Scala analysis: xen12-wilson-38-4C1-tetrany-07
1-5-7-11 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 5/4 386.313714 major third 2: 11/8 551.317942 undecimal semi-augmented fourth 3: 7/4 968.825906 harmonic seventh 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 5/4 386.3137 major third 2: 11/10 165.0042 Ptolemy's second, 4/5-tone 3: 14/11 417.5080 undecimal diminished fourth or major third 4: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 1: 1 8/7 231.174 cents septimal whole tone 1: 1 5/4 386.314 cents major third 1: 1 14/11 417.508 cents undecimal diminished fourth or major third 2: 1 11/8 551.318 cents undecimal semi-augmented fourth 2: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 2: 1 10/7 617.488 cents Euler's tritone 2: 1 16/11 648.682 cents undecimal semi-diminished fifth 3: 1 11/7 782.492 cents undecimal augmented fifth 3: 1 8/5 813.686 cents minor sixth 3: 1 7/4 968.826 cents harmonic 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 : 386.3 551.3 968.8 1200.0 386.3 : 165.0 582.5 813.7 1200.0 551.3 : 417.5 648.7 1035.0 1200.0 968.8 : 231.2 617.5 782.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 165.0042 .. 417.5080 cents 140/121, 252.5037 cents 11/10, 165.0042 cents 2: 551.3179 .. 648.6821 cents 128/121, 97.3641 cents 121/112, 133.8100 cents 3: 782.4920 .. 1034.9958 cents 140/121, 252.5037 cents 121/112, 133.8100 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 : 14/11, 417.5080 cents Average / Smallest step : 1.818135 Largest / Average step : 1.391693 Largest / Smallest step : 2.530286 Median interval of one step : 308.74390 cents, amount: 0 Least squares average step : 306.51424 cents, oct.: 1226.05698 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : CADB Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 133.80998 cents Scale diversity : 1.620672 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.498024 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 : 56/55, 31.1943 cents Number of recognisable fifths : 0 Best minor thirds form a closed circle Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 25.0000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Limited inverse transpositions with margin 221.3095 cents: 3 -- Rational properties -- Prime limit : 11 Odd number limit : 11 (O: 11 U: 11) Highest odd numerator or denominator: 11 Scale harmonicity : 0.025728 Average absolute harmonicity : 0.311913 Specific harmonicity : 0.156769 Fundamental : 1/8, -3.0000 octaves, 32.7032 Hz. Guide tone : 770, 9.5887 octaves, 201451.685 Hz. Exponens Consonantiae : 6.160000E+03, 12.58871 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 21.0, average 5.25000 Mersenne's string divisions : 1881 Sum of van Prooijen's expressibility: 2.58546, average 0.64637 Sum of Tenney's harmonic distance : 4.99370, average 1.24843 Vogel's harmonic complexity : 7.25000 Wille's k value : 5 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 23.96039, average 2.39604 Lattice compactness (without 2's) : 10.24264, average 1.02426 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -3 .. 1 -1.50000 8 1 5: 0 .. 1 0.25000 1 1 7: 0 .. 1 0.25000 1 1 11: 0 .. 1 0.25000 1 1 Average exponent except 2's : 3 / 4 = 0.75000 Average absolute exponent except 2's: 3 / 4 = 0.75000 Scale is weakly epimorphic with val: <4 9 10 15| Scale is JI-epimorphic with val: <4 9 11 14| = patent Scale is weakly epimorphic with val: <4 10 11 13|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 60.3262 c. M: 86.3137 c. 5: 2 0 2 1 P D3 SD: 59.0366 c. M:-93.6863 c. 6: 2 1 2 1 SP B ME SD: 29.7030 c. M:-48.6821 c. Messiaen truncated mode 6 inverse 9: 3 1 3 2 SP D3 SD: 21.0386 c. M: 35.4926 c. 15: 5 2 5 3 SP D3 SD: 9.2275 c. M:-13.6863 c. 22: 7 3 8 4 SP SD: 7.4731 c. M:-12.9923 c. 28: 9 4 10 5 SP SD: 8.9374 c. M:-16.8884 c. 31: 10 4 11 6 SP SD: 4.7386 c. M: 9.3825 c. 35: 11 5 12 7 SP SD: 6.5105 c. M: 9.1709 c. 37: 12 5 13 7 SP SD: 2.5233 c. M:-4.1471 c. 68: 22 9 24 13 SP SD: 2.4969 c. M: 4.2591 c. 72: 23 10 25 14 SP SD: 1.9546 c. M: 2.9804 c. 78: 25 11 27 15 SP SD: 1.5362 c. M:-2.5282 c. 109: 35 15 38 21 SP SD: 0.6565 c. M: 0.9926 c. 146: 47 20 51 28 SP SD: 0.6075 c. M:-1.0371 c. 224: 72 31 78 43 SP SD: 0.5580 c. M:-0.8170 c. 233: 75 32 81 45 SP SD: 0.3183 c. M: 0.5856 c. 270: 87 37 94 52 SP SD: 0.2070 c. M:-0.3530 c. 379: 122 52 132 73 SP SD: 0.1989 c. M: 0.3945 c. 457: 147 63 159 88 SP SD: 0.1750 c. M: 0.3181 c. 503: 162 69 175 97 SP SD: 0.1836 c. M: 0.2374 c. 581: 187 80 202 112 SP SD: 0.1127 c. M: 0.1512 c. 618: 199 85 215 119 SP SD: 0.0991 c. M:-0.1384 c. 727: 234 100 253 140 SP SD: 0.0559 c. M:-0.0874 c. 851: 274 117 296 164 SP SD: 0.0527 c. M: 0.0833 c. 960: 309 132 334 185 SP SD: 0.0601 c. M: 0.0759 c. 997: 321 137 347 192 SP SD: 0.0564 c. M:-0.0808 c. 1230: 396 169 428 237 SP SD: 0.0559 c. M: 0.0984 c. 1308: 421 180 455 252 SP SD: 0.0484 c. M: 0.0752 c. 1578: 508 217 549 304 SP SD: 0.0069 c. M:-0.0129 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 75.3185 cents 3 x 4:5:6 S SD: 33.2878 cents 5:6:7:9:10 SD: 22.8394 cents 6 x 8:11:12 SD: 32.1873 cents 7:9:10:12:14 SD: 22.4043 cents 8:10:11:14:16 SD: 0.0000 cents