Scala analysis: xen12-wilson-09-4C2-hexany-00
1-3-7-9 4C2 Hexany, Figure 9
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: 7/6 266.870906 septimal minor third 3: 21/16 470.780907 narrow fourth 4: 3/2 701.955001 perfect fifth 5: 7/4 968.825906 harmonic seventh 6: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 9/8 203.9100 major whole tone 2: 28/27 62.9609 Archytas' 1/3-tone 3: 9/8 203.9100 major whole tone 4: 8/7 231.1741 septimal whole tone 5: 7/6 266.8709 septimal minor third 6: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 9/8 203.910 cents major whole tone 1: 2 8/7 231.174 cents septimal whole tone 1: 1 7/6 266.871 cents septimal minor third 2: 2 7/6 266.871 cents septimal minor third 2: 2 9/7 435.084 cents septimal major third, BP third 2: 2 4/3 498.045 cents perfect fourth 3: 1 21/16 470.781 cents narrow fourth 3: 2 4/3 498.045 cents perfect fourth 3: 2 3/2 701.955 cents perfect fifth 3: 1 32/21 729.219 cents wide fifth 4: 2 3/2 701.955 cents perfect fifth 4: 2 14/9 764.916 cents septimal minor sixth 4: 2 12/7 933.129 cents septimal major sixth 5: 1 12/7 933.129 cents septimal major sixth 5: 2 7/4 968.826 cents harmonic seventh 5: 2 16/9 996.090 cents Pythagorean minor seventh 5: 1 27/14 1137.039 cents septimal major seventh Highest number of different intervals for one interval class: 4 Average number of different intervals per interval class: 3.60000 = 18/5
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 0.0 : 203.9 266.9 470.8 702.0 968.8 1200.0 203.9 : 63.0 266.9 498.0 764.9 996.1 1200.0 266.9 : 203.9 435.1 702.0 933.1 1137.0 1200.0 470.8 : 231.2 498.0 729.2 933.1 996.1 1200.0 702.0 : 266.9 498.0 702.0 764.9 968.8 1200.0 968.8 : 231.2 435.1 498.0 702.0 933.1 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 62.9609 .. 266.8709 cents 9/8, 203.9100 cents 28/27, 62.9609 cents 2: 266.8709 .. 498.0450 cents 8/7, 231.1741 cents 1/1, 0.0000 cents 3: 470.7809 .. 729.2191 cents 512/441, 258.4382 cents 63/64,-27.2641 cents 4: 701.9550 .. 933.1291 cents 8/7, 231.1741 cents 63/64,-27.2641 cents 5: 933.1291 .. 1137.0391 cents 9/8, 203.9100 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 6 -- Interval properties -- Smallest interval : 28/27, 62.9609 cents, class 1 Average step (divided formal octave): 200.0000 cents Largest one step interval : 7/6, 266.8709 cents Average / Smallest step : 3.176574 Largest / Average step : 1.334355 Largest / Smallest step : 4.238677 Median interval of one step : 217.54205 cents, amount: 0 Least squares average step : 186.83455 cents, oct.: 1121.00730 cents Scale is not proper Step pattern alph. order: ABACDC Step pattern size order : BABCDC Scale is not a Constant Structure Scale diversity : 1.247980 Lumma stability : 0.104935 Lumma impropriety factor : 0.045440 Rothenberg efficiency : 0.583333 redundancy: 0.416667 Efficiency x scale size : 3.500000 Number of different interval sizes : 14 = 2.80000 / class Number of one step interval sizes : 4 Highest interval variety : 4 Mean interval variety : 3.60000 = 18/5 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 64/63, 27.2641 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 4 Most common triad is 0.0 498.045 701.955 cents, amount: 2 Number of recognisable fifths : 4, average 701.9550 cents All steps are superparticular (epimoric) Length of longest harmonic part : 3 at degree 4 Length of longest subharmonic part : 3 at degree 2 Formal octave complements present : 1 = 16.6667% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval classes 3 and 4 combined Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 4-5 -- Rational properties -- Prime limit : 7 Odd number limit : 27 (O: 27 U: 27) Highest odd numerator or denominator: 21 Scale harmonicity : 0.042945 Average absolute harmonicity : 0.267464 Specific harmonicity : 0.211728 Fundamental : 1/48, -5.5850 octaves, 5.4505 Hz. Guide tone : 126, 6.9773 octaves, 32964.821 Hz. Exponens Consonantiae : 6.048000E+03, 12.56224 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 43.0, average 7.16667 Mersenne's string divisions : 1349205 Sum of van Prooijen's expressibility: 4.44378, average 0.74063 Sum of Tenney's harmonic distance : 8.53326, average 1.42221 Vogel's harmonic complexity : 10.33333 Wille's k value : 31 Wilson's harmonic complexity : 16 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 56.29214, average 2.68058 Lattice compactness (without 2's) : 30.11969, average 1.43427 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.66667 12 1 3: -1 .. 2 0.50000 5 2 7: 0 .. 1 0.50000 3 3 Average exponent except 2's : 6 / 6 = 1.00000 Average absolute exponent except 2's: 8 / 6 = 1.33333 Scale is weakly epimorphic with val: <6 10 15| Scale is weakly epimorphic with val: <6 10 17| = patent Scale is weakly epimorphic with val: <6 10 19|
FIT/MODE
6: 1 0 1 1 2 1 N D3 SD: 58.9683 c. M: 101.9550 c. 7: 1 1 1 1 2 1 P M ME SD: 45.7437 c. M:-75.9862 c. 8: 1 1 1 2 1 2 P D3 SD: 43.7436 c. M: 68.8259 c. 9: 1 1 1 2 2 2 N SD: 45.6363 c. M: 70.7809 c. 10: 2 0 2 2 2 2 P M DE SD: 20.4656 c. M:-36.0900 c. 12: 2 1 2 2 3 2 P G D3 SD: 22.1443 c. M:-33.1291 c. Minor Hexatonic, Raga Manirangu, Nayaki, Palasi, Pushpalithika (Puspalatika), Suha Sughrai, Yo: Japan, Eskimo Hexatonic 1 (Alaska: King Island) 14: 2 1 2 3 3 3 N G SD: 25.3951 c. M: 42.2095 c. 15: 3 0 3 3 3 3 P M DE SD: 20.4656 c. M:-36.0900 c. 17: 3 1 3 3 4 3 P G D3 SD: 14.3651 c. M:-23.3367 c. 22: 4 1 4 4 5 4 P G D3 SD: 11.9920 c. M:-20.1282 c. 26: 4 2 4 5 6 5 N SD: 10.4242 c. M: 19.2946 c. 27: 5 1 5 5 6 5 P G D3 SD: 11.7420 c. M:-18.3122 c. 28: 5 1 5 5 7 5 N D3 SD: 11.1929 c. M:-16.8884 c. 30: 5 2 5 6 6 6 P SD: 10.6158 c. M:-18.0450 c. 31: 5 2 5 6 7 6 N SD: 5.6482 c. M: 10.3616 c. 36: 6 2 6 7 8 7 N SD: 2.6058 c. M: 4.1142 c. 41: 7 2 7 8 9 8 N SD: 2.1657 c. M: 3.4563 c. 77: 13 4 13 15 17 15 N SD: 1.9652 c. M: 3.2484 c. 89: 15 5 15 17 20 17 N SD: 1.6518 c. M:-2.7920 c. 94: 16 5 16 18 21 18 N SD: 0.9982 c. M:-1.5595 c. 130: 22 7 22 25 29 25 N SD: 0.5333 c. M: 0.8331 c. 135: 23 7 23 26 30 26 N SD: 0.2920 c. M:-0.5344 c. 265: 45 14 45 51 59 51 N SD: 0.1790 c. M:-0.2989 c. 306: 52 16 52 59 68 59 N SD: 0.1405 c. M: 0.2042 c. 400: 68 21 68 77 89 77 N SD: 0.1324 c. M:-0.2191 c. 436: 74 23 74 84 97 84 N SD: 0.1304 c. M: 0.2403 c. 441: 75 23 75 85 98 85 N SD: 0.1249 c. M: 0.2042 c. 571: 97 30 97 110 127 110 N SD: 0.0308 c. M: 0.0571 c. 706: 120 37 120 136 157 136 N SD: 0.0315 c. M:-0.0560 c. 1277: 217 67 217 246 284 246 N SD: 0.0059 c. M:-0.0100 c.
FIT/HARMONIC
1 x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x 4 S SD: 0.0000 cents 3 x x 4 x 5:6 S SD: 29.5861 cents 4 x x 5:6:7:8 S SD: 21.1168 cents 5 x 6:7:8:9:10 S SD: 34.4818 cents 6 x 7:8:9:11:12 SD: 17.0053 cents 7:8 x 9:11:12:14 SD: 19.7768 cents 8:9 x 11:12:14:16 SD: 16.1074 cents 10:11:12:13:15:18:20 SD: 13.4838 cents 12 x 14:16:18:21:24 S SD: 5.4528 cents 13 x 15:17:20:23:26 SD: 10.3643 cents 14:16 x 18:21:25:28 SD: 11.3858 cents 16:18:19:21:24:28:32 SD: 5.1070 cents 20 x 23:26:30:35:40 SD: 5.9833 cents 23:26:27:30:35:40:46 SD: 5.3690 cents 24:27:28:32:36:42:48 S SD: 4.5440 cents 30:34:35:39:45:53:60 SD: 4.4316 cents 31:35:36:41:47:54:62 SD: 4.3607 cents 32:36:37:42:48:56:64 SD: 2.5878 cents 42:47:49:55:63:74:84 SD: 2.5688 cents 48:54:56:63:72:84:96 S SD: 0.0000 cents