c. 5: 0 1 4 N G T3 SD: 13.6856 c. M: 22.9306 c. 6: 0 1 5 N G T3 SD: 14.5840 c. M: 22.9306 c. 10: 0 2 8 N G T3 SD: 13.6856 c. M: 22.9306 c. 11: 0 2 9 N G T3 SD: 13.3555 c. M: 22.9306 c. 13: 1 1 11 N M DE S SD: 13.2276 c. M: 16.9807 c. 14: 1 2 11 N T3 SD: 10.5203 c. M:-13.1209 c. 15: 1 2 12 N T3 SD: 6.8701 c. M:-10.2724 c. 16: 1 2 13 N T3 SD: 4.7344 c. M:-8.1972 c. 17: 1 2 14 N T3 SD: 4.9384 c. M:-6.3662 c. 20: 1 3 16 N T3 SD: 3.6496 c. M:-6.0060 c. 21: 1 3 17 N T3 SD: 0.8587 c. M:-1.2627 c. 43: 2 6 35 N T3 SD: 0.5613 c. M: 0.9435 c. 64: 3 9 52 N T3 SD: 0.2712 c. M:-0.4153 c. 85: 4 12 69 N T3 SD: 0.3046 c. M:-0.5068 c. 133: 6 19 108 N T3 SD: 0.2671 c. M: 0.4624 c. 154: 7 22 125 N T3 SD: 0.1996 c. M: 0.2922 c. 176: 8 25 143 N T3 SD: 0.2110 c. M: 0.2922 c. 197: 9 28 160 N T3 SD: 0.1083 c. M: 0.1773 c. 218: 10 31 177 N T3 SD: 0.0619 c. M: 0.0845 c. 261: 12 37 212 N T3 SD: 0.0608 c. M: 0.1003 c. 282: 13 40 229 N T3 SD: 0.0167 c. M:-0.0289 c. 761: 35 108 618 N T3 SD: 0.0166 c. M: 0.0244 c. 782: 36 111 635 N T3 SD: 0.0112 c. M:-0.0193 c. 1043: 48 148 847 N T3 SD: 0.0084 c. M: 0.0107 c. 1325: 61 188 1076 N T3 SD: 0.0048 c. M: 0.0081 c. 1607: 74 228 1305 N T3 SD: 0.0043 c. M: 0.0065 c. 1825: 84 259 1482 N T3 SD: 0.0042 c. M: 0.0069 c. 2107: 97 299 1711 N T3 SD: 0.0017 c. M: 0.0021 c. 2389: 110 339 1940 N T3 SD: 0.0014 c. M:-0.0019 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: 86.6339 cents 7 x 8:9 S SD: 75.6470 cents 8 x 9:11 SD: 61.2488 cents 9 x 10:12 S SD: 44.4003 cents 10 x 11:13 SD: 41.8906 cents 11 x 12:15 S SD: 34.5201 cents 12 x 13:16 SD: 22.4848 cents 13 x 14:17 SD: 24.1551 cents 14 x 15:19 SD: 20.0414 cents 15 x 16:20 S SD: 9.0641 cents 16 x 17:21 SD: 14.7666 cents 17 x 18:23 SD: 12.9172 cents 18 x 19:24 SD: 0.0000 cents 19 x 20:25 S SD: 11.7140 cents 20 x 21:27 SD: 11.6831 cents 21 x 22:28 SD: 6.5330 cents 22 x 23:29 SD: 12.9285 cents 23 x 24:31 SD: 13.6675 cents 24 x 25:32 SD: 11.4653 cents 25 x 26:33 SD: 15.5191 cents 26 x 27:35 SD: 16.3815 cents 27 x 29:36 SD: 15.0546 cents 28 x 30:37 SD: 15.0730 cents 29 x 31:39 SD: 13.2145 cents 30:31:32:40 S SD: 12.7955 cents 31:32:33:41 SD: 12.6352 cents 32:33:34:43 SD: 11.6954 cents 33:34:35:44 SD: 9.9720 cents 35:36:37:47 SD: 9.5818 cents 36:37:38:48 SD: 8.1678 cents 39:40:41:52 SD: 7.3496 cents 47:48:50:63 SD: 7.0696 cents 48:49:51:64 SD: 5.6946 cents 50:51:53:67 SD: 5.3369 cents 51:52:54:68 SD: 3.9839 cents 54:55:57:72 SD: 2.9454 cents 57:58:60:76 SD: 2.8789 cents 68:69:72:91 SD: 2.8770 cents 69:70:73:92 SD: 1.4749 cents 72:73:76:96 SD: 0.3163 cents 234:237:247:312 SD: 0.2921 cents 306:310:323:408 SD: 0.1489 cents 378:383:399:504 SD: 0.0603 cents 450:456:475:600 SD: 0.0000 cents