Scala analysis: xen12-wilson-08-4C3-tetrany-01
1-3-7-11 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/8 551.317942 undecimal semi-augmented fourth 2: 11/7 782.492036 undecimal augmented fifth 3: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 12/11 150.6371 undecimal neutral second, 3/4-tone 1: 11/8 551.3179 undecimal semi-augmented fourth 2: 8/7 231.1741 septimal whole tone 3: 7/6 266.8709 septimal minor third 4: 12/11 150.6371 undecimal neutral second, 3/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 4/3 498.045 cents perfect fourth 2: 1 3/2 701.955 cents perfect fifth 2: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 12/7 933.129 cents septimal major sixth 3: 1 7/4 968.826 cents harmonic seventh 3: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 4.00000 = 4
SHOW/LINE/CENTS INTERVALS
1 2 3 4 0.0 : 551.3 782.5 1049.4 1200.0 551.3 : 231.2 498.0 648.7 1200.0 782.5 : 266.9 417.5 968.8 1200.0 1049.4: 150.6 702.0 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 551.3179 cents 121/96, 400.6809 cents 12/11, 150.6371 cents 2: 417.5080 .. 782.4920 cents 121/98, 364.9841 cents 112/121,-133.8100 cents 3: 648.6821 .. 1049.3629 cents 121/96, 400.6809 cents 112/121,-133.8100 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 12/11, 150.6371 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 11/8, 551.3179 cents Average / Smallest step : 1.991542 Largest / Average step : 1.837726 Largest / Smallest step : 3.659909 Median interval of one step : 249.02250 cents, amount: 0 Least squares average step : 335.47969 cents, oct.: 1341.91878 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : DBCA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 53.27294 cents Scale diversity : 1.710650 Lumma stability : 0.251062 Lumma impropriety factor : 0.223017 Rothenberg efficiency : 0.500000 redundancy: 0.500000 Efficiency x scale size : 2.000000 Number of different interval sizes : 12 = 4.00000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 4.00000 = 4 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 49/48, 35.6968 cents Number of recognisable fifths : 1, average 701.9550 cents Best minor thirds form a closed circle Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.028462 Average absolute harmonicity : 0.282027 Specific harmonicity : 0.139742 Fundamental : 1/168, -7.3923 octaves, 1.5573 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 3.696000E+03, 11.85175 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 28.5, average 7.12500 Mersenne's string divisions : 5814 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 5.95155, average 1.48789 Vogel's harmonic complexity : 18.00000 Wille's k value : 115 Wilson's harmonic complexity : 21 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 22.74358, average 2.27436 Lattice compactness (without 2's) : 11.07107, average 1.10711 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 5 1 3: -1 .. 0 -0.25000 1 7: -1 .. 0 -0.25000 1 11: 0 .. 1 0.75000 3 3 Average exponent except 2's : 1 / 4 = 0.25000 Average absolute exponent except 2's: 5 / 4 = 1.25000 Scale is weakly epimorphic with val: <4 5 10 15| Scale is weakly epimorphic with val: <4 5 11 14| Scale is JI-epimorphic with val: <4 6 11 13| Scale is weakly epimorphic with val: <4 7 10 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 172.3175 c. M: 251.3179 c. 5: 2 1 1 1 P M ME SD: 65.1484 c. M: 89.3629 c. 6: 3 1 1 1 N M DE SD: 35.7532 c. M: 49.3629 c. 8: 4 1 2 1 N D3 SD: 29.2664 c. M:-48.6821 c. 9: 4 2 2 1 N SD: 15.2430 c. M: 17.9846 c. 15: 7 3 3 2 N SD: 10.8348 c. M:-17.5080 c. 17: 8 3 4 2 N SD: 8.7321 c. M:-13.3879 c. 26: 12 5 6 3 N SD: 6.3076 c. M:-12.1755 c. 31: 14 6 7 4 N SD: 6.6059 c. M: 9.3825 c. 32: 15 6 7 4 N SD: 6.1344 c. M:-11.1821 c. 37: 17 7 8 5 N SD: 6.1186 c. M: 11.5251 c. 40: 18 8 9 5 N SD: 5.8033 c. M: 11.3179 c. 41: 19 8 9 5 N SD: 5.0346 c. M:-7.7519 c. 46: 21 9 10 6 N SD: 3.4218 c. M: 5.8847 c. 54: 25 10 12 7 N SD: 4.0116 c. M: 4.9185 c. 55: 25 11 12 7 N SD: 3.4469 c. M: 5.8634 c. 57: 26 11 13 7 N SD: 3.1164 c. M: 3.9495 c. 63: 29 12 14 8 N SD: 1.2788 c. M: 1.7439 c. 72: 33 14 16 9 N SD: 0.8442 c. M: 1.3179 c. 135: 62 26 30 17 N SD: 0.2917 c. M: 0.4741 c. 342: 157 66 76 43 N SD: 0.2516 c. M: 0.4407 c. 359: 165 69 80 45 N SD: 0.2213 c. M: 0.3193 c. 431: 198 83 96 54 N SD: 0.1589 c. M:-0.2890 c. 566: 260 109 126 71 N SD: 0.1044 c. M: 0.1599 c. 701: 322 135 156 88 N SD: 0.1048 c. M: 0.1811 c. 836: 384 161 186 105 N SD: 0.1220 c. M: 0.1954 c. 877: 403 169 195 110 N SD: 0.1203 c. M:-0.1762 c. 940: 432 181 209 118 N SD: 0.0910 c. M:-0.1714 c. 1012: 465 195 225 127 N SD: 0.0704 c. M:-0.1167 c. 1075: 494 207 239 135 N SD: 0.0697 c. M:-0.1239 c. 1147: 527 221 255 144 N SD: 0.0402 c. M:-0.0712 c. 1282: 589 247 285 161 N SD: 0.0372 c. M: 0.0650 c. 1578: 725 304 351 198 N SD: 0.0351 c. M:-0.0667 c. 1641: 754 316 365 206 N SD: 0.0340 c. M:-0.0532 c. 1713: 787 330 381 215 N SD: 0.0125 c. M:-0.0241 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 40.2685 cents 3:4:5 x 6 S SD: 38.3186 cents 4 x 6:7:8 S SD: 37.9655 cents 5:7:8:9:10 SD: 13.5906 cents 11:15:17:20:22 SD: 8.8226 cents 14:19:22:26:28 SD: 7.9498 cents 16:22:25:29:32 SD: 5.5271 cents 19:26:30:35:38 SD: 3.5840 cents 24:33:38:44:48 SD: 3.2665 cents 30:41:47:55:60 SD: 2.9407 cents 35:48:55:64:70 SD: 1.5919 cents 56:77:88:103:112 SD: 1.4029 cents 61:84:96:112:122 SD: 1.1164 cents 72:99:113:132:144 SD: 0.5468 cents 96:132:151:176:192 SD: 0.4097 cents 168:231:264:308:336 SD: 0.0000 cents