Scala analysis: 105_E13
Enharmonic tetrachord 48/47 * 47/45 * 5/4
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 48/47 36.448379 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: 48/47 36.4484 2: 47/45 75.2829 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 48/47 36.448 cents 1: 1 47/45 75.283 cents 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 60/47 422.762 cents 2: 1 47/36 461.597 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 : 36.4 111.7 498.0 36.4 : 75.3 461.6 498.0 111.7: 386.3 422.8 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 36.4484 .. 386.3137 cents 235/192, 349.8653 cents 48/47, 36.4484 cents 2: 111.7313 .. 461.5966 cents 235/192, 349.8653 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 48/47, 36.4484 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 4.554798 Largest / Average step : 2.326981 Largest / Smallest step : 10.598927 Median interval of one step : 47/45, 75.2829 cents, amount: 1 Least squares average step : 125.28900 cents, oct.: 375.86699 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1052-tone equal temperament with octave 4/3 degrees: 77 236 1052 Least number of segments generator : 527 of 249.496 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 857 of 405.727 cents and inv. generated superset size: 18 = 15 more = 600.000% 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 36.44838 cents Scale diversity : 0.473969 Lumma stability : 0.146366 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 : 48/47, 36.4484 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 : 47 Odd number limit : 47 (O: 47 U: 47) Highest odd numerator or denominator: 47 Scale harmonicity : 0.063559 Fundamental : 1/705, -9.4615 octaves, 0.3711 Hz. Guide tone : 48, 5.5850 octaves, 12558.027 Hz. Exponens Consonantiae : 3.384000E+04, 15.04644 octaves Euler's gradus suavitatis : 59 Sum of Mann's harmonic distance : 66.5, average 22.16667 Mersenne's string divisions : 20615 Sum of van Prooijen's expressibility: 3.32531, average 1.10844 Sum of Tenney's harmonic distance : 6.81273, average 2.27091 Vogel's harmonic complexity : 40.00000 Wille's k value : 117 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 17.90238, average 2.98373 Lattice compactness (without 2's) : 8.65028, average 1.44171 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 4 3.33333 10 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.33333 1 1 47: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-3 / 3 =-1.00000 Average absolute exponent except 2's: 5 / 3 = 1.66667 Scale is weakly epimorphic with val: <7 10 15 39| Scale is weakly epimorphic with val: <7 10 15 42| Scale is JI-epimorphic with val: <7 11 15 38| Scale is weakly epimorphic with val: <7 11 15 41| Scale is weakly epimorphic with val: <7 11 16 37| Scale is weakly epimorphic with val: <7 11 16 40| Scale is weakly epimorphic with val: <7 11 16 43| Scale is weakly epimorphic with val: <7 11 18 38| Scale is weakly epimorphic with val: <7 11 18 41| Scale is weakly epimorphic with val: <7 11 19 37| Scale is weakly epimorphic with val: <7 11 19 40| Scale is weakly epimorphic with val: <7 11 19 43| Scale is weakly epimorphic with val: <7 12 15 37| Scale is weakly epimorphic with val: <7 12 18 37| Scale is weakly epimorphic with val: <8 11 17 40| Scale is weakly epimorphic with val: <8 11 18 39| Scale is weakly epimorphic with val: <8 11 18 42| Scale is weakly epimorphic with val: <8 12 15 41| Scale is weakly epimorphic with val: <8 12 17 39| Scale is weakly epimorphic with val: <8 12 17 42| Scale is weakly epimorphic with val: <8 12 18 41|
FIT/MODE
3: 0 1 2 N G T3 SD: 37.7501 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 22.2996 c. M: 36.4484 c. 5: 0 1 4 N G T3 SD: 22.1768 c. M: 36.4484 c. 8: 1 1 6 N M DE S SD: 16.6267 c. M:-25.8072 c. 9: 1 1 7 N M DE S SD: 10.9231 c. M:-18.8900 c. 10: 1 1 8 N M DE S SD: 10.4137 c. M:-13.3561 c. 12: 1 2 9 N T3 SD: 7.9348 c. M:-12.7800 c. 13: 1 2 10 N T3 SD: 2.1388 c. M:-3.2022 c. 27: 2 4 21 N T3 SD: 0.6606 c. M: 1.0546 c. 40: 3 6 31 N T3 SD: 0.5559 c. M:-0.9050 c. 67: 5 10 52 N T3 SD: 0.4357 c. M:-0.7192 c. 94: 7 14 73 N T3 SD: 0.4571 c. M:-0.6401 c. 107: 8 16 83 N T3 SD: 0.4555 c. M:-0.7886 c. 111: 8 17 86 N T3 SD: 0.4085 c. M: 0.5532 c. 125: 9 19 97 N T3 SD: 0.3539 c. M: 0.5891 c. 138: 10 21 107 N T3 SD: 0.2238 c. M: 0.3582 c. 165: 12 25 128 N T3 SD: 0.1340 c. M: 0.2269 c. 178: 13 27 138 N T3 SD: 0.1172 c. M:-0.1889 c. 192: 14 29 149 N T3 SD: 0.1337 c. M: 0.1900 c. 205: 15 31 159 N T3 SD: 0.0149 c. M:-0.0252 c. 642: 47 97 498 N T3 SD: 0.0139 c. M: 0.0203 c. 847: 62 128 657 N T3 SD: 0.0072 c. M: 0.0093 c. 1052: 77 159 816 N T3 SD: 0.0035 c. M:-0.0055 c. 1257: 92 190 975 N T3 SD: 0.0024 c. M:-0.0036 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 23:24:25:31 SD: 17.6406 cents 24:25:26:32 SD: 14.4981 cents 25:26:27:33 SD: 13.9622 cents 26:27:28:35 S SD: 12.3985 cents 27:28:29:36 SD: 9.6980 cents 29:30:31:39 SD: 9.0030 cents 30:31:32:40 S SD: 6.7728 cents 33:34:35:44 SD: 6.0497 cents 39:40:42:52 SD: 6.0458 cents 41:42:44:55 S SD: 5.2630 cents 42:43:45:56 SD: 2.9412 cents 45:46:48:60 S SD: 0.5341 cents 195:199:208:260 SD: 0.4317 cents 240:245:256:320 SD: 0.2505 cents 285:291:304:380 SD: 0.1266 cents 330:337:352:440 SD: 0.0364 cents 375:383:400:500 SD: 0.0321 cents