Scala analysis: xen12-wilson-38-4C3-tetrany-00
1-3-5-7 4C3 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: 7/5 582.512193 septimal or Huygens' tritone, BP 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: 7/6 266.8709 septimal minor third 2: 6/5 315.6413 minor third 3: 5/4 386.3137 major third 4: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 1: 1 6/5 315.641 cents minor third 1: 1 5/4 386.314 cents major 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 8/5 813.686 cents 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 7/4 968.826 cents harmonic 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 : 266.9 582.5 968.8 1200.0 266.9 : 315.6 702.0 933.1 1200.0 582.5 : 386.3 617.5 884.4 1200.0 968.8 : 231.2 498.0 813.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 231.1741 .. 386.3137 cents 35/32, 155.1396 cents 8/7, 231.1741 cents 2: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 16/15, 111.7313 cents 3: 813.6863 .. 968.8259 cents 35/32, 155.1396 cents 16/15, 111.7313 cents
SHOW DATA
Number of notes : 4 -- Interval properties -- Smallest interval : 8/7, 231.1741 cents, class 1 Average step (divided formal octave): 300.0000 cents Largest one step interval : 5/4, 386.3137 cents Average / Smallest step : 1.297723 Largest / Average step : 1.287712 Largest / Smallest step : 1.671094 Median interval of one step : 291.25610 cents, amount: 0 Least squares average step : 304.61243 cents, oct.: 1218.44973 cents Scale is strictly 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 111.73129 cents Scale diversity : 1.564349 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.571509 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 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Scale is subharmonic, base degree is: 3 Formal octave complements present : 1 = 25.0000% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 7 (O: 7 U: 7) Highest odd numerator or denominator: 7 Scale harmonicity : 0.044738 Average absolute harmonicity : 0.303249 Specific harmonicity : 0.223252 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 14, 3.8074 octaves, 3662.758 Hz. Exponens Consonantiae : 8.400000E+02, 9.71425 octaves Euler's gradus suavitatis : 16 Sum of Mann's harmonic distance : 19.5, average 4.87500 Mersenne's string divisions : 1716 Sum of van Prooijen's expressibility: 2.53529, average 0.63382 Sum of Tenney's harmonic distance : 4.91551, average 1.22888 Vogel's harmonic complexity : 12.75000 Wille's k value : 52 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 19.10848, average 1.91085 Lattice compactness (without 2's) : 11.07107, average 1.10711 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.50000 4 1 3: -1 .. 0 -0.25000 1 5: -1 .. 0 -0.25000 1 7: 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 5 10 11| Scale is JI-epimorphic with val: <4 6 9 11| = patent Scale is weakly epimorphic with val: <4 7 9 10|
FIT/MODE
4: 1 1 1 1 SP B ME I SD: 39.1802 c. M: 68.8259 c. 6: 1 2 2 1 P D3 I SD: 37.9123 c. M: 66.8709 c. 9: 2 2 3 2 SP M ME SD: 30.3246 c. M: 49.1789 c. 10: 2 3 3 2 SP D3 I SD: 16.6265 c. M: 26.8709 c. 14: 3 4 4 3 SP D3 I SD: 16.3923 c. M: 25.9688 c. 15: 3 4 5 3 SP SD: 18.0744 c. M: 26.8709 c. 17: 4 4 6 3 SP SD: 15.2765 c. M:-19.4094 c. 19: 4 5 6 4 SP SD: 14.6777 c. M: 21.4575 c. 21: 5 5 7 4 SP SD: 11.0079 c. M:-18.8434 c. 22: 5 6 7 4 SP SD: 11.2796 c. M:-17.4878 c. 26: 6 7 8 5 SP SD: 10.0875 c. M:-17.4878 c. 27: 6 7 9 5 SP SD: 5.0644 c. M:-8.9519 c. 31: 7 8 10 6 SP SD: 2.3154 c. M:-4.0968 c. 41: 9 11 13 8 SP SD: 2.6890 c. M: 3.4563 c. 58: 13 15 19 11 SP SD: 2.6226 c. M:-3.5879 c. 68: 15 18 22 13 SP SD: 1.3981 c. M: 2.1650 c. 72: 16 19 23 14 SP SD: 1.1596 c. M: 2.1592 c. 99: 22 26 32 19 SP SD: 0.5662 c. M:-0.8711 c. 140: 31 37 45 27 SP SD: 0.6167 c. M: 1.1566 c. 171: 38 45 55 33 SP SD: 0.2285 c. M: 0.4049 c. 270: 60 71 87 52 SP SD: 0.1801 c. M: 0.2900 c. 441: 98 116 142 85 SP SD: 0.1545 c. M: 0.2042 c. 836: 186 220 269 161 SP SD: 0.1481 c. M:-0.2629 c. 935: 208 246 301 180 SP SD: 0.1201 c. M:-0.1616 c. 1007: 224 265 324 194 SP SD: 0.1088 c. M:-0.2088 c. 1106: 246 291 356 213 SP SD: 0.0755 c. M:-0.1280 c. 1205: 268 317 388 232 SP SD: 0.0752 c. M:-0.1367 c. 1209: 269 318 389 233 SP SD: 0.0979 c. M:-0.1266 c. 1236: 275 325 398 238 SP SD: 0.0801 c. M:-0.1194 c. 1277: 284 336 411 246 SP SD: 0.0518 c. M:-0.1033 c. 1308: 291 344 421 252 SP SD: 0.0589 c. M:-0.1016 c. 1376: 306 362 443 265 SP SD: 0.0420 c. M:-0.0694 c. 1407: 313 370 453 271 SP SD: 0.0457 c. M:-0.0801 c. 1479: 329 389 476 285 SP SD: 0.0507 c. M:-0.0662 c. 1547: 344 407 498 298 SP SD: 0.0250 c. M:-0.0347 c. 1578: 351 415 508 304 SP SD: 0.0248 c. M:-0.0492 c. 1848: 411 486 595 356 SP SD: 0.0233 c. M: 0.0447 c. 2019: 449 531 650 389 SP SD: 0.0273 c. M: 0.0456 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x 3 x 4 S SD: 59.7214 cents 3 x 4:5:6 S SD: 39.8182 cents 5:6:7:9:10 SD: 17.2429 cents 7:8:10:12:14 S SD: 15.3538 cents 11:13:15:19:22 SD: 13.8902 cents 12:14:17:21:24 SD: 5.1221 cents 23:27:32:40:46 SD: 4.6611 cents 25:29:35:44:50 SD: 3.4977 cents 35:41:49:61:70 SD: 2.4983 cents 43:50:60:75:86 SD: 2.4947 cents 47:55:66:82:94 SD: 2.2774 cents 48:56:67:84:96 SD: 1.2900 cents 60:70:84:105:120 S SD: 0.0000 cents