Scala analysis: xen12-wilson-38-4C3-tetrany-06
1-5-7-9 4C3 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 9/7 435.084095 septimal major third, BP third 3: 9/5 1017.596288 just minor seventh, BP seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 9/8 203.9100 major whole tone 2: 8/7 231.1741 septimal whole tone 3: 7/5 582.5122 septimal or Huygens' tritone, BP fourth 4: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 1 9/8 203.910 cents major whole tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 1 5/4 386.314 cents major third 2: 1 9/7 435.084 cents septimal major third, BP third 2: 1 14/9 764.916 cents septimal minor sixth 2: 1 8/5 813.686 cents minor sixth 3: 1 10/7 617.488 cents Euler's tritone 3: 1 7/4 968.826 cents harmonic seventh 3: 1 16/9 996.090 cents Pythagorean minor seventh 3: 1 9/5 1017.596 cents just minor seventh, BP 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 : 203.9 435.1 1017.6 1200.0 203.9 : 231.2 813.7 996.1 1200.0 435.1 : 582.5 764.9 968.8 1200.0 1017.6: 182.4 386.3 617.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 582.5122 cents 63/50, 400.1085 cents 10/9, 182.4037 cents 2: 386.3137 .. 813.6863 cents 32/25, 427.3726 cents 25/28,-196.1985 cents 3: 617.4878 .. 1017.5963 cents 63/50, 400.1085 cents 25/28,-196.1985 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 10/9, 182.4037 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 7/5, 582.5122 cents Average / Smallest step : 1.644703 Largest / Average step : 1.941707 Largest / Smallest step : 3.193533 Median interval of one step : 217.54205 cents, amount: 0 Least squares average step : 297.56224 cents, oct.: 1190.24894 cents Scale is not proper Step pattern alph. order: ABCD Step pattern size order : BCDA Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 34.97561 cents Scale diversity : 1.556060 Lumma stability : 0.304006 Lumma impropriety factor : 0.326997 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 : 81/80, 21.5063 cents Number of recognisable fifths : 0 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 3 at degree 3 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 Limited inverse transpositions with margin 400.1085 cents: 1 -- Rational properties -- Prime limit : 7 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 9 Scale harmonicity : 0.038433 Average absolute harmonicity : 0.317312 Specific harmonicity : 0.217878 Fundamental : 1/280, -8.1293 octaves, 0.9344 Hz. Guide tone : 18, 4.1699 octaves, 4709.260 Hz. Exponens Consonantiae : 5.040000E+03, 12.29921 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 25.0, average 6.25000 Mersenne's string divisions : 5712 Sum of van Prooijen's expressibility: 2.86273, average 0.71568 Sum of Tenney's harmonic distance : 5.61092, average 1.40273 Vogel's harmonic complexity : 16.00000 Wille's k value : 157 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 26.18757, average 2.61876 Lattice compactness (without 2's) : 16.35849, average 1.63585 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -0.50000 4 1 3: 0 .. 2 1.50000 6 1 5: -1 .. 0 -0.25000 1 1 7: -1 .. 0 -0.25000 1 1 Average exponent except 2's : 4 / 4 = 1.00000 Average absolute exponent except 2's: 8 / 4 = 2.00000 Scale is weakly epimorphic with val: <4 5 9 11| Scale is weakly epimorphic with val: <4 7 9 11|
FIT/MODE
4: 1 0 2 1 N T3 SD: 101.6242 c. M: 135.0841 c. 5: 1 1 2 1 P M ME SD: 40.7347 c. M: 57.5963 c. 6: 1 1 3 1 N M DE SD: 19.7219 c. M: 35.0841 c. 11: 2 2 5 2 N M DE SD: 19.2704 c. M: 35.7781 c. 13: 2 3 6 2 N SD: 16.4089 c. M:-26.4544 c. 17: 3 3 8 3 N M DE SD: 16.2579 c. M: 29.3610 c. 19: 3 4 9 3 N SD: 8.7705 c. M: 14.4363 c. 25: 4 5 12 4 N SD: 7.8014 c. M: 11.9100 c. 28: 5 5 14 4 N SD: 8.2238 c. M:-10.9751 c. 31: 5 6 15 5 N SD: 8.9113 c. M: 11.1447 c. 33: 6 6 16 5 N SD: 7.1705 c. M:-14.2718 c. 39: 7 7 19 6 N SD: 6.2285 c. M:-11.4746 c. 41: 7 8 20 6 N SD: 3.9567 c. M:-6.7940 c. 47: 8 9 23 7 N SD: 1.9202 c. M:-3.6803 c. 72: 12 14 35 11 N SD: 2.1919 c. M: 3.9100 c. 93: 16 18 45 14 N SD: 2.3821 c. M:-3.6256 c. 99: 17 19 48 15 N SD: 1.2850 c. M:-2.1506 c. 105: 18 20 51 16 N SD: 1.0122 c. M:-1.8043 c. 124: 21 24 60 19 N SD: 0.8338 c. M: 1.4673 c. 152: 26 29 74 23 N SD: 0.9048 c. M:-1.3532 c. 165: 28 32 80 25 N SD: 0.7168 c. M:-1.2795 c. 171: 29 33 83 26 N SD: 0.2023 c. M: 0.4012 c. 389: 66 75 189 59 N SD: 0.2601 c. M:-0.3986 c. 441: 75 85 214 67 N SD: 0.1745 c. M:-0.2901 c. 447: 76 86 217 68 N SD: 0.1316 c. M: 0.1848 c. 612: 104 118 297 93 N SD: 0.1082 c. M:-0.2100 c. 618: 105 119 300 94 N SD: 0.0906 c. M: 0.1326 c. 789: 134 152 383 120 N SD: 0.0914 c. M: 0.1077 c. 888: 151 171 431 135 N SD: 0.0778 c. M:-0.1441 c. 1059: 180 204 514 161 N SD: 0.0390 c. M:-0.0560 c. 1230: 209 237 597 187 N SD: 0.0262 c. M:-0.0379 c. 2336: 397 450 1134 355 N SD: 0.0265 c. M:-0.0407 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 133.4355 cents 3 x 4:5:6 S SD: 49.1215 cents 4 x 5:7:8 SD: 22.9906 cents 5:6 x 9:10 S SD: 37.2438 cents 6:7:8:11:12 SD: 23.6343 cents 7:8:9:13:14 SD: 15.1466 cents 10:11:13:18:20 SD: 10.8386 cents 14:16:18:25:28 SD: 7.6388 cents 15:17:19:27:30 SD: 7.2065 cents 17:19:22:31:34 SD: 6.8993 cents 24:27:31:43:48 SD: 2.8337 cents 25:28:32:45:50 SD: 2.7264 cents 31:35:40:56:62 SD: 2.6821 cents 39:44:50:70:78 SD: 2.1368 cents 49:55:63:88:98 SD: 1.3895 cents 56:63:72:101:112 SD: 0.8579 cents 80:90:103:144:160 SD: 0.6007 cents 105:118:135:189:210 SD: 0.4582 cents 161:181:207:290:322 SD: 0.4224 cents 175:197:225:315:350 SD: 0.2747 cents 200:225:257:360:400 SD: 0.2405 cents 224:252:288:403:448 SD: 0.2147 cents 280:315:360:504:560 SD: 0.0000 cents