Scala analysis: 112_E13
Enharmonic tetrachord 76/75 * 20/19 * 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 76/75 22.930588 2: 16/15 111.731285 minor diatonic semitone 3: 4/3 498.044999 perfect fourth
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 76/75 22.9306 2: 20/19 88.8007 small undevicesimal semitone 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 76/75 22.931 cents 1: 1 20/19 88.801 cents small undevicesimal semitone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 19/15 409.244 cents undevicesimal ditone 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 : 22.9 111.7 498.0 22.9 : 88.8 475.1 498.0 111.7: 386.3 409.2 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.9306 .. 386.3137 cents 375/304, 363.3831 cents 76/75, 22.9306 cents 2: 111.7313 .. 475.1144 cents 375/304, 363.3831 cents 64/75,-274.5824 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 : 5/4, 386.3137 cents Average / Smallest step : 7.239893 Largest / Average step : 2.326981 Largest / Smallest step : 16.847092 Median interval of one step : 20/19, 88.8007 cents, amount: 1 Least squares average step : 124.32344 cents, oct.: 372.97032 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1520-tone equal temperament with octave 4/3 degrees: 70 341 1520 Least number of segments generator : 761 of 249.350 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1057 of 346.338 cents and inv. generated superset size: 28 = 25 more = 933.333% 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 : 0.412316 Lumma stability : 0.092082 Lumma impropriety factor : 0.551321 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 All steps are superparticular (epimoric) 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 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 : 0.018666 Average absolute harmonicity : 0.103402 Specific harmonicity : 0.095742 Fundamental : 1/75, -6.2288 octaves, 3.4883 Hz. Guide tone : 304, 8.2479 octaves, 79534.172 Hz. Exponens Consonantiae : 2.280000E+04, 14.47675 octaves Euler's gradus suavitatis : 33 Sum of Mann's harmonic distance : 94.5, average 31.50000 Mersenne's string divisions : 32767 Sum of van Prooijen's expressibility: 3.52827, average 1.17609 Sum of Tenney's harmonic distance : 7.21527, average 2.40509 Vogel's harmonic complexity : 14.00000 Wille's k value : 12 Wilson's harmonic complexity : 32 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 16.56261, average 2.76044 Lattice compactness (without 2's) : 9.51398, average 1.58566 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 2.66667 8 3: -1 ..-1 -1.00000 3 1 5: -2 .. 0 -1.00000 3 1 19: 0 .. 1 0.33333 1 1 Average exponent except 2's :-5 / 3 =-1.66667 Average absolute exponent except 2's: 7 / 3 = 2.33333 Scale is weakly epimorphic with val: <6 10 16 33| Scale is weakly epimorphic with val: <7 10 15 28| Scale is weakly epimorphic with val: <7 10 15 31| Scale is weakly epimorphic with val: <7 10 15 34| Scale is weakly epimorphic with val: <7 10 16 31| Scale is JI-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 16 28| Scale is weakly epimorphic with val: <7 11 16 31| Scale is weakly epimorphic with val: <7 11 16 34| 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 11 19 28| Scale is weakly epimorphic with val: <7 11 19 31| Scale is weakly epimorphic with val: <7 11 19 34| Scale is weakly epimorphic with val: <7 12 15 31| Scale is weakly epimorphic with val: <8 11 17 32| Scale is weakly epimorphic with val: <8 11 18 29| Scale is weakly epimorphic with val: <8 11 18 32| Scale is weakly epimorphic with val: <8 12 15 29| Scale is weakly epimorphic with val: <8 12 17 29| Scale is weakly epimorphic with val: <8 12 17 32|
FIT/MODE
3: 0 1 2 N G T3 SD: 34.0222 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 15.1563 c. M: 22.9306 c. 5: 0 1 4 N G T3 SD: 14.9751 c. M: 22.9306 c. 9: 0 2 7 N G T3 SD: 13.2530 c. M: 22.9306 c. 13: 1 2 10 N T3 SD: 9.0704 c. M:-15.3806 c. 14: 1 2 11 N T3 SD: 7.8517 c. M:-12.6441 c. 15: 1 2 12 N T3 SD: 9.1737 c. M: 12.1223 c. 16: 1 3 12 N T3 SD: 8.7659 c. M:-12.7800 c. 17: 1 3 13 N T3 SD: 4.8406 c. M:-6.3662 c. 18: 1 3 14 N T3 SD: 2.8028 c. M:-4.7386 c. 22: 1 4 17 N T3 SD: 0.8601 c. M:-1.4608 c. 45: 2 8 35 N T3 SD: 0.7626 c. M: 1.0546 c. 63: 3 11 49 N T3 SD: 0.7593 c. M: 1.0546 c. 67: 3 12 52 N T3 SD: 0.3870 c. M: 0.6301 c. 85: 4 15 66 N T3 SD: 0.3741 c. M:-0.5068 c. 89: 4 16 69 N T3 SD: 0.3339 c. M: 0.5465 c. 107: 5 19 83 N T3 SD: 0.1981 c. M:-0.3425 c. 129: 6 23 100 N T3 SD: 0.1905 c. M:-0.2343 c. 152: 7 27 118 N T3 SD: 0.1885 c. M: 0.3265 c. 174: 8 31 135 N T3 SD: 0.0609 c. M: 0.1005 c. 196: 9 35 152 N T3 SD: 0.0558 c. M:-0.0747 c. 303: 14 54 235 N T3 SD: 0.0527 c. M:-0.0814 c. 370: 17 66 287 N T3 SD: 0.0277 c. M: 0.0474 c. 477: 22 85 370 N T3 SD: 0.0239 c. M:-0.0400 c. 651: 30 116 505 N T3 SD: 0.0233 c. M: 0.0346 c. 673: 31 120 522 N T3 SD: 0.0103 c. M:-0.0143 c. 847: 39 151 657 N T3 SD: 0.0055 c. M: 0.0093 c. 1520: 70 271 1179 N T3 SD: 0.0034 c. M:-0.0057 c. 1890: 87 337 1466 N T3 SD: 0.0027 c. M: 0.0047 c. 2367: 109 422 1836 N T3 SD: 0.0029 c. M:-0.0043 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: 77.5698 cents 7 x 8:9 S SD: 67.5105 cents 8 x 9:11 SD: 53.2328 cents 9 x 10:12 S SD: 35.3362 cents 10 x 11:13 SD: 34.4934 cents 11 x 12:15 S SD: 27.5105 cents 12 x 13:16 SD: 13.4207 cents 13 x 14:17 SD: 18.7389 cents 14 x 15:19 SD: 15.7988 cents 15 x 16:20 S SD: 0.0000 cents 16 x 17:21 SD: 14.0467 cents 17 x 18:23 SD: 14.1599 cents 18 x 19:24 SD: 9.0641 cents 19 x 20:25 S SD: 16.2144 cents 20 x 21:27 SD: 17.3627 cents 21 x 22:28 SD: 15.5971 cents 22 x 23:29 SD: 20.0048 cents 23 x 25:31 SD: 18.8048 cents 24 x 26:32 SD: 13.4207 cents 25 x 27:33 SD: 13.8317 cents 29:30:31:39 SD: 12.9682 cents 30:31:32:40 S SD: 11.2788 cents 33:34:35:44 SD: 10.1324 cents 39:40:42:52 SD: 8.8900 cents 40:41:43:53 SD: 8.7692 cents 41:42:44:55 S SD: 7.9896 cents 42:43:45:56 SD: 6.4681 cents 44:45:47:59 SD: 6.3022 cents 45:46:48:60 S SD: 5.0400 cents 48:49:51:64 SD: 4.8177 cents 56:57:60:75 S SD: 4.4522 cents 57:58:61:76 SD: 3.0525 cents 60:61:64:80 SD: 1.8952 cents 72:73:77:96 SD: 1.5338 cents 75:76:80:100 S SD: 0.0000 cents