Scala analysis: xen12-wilson-38-4C1-tetrany-10
3-5-7-9 4C1 Tetrany, Figure 38
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 7/6 266.870906 septimal minor third 2: 3/2 701.955001 perfect fifth 3: 5/3 884.358713 major sixth, BP sixth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 6/5 315.6413 minor third 1: 7/6 266.8709 septimal minor third 2: 9/7 435.0841 septimal major third, BP third 3: 10/9 182.4037 minor whole tone 4: 6/5 315.6413 minor third
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 10/9 182.404 cents minor whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 6/5 315.641 cents minor third 1: 1 9/7 435.084 cents septimal major third, BP third 2: 1 4/3 498.045 cents perfect 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 3/2 701.955 cents perfect fifth 3: 1 14/9 764.916 cents septimal minor sixth 3: 1 5/3 884.359 cents major sixth, BP sixth 3: 1 12/7 933.129 cents septimal major sixth 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 : 266.9 702.0 884.4 1200.0 266.9 : 435.1 617.5 933.1 1200.0 702.0 : 182.4 498.0 764.9 1200.0 884.4 : 315.6 582.5 1017.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 182.4037 .. 435.0841 cents 81/70, 252.6804 cents 10/9, 182.4037 cents 2: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 28/27, 62.9609 cents 3: 764.9159 .. 1017.5963 cents 81/70, 252.6804 cents 28/27, 62.9609 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 : 9/7, 435.0841 cents Average / Smallest step : 1.644703 Largest / Average step : 1.450280 Largest / Smallest step : 2.385281 Median interval of one step : 291.25610 cents, amount: 0 Least squares average step : 304.12857 cents, oct.: 1216.51427 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : BDAC Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 62.96090 cents Scale diversity : 1.694163 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.408941 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 : 50/49, 34.9756 cents Number of recognisable fifths : 1, average 701.9550 cents Best minor thirds form a closed circle Length of longest harmonic part : 2 at degree 3 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 class 2 -- Rational properties -- Prime limit : 7 Odd number limit : 9 (O: 9 U: 9) Highest odd numerator or denominator: 7 Scale harmonicity : 0.041634 Average absolute harmonicity : 0.363673 Specific harmonicity : 0.241757 Fundamental : 1/6, -2.5850 octaves, 43.6043 Hz. Guide tone : 210, 7.7142 octaves, 54941.369 Hz. Exponens Consonantiae : 1.260000E+03, 10.29921 octaves Euler's gradus suavitatis : 17 Sum of Mann's harmonic distance : 14.5, average 3.62500 Mersenne's string divisions : 1560 Sum of van Prooijen's expressibility: 2.02119, average 0.50530 Sum of Tenney's harmonic distance : 3.87852, average 0.96963 Vogel's harmonic complexity : 6.00000 Wille's k value : 4 Wilson's harmonic complexity : 18 Rectangular lattice diameter : 4 Triangular lattice diameter : 2 Lattice compactness : 18.39569, average 1.83957 Lattice compactness (without 2's) : 13.54320, average 1.35432 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -1 .. 1 -0.25000 3 1 3: -1 .. 1 -0.25000 3 1 5: 0 .. 1 0.25000 1 1 7: 0 .. 1 0.25000 1 1 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 5 8 11| Scale is JI-epimorphic with val: <4 6 9 11| = patent Scale is weakly epimorphic with val: <4 7 9 12|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 54.1687 c. M: 101.9550 c. 5: 1 2 1 1 P M ME SD: 41.1378 c. M:-75.6413 c. 8: 2 3 1 2 P T3 SD: 30.2097 c. M:-48.0450 c. 9: 2 3 2 2 SP M ME SD: 30.1820 c. M:-48.9746 c. 10: 2 4 1 3 P SD: 27.4562 c. M: 44.3587 c. 12: 3 4 2 3 SP T3 SD: 18.3440 c. M:-33.1291 c. 14: 3 5 2 4 SP SD: 16.5763 c. M: 27.2159 c. 15: 3 6 2 4 P SD: 16.3299 c. M: 26.8709 c. 19: 4 7 3 5 SP SD: 7.9825 c. M: 14.2393 c. 22: 5 8 3 6 SP SD: 7.4248 c. M: 11.6314 c. 26: 6 9 4 7 SP SD: 7.8963 c. M:-10.0522 c. 27: 6 10 4 7 SP SD: 5.1088 c. M:-9.1561 c. 31: 7 11 5 8 SP SD: 4.4495 c. M:-5.9639 c. 41: 9 15 6 11 SP SD: 3.6054 c. M: 6.3099 c. 46: 10 17 7 12 SP SD: 3.4817 c. M: 6.0013 c. 50: 11 18 8 13 SP SD: 3.7737 c. M: 5.9550 c. 53: 12 19 8 14 SP SD: 2.5051 c. M:-4.8272 c. 58: 13 21 9 15 SP SD: 2.9441 c. M:-5.2965 c. 68: 15 25 10 18 SP SD: 2.4563 c. M:-3.9274 c. 72: 16 26 11 19 SP SD: 1.1085 c. M: 1.9550 c. 99: 22 36 15 26 SP SD: 0.5996 c. M:-1.0753 c. 171: 38 62 26 45 SP SD: 0.1612 c. M: 0.2042 c. 441: 98 160 67 116 SP SD: 0.1108 c. M: 0.2042 c. 612: 136 222 93 161 SP SD: 0.1046 c. M: 0.2042 c. 665: 148 241 101 175 SP SD: 0.1232 c. M:-0.1968 c. 764: 170 277 116 201 SP SD: 0.1057 c. M:-0.1448 c. 783: 174 284 119 206 SP SD: 0.1093 c. M: 0.2042 c. 836: 186 303 127 220 SP SD: 0.0959 c. M: 0.1482 c. 935: 208 339 142 246 SP SD: 0.0689 c. M:-0.0810 c. 1106: 246 401 168 291 SP SD: 0.0520 c. M: 0.0911 c. 1277: 284 463 194 336 SP SD: 0.0494 c. M: 0.0987 c. 1376: 306 499 209 362 SP SD: 0.0492 c. M:-0.0799 c. 1448: 322 525 220 381 SP SD: 0.0543 c. M: 0.1046 c. 1506: 335 546 229 396 SP SD: 0.0629 c. M:-0.1034 c. 1547: 344 561 235 407 SP SD: 0.0442 c. M: 0.0665 c. 1578: 351 572 240 415 SP SD: 0.0448 c. M: 0.0539 c. 1677: 373 608 255 441 SP SD: 0.0430 c. M:-0.0778 c. 1749: 389 634 266 460 SP SD: 0.0397 c. M: 0.0682 c. 1848: 411 670 281 486 SP SD: 0.0293 c. M:-0.0569 c. 2019: 449 732 307 531 SP SD: 0.0231 c. M:-0.0395 c. 2190: 487 794 333 576 SP SD: 0.0248 c. M: 0.0372 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 0.0000 cents 3 x x 5:6 SD: 0.0000 cents 5:6 x 8:10 S SD: 28.6223 cents 6:7:9:10:12 SD: 0.0000 cents