Scala analysis: 113_E13
Enharmonic tetrachord 96/95 * 19/18 * 5/4, Wilson
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 96/95 18.128271 19th-partial chroma 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: 96/95 18.1283 19th-partial chroma 2: 19/18 93.6030 undevicesimal semitone 3: 5/4 386.3137 major third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 96/95 18.128 cents 19th-partial chroma 1: 1 19/18 93.603 cents undevicesimal semitone 1: 1 5/4 386.314 cents major third 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 24/19 404.442 cents smaller undevicesimal major third 2: 1 95/72 479.917 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 : 18.1 111.7 498.0 18.1 : 93.6 479.9 498.0 111.7: 386.3 404.4 498.0 498.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 18.1283 .. 386.3137 cents 475/384, 368.1854 cents 96/95, 18.1283 cents 2: 111.7313 .. 479.9167 cents 475/384, 368.1854 cents 64/75,-274.5824 cents
SHOW DATA
Number of notes : 3 -- Interval properties -- Smallest interval : 96/95, 18.1283 cents, class 1 Average step (divided formal octave): 166.0150 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 9.157796 Largest / Average step : 2.326981 Largest / Smallest step : 21.310014 Median interval of one step : 19/18, 93.6030 cents, amount: 1 Least squares average step : 123.98042 cents, oct.: 371.94125 cents Scale is not proper Scale has trivalence property Scale is a mode of a 1676-tone equal temperament with octave 4/3 degrees: 61 376 1676 Least number of segments generator : 839 of 249.320 cents and inv. number of contiguous generator circle segments: 1 Shortest superset generator : 1483 of 440.693 cents and inv. generated superset size: 29 = 26 more = 966.667% 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 18.12827 cents Scale diversity : 0.385445 Lumma stability : 0.072798 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 : 96/95, 18.1283 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 : 95 (O: 95 U: 95) Highest odd numerator or denominator: 95 Scale harmonicity : 0.019670 Average absolute harmonicity : 0.103858 Specific harmonicity : 0.097810 Fundamental : 1/285, -8.1548 octaves, 0.9180 Hz. Guide tone : 96, 6.5850 octaves, 25116.054 Hz. Exponens Consonantiae : 2.736000E+04, 14.73978 octaves Euler's gradus suavitatis : 32 Sum of Mann's harmonic distance : 114.5, average 38.16667 Mersenne's string divisions : 41447 Sum of van Prooijen's expressibility: 3.63094, average 1.21031 Sum of Tenney's harmonic distance : 7.41939, average 2.47313 Vogel's harmonic complexity : 20.00000 Wille's k value : 47 Wilson's harmonic complexity : 30 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 20.32875, average 3.38813 Lattice compactness (without 2's) : 9.83182, average 1.63864 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 2 .. 5 3.66667 11 3: -1 .. 1 -0.33333 3 1 5: -1 .. 0 -0.66667 2 1 19: -1 .. 0 -0.33333 1 1 Average exponent except 2's :-4 / 3 =-1.33333 Average absolute exponent except 2's: 6 / 3 = 2.00000 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 JI-epimorphic with val: <7 11 15 30| Scale is weakly epimorphic with val: <7 11 15 33| 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 30| Scale is weakly epimorphic with val: <7 11 18 33| 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 29| Scale is weakly epimorphic with val: <8 11 17 31| 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 34| Scale is weakly epimorphic with val: <8 12 17 30| Scale is weakly epimorphic with val: <8 12 17 33| Scale is weakly epimorphic with val: <8 12 18 31|
FIT/MODE
3: 0 1 2 N G T3 SD: 33.0422 c. M:-54.2837 c. 4: 0 1 3 N G T3 SD: 12.8057 c. M: 18.1283 c. 5: 0 1 4 N G T3 SD: 12.5908 c. M: 18.1283 c. 9: 0 2 7 N G T3 SD: 10.4841 c. M: 18.1283 c. 17: 1 3 13 N T3 SD: 7.1764 c. M:-11.1685 c. 18: 1 3 14 N T3 SD: 5.5420 c. M:-9.5409 c. 19: 1 3 15 N T3 SD: 6.1289 c. M:-8.0846 c. 21: 1 4 16 N T3 SD: 5.1043 c. M:-6.8509 c. 22: 1 4 17 N T3 SD: 2.7371 c. M:-4.5101 c. 23: 1 4 18 N T3 SD: 2.8523 c. M:-3.5259 c. 26: 1 5 20 N T3 SD: 1.9416 c. M:-3.2022 c. 27: 1 5 21 N T3 SD: 0.6359 c. M: 1.0546 c. 53: 2 10 41 N T3 SD: 0.7099 c. M:-1.0336 c. 58: 2 11 45 N T3 SD: 0.5540 c. M: 0.9543 c. 80: 3 15 62 N T3 SD: 0.3692 c. M:-0.5484 c. 107: 4 20 83 N T3 SD: 0.2833 c. M:-0.4902 c. 111: 4 21 86 N T3 SD: 0.2752 c. M:-0.4410 c. 138: 5 26 107 N T3 SD: 0.0982 c. M:-0.1484 c. 165: 6 31 128 N T3 SD: 0.0298 c. M: 0.0485 c. 303: 11 57 235 N T3 SD: 0.0363 c. M: 0.0474 c. 468: 17 88 363 N T3 SD: 0.0220 c. M: 0.0369 c. 633: 23 119 491 N T3 SD: 0.0187 c. M: 0.0318 c. 798: 29 150 619 N T3 SD: 0.0186 c. M: 0.0289 c. 878: 32 165 681 N T3 SD: 0.0168 c. M:-0.0237 c. 1043: 38 196 809 N T3 SD: 0.0106 c. M:-0.0172 c. 1208: 44 227 937 N T3 SD: 0.0072 c. M:-0.0124 c. 1373: 50 258 1065 N T3 SD: 0.0064 c. M:-0.0088 c. 1511: 55 284 1172 N T3 SD: 0.0043 c. M:-0.0075 c. 1676: 61 315 1300 N T3 SD: 0.0014 c. M:-0.0020 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 26 x 28:35 S SD: 11.7146 cents 33:34:35:44 SD: 11.6581 cents 36:37:38:48 SD: 11.4865 cents 39:40:42:52 SD: 10.1931 cents 40:41:43:53 SD: 10.0305 cents 41:42:44:55 S SD: 9.2977 cents 42:43:45:56 SD: 7.9625 cents 44:45:47:59 SD: 7.7025 cents 45:46:48:60 S SD: 6.6408 cents 48:49:51:64 SD: 6.2766 cents 54:55:58:72 SD: 6.0511 cents 55:56:59:73 SD: 6.0474 cents 56:57:60:75 S SD: 5.5330 cents 57:58:61:76 SD: 4.4205 cents 60:61:64:80 SD: 3.4959 cents 72:73:77:96 SD: 2.4347 cents 75:76:80:100 S SD: 1.6008 cents 87:88:93:116 SD: 1.3597 cents 90:91:96:120 SD: 0.3339 cents 195:197:208:260 SD: 0.1542 cents 285:288:304:380 S SD: 0.0000 cents