Scala analysis: xen12-wilson-38-4C3-tetrany-07
1-5-7-11 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: 11/8 551.317942 undecimal semi-augmented fourth 3: 11/7 782.492036 undecimal augmented fifth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/11 417.5080 undecimal diminished fourth or major third 1: 11/10 165.0042 Ptolemy's second, 4/5-tone 2: 5/4 386.3137 major third 3: 8/7 231.1741 septimal whole tone 4: 14/11 417.5080 undecimal diminished fourth or major third
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 : 165.0 551.3 782.5 1200.0 165.0 : 386.3 617.5 1035.0 1200.0 551.3 : 231.2 648.7 813.7 1200.0 782.5 : 417.5 582.5 968.8 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 : 280.50387 cents, oct.: 1122.01550 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : ACBD 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 Limited inverse transpositions with margin 221.3095 cents: 1 -- 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 : 0.280357 Specific harmonicity : 0.128976 Fundamental : 1/280, -8.1293 octaves, 0.9344 Hz. Guide tone : 22, 4.4594 octaves, 5755.762 Hz. Exponens Consonantiae : 6.160000E+03, 12.58871 octaves Euler's gradus suavitatis : 25 Sum of Mann's harmonic distance : 30.5, average 7.62500 Mersenne's string divisions : 2394 Sum of van Prooijen's expressibility: 3.12418, average 0.78104 Sum of Tenney's harmonic distance : 6.17340, average 1.54335 Vogel's harmonic complexity : 19.50000 Wille's k value : 192 Wilson's harmonic complexity : 23 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 5: -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 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: 92.7388 c. M:-134.9958 c. 6: 1 2 1 2 SP B ME SD: 31.2297 c. M:-48.6821 c. Messiaen truncated mode 6 8: 1 3 1 3 SP B DE SD: 30.2109 c. M:-48.6821 c. 9: 1 3 2 3 SP D3 SD: 20.2053 c. M: 31.6709 c. 14: 2 4 3 5 SP SD: 19.5899 c. M: 37.0322 c. 15: 2 5 3 5 SP D3 SD: 10.0865 c. M:-17.5080 c. 20: 3 6 4 7 SP SD: 9.4760 c. M:-14.9958 c. 22: 3 7 4 8 SP SD: 9.8968 c. M: 18.8557 c. 28: 4 9 5 10 SP SD: 7.0285 c. M: 11.0635 c. 29: 4 9 6 10 SP SD: 6.9511 c. M: 13.3869 c. 31: 4 10 6 11 SP SD: 8.0659 c. M: 10.1655 c. 35: 5 11 7 12 SP SD: 4.6307 c. M:-6.4243 c. 37: 5 12 7 13 SP SD: 2.5000 c. M: 4.1137 c. 52: 7 17 10 18 SP SD: 2.3933 c. M: 3.4658 c. 72: 10 23 14 25 SP SD: 1.1411 c. M:-1.6624 c. 109: 15 35 21 38 SP SD: 0.6047 c. M: 0.8592 c. 161: 22 52 31 56 SP SD: 0.5310 c. M: 1.0291 c. 233: 32 75 45 81 SP SD: 0.2318 c. M:-0.3406 c. 342: 47 110 66 119 SP SD: 0.2258 c. M: 0.4407 c. 385: 53 124 74 134 SP SD: 0.2221 c. M:-0.3704 c. 457: 63 147 88 159 SP SD: 0.2176 c. M:-0.4225 c. 494: 68 159 95 172 SP SD: 0.1837 c. M: 0.3058 c. 509: 70 164 98 177 SP SD: 0.2077 c. M:-0.3520 c. 546: 75 176 105 190 SP SD: 0.1893 c. M:-0.3304 c. 581: 80 187 112 202 SP SD: 0.2005 c. M:-0.2963 c. 618: 85 199 119 215 SP SD: 0.0744 c. M:-0.1384 c. 727: 100 234 140 253 SP SD: 0.0574 c. M: 0.0986 c. 960: 132 309 185 334 SP SD: 0.0343 c. M: 0.0679 c. 1345: 185 433 259 468 SP SD: 0.0431 c. M:-0.0575 c. 1578: 217 508 304 549 SP SD: 0.0131 c. M:-0.0175 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 40.2685 cents 3 x 4:5:6 S SD: 38.3186 cents 4 x x 6:8 S SD: 40.2685 cents 5:6:7:8:10 S SD: 39.2410 cents 6:7:8:9:12 S SD: 35.0901 cents 7:8:10:11:14 SD: 23.3946 cents 8:9:11:13:16 SD: 17.4675 cents 9:10:12:14:18 SD: 14.6835 cents 10:11:14:16:20 SD: 11.0288 cents 11:12:15:17:22 SD: 8.8226 cents 18:20:25:28:36 SD: 7.5598 cents 19:21:26:30:38 SD: 3.5840 cents 21:23:29:33:42 SD: 2.6497 cents 40:44:55:63:80 SD: 0.9825 cents 91:100:125:143:182 SD: 0.6118 cents 131:144:180:206:262 SD: 0.5203 cents 149:164:205:234:298 SD: 0.4573 cents 189:208:260:297:378 SD: 0.2943 cents 240:264:330:377:480 SD: 0.1640 cents 280:308:385:440:560 SD: 0.0000 cents