Scala analysis: xen12-wilson-08-4C3-tetrany-10
3-7-9-11 4C3 Tetrany, Figure 8
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 11/9 347.407941 undecimal neutral third 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: 11/9 347.4079 undecimal neutral third 2: 9/7 435.0841 septimal major third, BP third 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 7/6 266.871 cents septimal minor third 1: 1 11/9 347.408 cents undecimal neutral third 1: 1 9/7 435.084 cents septimal major third, BP third 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 14/9 764.916 cents septimal minor sixth 3: 1 18/11 852.592 cents undecimal neutral sixth 3: 1 12/7 933.129 cents septimal major sixth 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 : 347.4 782.5 1049.4 1200.0 347.4 : 435.1 702.0 852.6 1200.0 782.5 : 266.9 417.5 764.9 1200.0 1049.4: 150.6 498.0 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 150.6371 .. 435.0841 cents 33/28, 284.4470 cents 12/11, 150.6371 cents 2: 417.5080 .. 782.4920 cents 121/98, 364.9841 cents 98/99,-17.5761 cents 3: 764.9159 .. 1049.3629 cents 33/28, 284.4470 cents 98/99,-17.5761 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 : 9/7, 435.0841 cents Average / Smallest step : 1.991542 Largest / Average step : 1.450280 Largest / Smallest step : 2.888294 Median interval of one step : 307.13942 cents, amount: 0 Least squares average step : 328.68269 cents, oct.: 1314.73078 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : CDBA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 17.57613 cents Scale diversity : 1.654335 Lumma stability : 0.251062 Lumma impropriety factor : 0.029294 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 : 99/98, 17.5761 cents Number of recognisable fifths : 1, average 701.9550 cents Best minor thirds form a closed circle Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.027932 Average absolute harmonicity : 0.280855 Specific harmonicity : 0.135207 Fundamental : 1/126, -6.9773 octaves, 2.0764 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 2.772000E+03, 11.43671 octaves Euler's gradus suavitatis : 23 Sum of Mann's harmonic distance : 29.0, average 7.25000 Mersenne's string divisions : 3060 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.00270, average 1.50067 Vogel's harmonic complexity : 18.25000 Wille's k value : 115 Wilson's harmonic complexity : 24 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 18.39569, average 1.83957 Lattice compactness (without 2's) : 14.77927, average 1.47793 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 0.00000 2 1 3: -2 .. 0 -0.75000 3 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: 7 / 4 = 1.75000 Scale is weakly epimorphic with val: <4 5 12 15| Scale is JI-epimorphic with val: <4 6 11 13| Scale is weakly epimorphic with val: <4 7 12 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 120.2707 c. M: 182.4920 c. 5: 1 2 1 1 P M ME SD: 76.5302 c. M: 107.4079 c. 6: 2 2 1 1 P D3 S SD: 37.1118 c. M:-52.5921 c. 8: 2 3 2 1 P G D3 SD: 28.7387 c. M: 47.4079 c. 9: 3 3 2 1 P SD: 29.0339 c. M:-52.5921 c. 11: 3 4 3 1 P G D3 SD: 24.9351 c. M:-41.5461 c. 14: 4 5 3 2 P SD: 11.9937 c. M: 20.7915 c. 17: 5 6 4 2 P SD: 6.2525 c. M:-9.4606 c. 31: 9 11 7 4 P SD: 4.6765 c. M: 8.2985 c. 38: 11 14 8 5 N SD: 5.0353 c. M: 7.2577 c. 41: 12 15 9 5 N SD: 4.8237 c. M:-7.7519 c. 48: 14 17 11 6 P SD: 3.9767 c. M: 7.4920 c. 49: 14 18 11 6 N SD: 2.9909 c. M: 4.5508 c. 55: 16 20 12 7 N SD: 1.9986 c. M:-2.9625 c. 72: 21 26 16 9 N SD: 1.3993 c. M:-2.5921 c. 80: 23 29 18 10 N SD: 1.7617 c. M: 2.4920 c. 86: 25 31 19 11 N SD: 1.6864 c. M: 2.8513 c. 103: 30 37 23 13 N SD: 1.4795 c. M:-2.1066 c. 104: 30 38 23 13 N SD: 1.2735 c. M:-2.1233 c. 118: 34 43 26 15 N SD: 1.2893 c. M: 1.9053 c. 121: 35 44 27 15 N SD: 1.0690 c. M:-1.8767 c. 135: 39 49 30 17 N SD: 0.4602 c. M: 0.7413 c. 207: 60 75 46 26 N SD: 0.2214 c. M:-0.4181 c. 342: 99 124 76 43 N SD: 0.1230 c. M: 0.2401 c. 549: 159 199 122 69 N SD: 0.1135 c. M: 0.1826 c. 701: 203 254 156 88 N SD: 0.1024 c. M: 0.1811 c. 805: 233 292 179 101 N SD: 0.0805 c. M:-0.1167 c. 1012: 293 367 225 127 N SD: 0.0634 c. M:-0.1167 c. 1147: 332 416 255 144 N SD: 0.0496 c. M:-0.0712 c. 1299: 376 471 289 163 N SD: 0.0489 c. M: 0.0638 c. 1354: 392 491 301 170 N SD: 0.0416 c. M:-0.0781 c. 1506: 436 546 335 189 N SD: 0.0226 c. M:-0.0394 c. 1848: 535 670 411 232 N SD: 0.0140 c. M: 0.0245 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: 60.6157 cents 4:5:6:7:8 H SD: 30.0895 cents 5:6:8:9:10 S SD: 13.6732 cents 9:11:14:17:18 SD: 13.6473 cents 12:15:19:22:24 SD: 10.2603 cents 13:16:20:24:26 SD: 10.1194 cents 14:17:22:26:28 SD: 6.2561 cents 18:22:28:33:36 SD: 4.3940 cents 23:28:36:42:46 SD: 2.9689 cents 35:43:55:64:70 SD: 2.5092 cents 40:49:63:73:80 SD: 2.4122 cents 49:60:77:90:98 SD: 1.1345 cents 54:66:85:99:108 SD: 0.7280 cents 72:88:113:132:144 SD: 0.5468 cents 126:154:198:231:252 SD: 0.0000 cents