Scala analysis: xen12-wilson-06d-minor-tetrad
1-3-5-7 minor tetrad, Figure 6d
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 8/7 231.174094 septimal whole tone 2: 4/3 498.044999 perfect fourth 3: 8/5 813.686286 minor sixth 4: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 5/4 386.3137 major third 1: 8/7 231.1741 septimal whole tone 2: 7/6 266.8709 septimal minor third 3: 6/5 315.6413 minor third 4: 5/4 386.3137 major third
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 : 231.2 498.0 813.7 1200.0 231.2 : 266.9 582.5 968.8 1200.0 498.0 : 315.6 702.0 933.1 1200.0 813.7 : 386.3 617.5 884.4 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 : 282.27743 cents, oct.: 1129.10973 cents Scale is strictly proper Step pattern alph. order: ABCD Step pattern size order : ABCD 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) Steps are strictly increasing Length of longest harmonic part : 1 at degree 0 Scale is subharmonic, base degree is: 0 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 : 0.348984 Specific harmonicity : 0.267638 Fundamental : 1/105, -6.7142 octaves, 2.4917 Hz. Guide tone : 8, 3.0000 octaves, 2093.005 Hz. Exponens Consonantiae : 8.400000E+02, 9.71425 octaves Euler's gradus suavitatis : 16 Sum of Mann's harmonic distance : 19.0, average 4.75000 Mersenne's string divisions : 1365 Sum of van Prooijen's expressibility: 2.02119, average 0.50530 Sum of Tenney's harmonic distance : 4.73046, average 1.18261 Vogel's harmonic complexity : 13.50000 Wille's k value : 52 Wilson's harmonic complexity : 15 Rectangular lattice diameter : 3 Triangular lattice diameter : 1 Lattice compactness : 20.32529, average 2.03253 Lattice compactness (without 2's) : 10.24264, average 1.02426 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: 1 .. 3 2.25000 9 1 3: -1 .. 0 -0.25000 1 1 5: -1 .. 0 -0.25000 1 1 7: -1 .. 0 -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 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: 75.1364 c. M:-101.9550 c. 5: 1 1 1 2 P M ME SD: 47.9078 c. M: 93.6863 c. 6: 1 1 2 2 P D3 S SD: 51.8940 c. M: 98.0450 c. 7: 1 2 2 2 SP M ME SD: 37.8212 c. M: 59.7455 c. 9: 2 2 2 3 SP M ME SD: 25.9437 c. M:-35.4926 c. 10: 2 2 3 3 SP D3 S SD: 16.5524 c. M:-26.3137 c. 12: 2 3 3 4 SP T3 SD: 17.0511 c. M: 31.1741 c. Raga Haripriya 15: 3 3 4 5 SP SD: 12.1535 c. M: 18.0450 c. 19: 4 4 5 6 SP SD: 11.9037 c. M:-21.4575 c. 21: 4 5 5 7 SP SD: 10.6987 c. M:-16.2407 c. 22: 4 5 6 7 SP SD: 7.7448 c. M: 12.9923 c. 31: 6 7 8 10 SP SD: 2.6753 c. M:-5.1808 c. 46: 9 10 12 15 SP SD: 3.3035 c. M: 4.9906 c. 53: 10 12 14 17 SP SD: 2.4817 c. M: 4.7590 c. 68: 13 15 18 22 SP SD: 2.3570 c. M: 3.9274 c. 72: 14 16 19 23 SP SD: 2.0837 c. M:-2.9804 c. 84: 16 19 22 27 SP SD: 1.6549 c. M: 2.6027 c. 99: 19 22 26 32 SP SD: 1.0446 c. M: 1.5651 c. 130: 25 29 34 42 SP SD: 0.7480 c. M: 1.3786 c. 140: 27 31 37 45 SP SD: 0.5563 c. M: 0.9021 c. 171: 33 38 45 55 SP SD: 0.2854 c. M:-0.4049 c. 270: 52 60 71 87 SP SD: 0.2236 c. M: 0.3530 c. 441: 85 98 116 142 SP SD: 0.0836 c. M:-0.1184 c. 935: 180 208 246 301 SP SD: 0.0879 c. M: 0.1581 c. 966: 186 215 254 311 SP SD: 0.0756 c. M: 0.1182 c. 1106: 213 246 291 356 SP SD: 0.0486 c. M: 0.0710 c. 1277: 246 284 336 411 SP SD: 0.0482 c. M:-0.0960 c. 1376: 265 306 362 443 SP SD: 0.0542 c. M: 0.0799 c. 1407: 271 313 370 453 SP SD: 0.0348 c. M: 0.0440 c. 1547: 298 344 407 498 SP SD: 0.0273 c. M: 0.0489 c. 1578: 304 351 415 508 SP SD: 0.0270 c. M:-0.0539 c. 1848: 356 411 486 595 SP SD: 0.0253 c. M: 0.0499 c. 2019: 389 449 531 650 SP SD: 0.0205 c. M:-0.0295 c.
FIT/HARMONIC
1 x x x 2 S SD: 0.0000 cents 2 x x 3:4 S SD: 55.8656 cents 3 x 4:5:6 S SD: 23.5575 cents 4 x 5:6:8 S SD: 52.6706 cents 5:6:7:8:10 S SD: 29.8637 cents 6:7:8:10:12 S SD: 19.7940 cents 7:8:9:11:14 SD: 17.5662 cents 8:9:11:13:16 SD: 16.3970 cents 12:14:16:19:24 SD: 10.0090 cents 15:17:20:24:30 SD: 3.6218 cents 27:31:36:43:54 SD: 2.8337 cents 42:48:56:67:84 SD: 1.2900 cents 63:72:84:101:126 SD: 0.8579 cents 90:103:120:144:180 SD: 0.6007 cents 105:120:140:168:210 S SD: 0.0000 cents