Scala analysis: xen12-wilson-38-4C3-tetrany-08
1-5-9-11 4C3 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/10 165.004228 Ptolemy's second, 4/5-tone 2: 11/9 347.407941 undecimal neutral third 3: 11/8 551.317942 undecimal semi-augmented fourth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/11 648.6821 undecimal semi-diminished fifth 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 16/11 648.6821 undecimal semi-diminished fifth
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 16/11 648.682 cents undecimal semi-diminished fifth 2: 1 11/9 347.408 cents undecimal neutral third 2: 1 5/4 386.314 cents major third 2: 1 8/5 813.686 cents minor sixth 2: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 11/8 551.318 cents undecimal semi-augmented fourth 3: 1 16/9 996.090 cents Pythagorean minor seventh 3: 1 9/5 1017.596 cents just minor seventh, BP seventh 3: 1 20/11 1034.996 cents large minor seventh 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 : 165.0 347.4 551.3 1200.0 165.0 : 182.4 386.3 1035.0 1200.0 347.4 : 203.9 852.6 1017.6 1200.0 551.3 : 648.7 813.7 996.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 648.6821 cents 160/121, 483.6778 cents 11/10, 165.0042 cents 2: 347.4079 .. 852.5921 cents 162/121, 505.1841 cents 121/144,-301.2741 cents 3: 551.3179 .. 1034.9958 cents 160/121, 483.6778 cents 121/144,-301.2741 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 11/10, 165.0042 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 16/11, 648.6821 cents Average / Smallest step : 1.818135 Largest / Average step : 2.162274 Largest / Smallest step : 3.931306 Median interval of one step : 193.15686 cents, amount: 0 Least squares average step : 243.79246 cents, oct.: 975.16986 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : ABCD Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 97.36412 cents Scale diversity : 1.566594 Lumma stability : 0.275007 Lumma impropriety factor : 0.420987 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 : 100/99, 17.3995 cents Number of recognisable fifths : 0 Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 3 at degree 0 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 466.2783 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.029485 Average absolute harmonicity : 0.282206 Specific harmonicity : 0.143658 Fundamental : 1/360, -8.4919 octaves, 0.7267 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 7.920000E+03, 12.95128 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 31.5, average 7.87500 Mersenne's string divisions : 7980 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.28254, average 1.57064 Vogel's harmonic complexity : 18.75000 Wille's k value : 247 Wilson's harmonic complexity : 22 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 25.44359, average 2.54436 Lattice compactness (without 2's) : 14.53663, average 1.45366 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.75000 5 1 3: -2 .. 0 -0.50000 2 5: -1 .. 0 -0.25000 1 11: 0 .. 1 0.75000 3 3 Average exponent except 2's : 0 / 4 = 0.00000 Average absolute exponent except 2's: 6 / 4 = 1.50000 Scale is weakly epimorphic with val: <4 5 9 15| Scale is weakly epimorphic with val: <4 7 9 15|
FIT/MODE
4: 1 0 1 2 N D3 SD: 75.5667 c. M:-134.9958 c. 5: 1 0 1 3 N D3 SD: 74.5773 c. M: 107.4079 c. 6: 1 1 1 3 N M DE SD: 39.8766 c. M:-52.5921 c. 7: 1 1 1 4 N M DE SD: 18.9299 c. M: 37.0322 c. 13: 2 2 2 7 N M DE SD: 14.7243 c. M:-21.8228 c. 15: 2 2 3 8 N SD: 14.5912 c. M: 27.4079 c. 17: 2 3 3 9 N SD: 13.9429 c. M: 23.8278 c. 20: 3 3 3 11 N M DE SD: 11.3085 c. M:-14.9958 c. 21: 3 3 4 11 N SD: 10.7984 c. M:-20.1106 c. 22: 3 3 4 12 N SD: 10.5081 c. M: 20.1352 c. 24: 3 4 4 13 N SD: 7.6417 c. M: 15.0042 c. 28: 4 4 5 15 N SD: 4.8967 c. M:-6.4243 c. 35: 5 5 6 19 N SD: 4.1691 c. M:-6.4243 c. 52: 7 8 9 28 N SD: 2.2347 c. M: 3.4658 c. 59: 8 9 10 32 N SD: 1.7784 c. M: 2.2924 c. 72: 10 11 12 39 N SD: 1.6748 c. M:-2.5921 c. 87: 12 13 15 47 N SD: 1.3310 c. M: 2.5804 c. 124: 17 19 21 67 N SD: 0.5666 c. M:-0.9792 c. 159: 22 24 27 86 N SD: 0.5624 c. M:-1.0335 c. 183: 25 28 31 99 N SD: 0.5938 c. M: 1.0698 c. 211: 29 32 36 114 N SD: 0.3002 c. M: 0.4885 c. 283: 39 43 48 153 N SD: 0.2389 c. M:-0.3668 c. 335: 46 51 57 181 N SD: 0.1999 c. M:-0.3238 c. 342: 47 52 58 185 N SD: 0.2260 c. M: 0.4407 c. 459: 63 70 78 248 N SD: 0.2653 c. M:-0.3160 c. 466: 64 71 79 252 N SD: 0.1953 c. M: 0.2450 c. 494: 68 75 84 267 N SD: 0.1037 c. M:-0.1780 c. 618: 85 94 105 334 N SD: 0.1099 c. M:-0.1649 c. 677: 93 103 115 366 N SD: 0.0856 c. M: 0.1593 c. 836: 115 127 142 452 N SD: 0.0724 c. M: 0.1218 c. 960: 132 146 163 519 N SD: 0.0572 c. M:-0.0921 c. 1171: 161 178 199 633 N SD: 0.0110 c. M: 0.0170 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 75.3185 cents 3 x x 4:6 S SD: 26.6365 cents 4 x 5:6:8 S SD: 51.8600 cents 5 x 6:7:10 SD: 14.8406 cents 6 x 7:8:12 S SD: 32.1873 cents 7:8:9:10:14 SD: 32.0586 cents 8:9:10:11:16 SD: 13.7553 cents 10:11:12:14:20 SD: 11.1305 cents 13:14:16:18:26 SD: 10.1194 cents 18:20:22:25:36 SD: 6.1516 cents 19:21:23:26:38 SD: 5.0889 cents 27:30:33:37:54 SD: 4.5883 cents 31:34:38:43:62 SD: 4.1945 cents 32:35:39:44:64 SD: 2.7565 cents 40:44:49:55:80 SD: 0.9825 cents 90:99:110:124:180 SD: 0.8735 cents 99:109:121:136:198 SD: 0.5621 cents 131:144:160:180:262 SD: 0.5204 cents 139:153:170:191:278 SD: 0.4902 cents 149:164:182:205:298 SD: 0.4573 cents 171:188:209:235:342 SD: 0.3255 cents 189:208:231:260:378 SD: 0.2943 cents 261:287:319:359:522 SD: 0.2132 cents 320:352:391:440:640 SD: 0.1230 cents 360:396:440:495:720 SD: 0.0000 cents