Scala analysis: 08_wauchope_symmetrical
Two 10:12:15:18 chords rooted a 7:5 apart.
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 21/20 84.467193 minor semitone 2: 7/6 266.870906 septimal minor third 3: 5/4 386.313714 major third 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 3/2 701.955001 perfect fifth 6: 5/3 884.358713 major sixth, BP sixth 7: 7/4 968.825906 harmonic seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 8/7 231.1741 septimal whole tone 1: 21/20 84.4672 minor semitone 2: 10/9 182.4037 minor whole tone 3: 15/14 119.4428 major diatonic semitone 4: 28/25 196.1985 middle second 5: 15/14 119.4428 major diatonic semitone 6: 10/9 182.4037 minor whole tone 7: 21/20 84.4672 minor semitone 8: 8/7 231.1741 septimal whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 21/20 84.467 cents minor semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 1 28/25 196.198 cents middle second 1: 1 8/7 231.174 cents septimal whole tone 2: 2 7/6 266.871 cents septimal minor third 2: 2 25/21 301.847 cents BP second, quasi-equal minor third 2: 4 6/5 315.641 cents minor third 3: 2 5/4 386.314 cents major third 3: 1 63/50 400.108 cents quasi-equal major third 3: 1 9/7 435.084 cents septimal major third, BP third 3: 4 4/3 498.045 cents perfect fourth 4: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 4: 4 10/7 617.488 cents Euler's tritone 5: 4 3/2 701.955 cents perfect fifth 5: 1 14/9 764.916 cents septimal minor sixth 5: 1 100/63 799.892 cents quasi-equal minor sixth 5: 2 8/5 813.686 cents minor sixth 6: 4 5/3 884.359 cents major sixth, BP sixth 6: 2 42/25 898.153 cents quasi-equal major sixth 6: 2 12/7 933.129 cents septimal major sixth 7: 1 7/4 968.826 cents harmonic seventh 7: 1 25/14 1003.802 cents middle minor seventh 7: 2 9/5 1017.596 cents just minor seventh, BP seventh 7: 2 28/15 1080.557 cents grave major seventh 7: 2 40/21 1115.533 cents acute major seventh Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 3.71429 = 26/7
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 0.0 : 84.5 266.9 386.3 582.5 702.0 884.4 968.8 1200.0 84.5 : 182.4 301.8 498.0 617.5 799.9 884.4 1115.5 1200.0 266.9 : 119.4 315.6 435.1 617.5 702.0 933.1 1017.6 1200.0 386.3 : 196.2 315.6 498.0 582.5 813.7 898.2 1080.6 1200.0 582.5 : 119.4 301.8 386.3 617.5 702.0 884.4 1003.8 1200.0 702.0 : 182.4 266.9 498.0 582.5 764.9 884.4 1080.6 1200.0 884.4 : 84.5 315.6 400.1 582.5 702.0 898.2 1017.6 1200.0 968.8 : 231.2 315.6 498.0 617.5 813.7 933.1 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 231.1741 cents 160/147, 146.7069 cents 21/20, 84.4672 cents 2: 266.8709 .. 315.6413 cents 36/35, 48.7704 cents 49/48, 35.6968 cents 3: 386.3137 .. 498.0450 cents 16/15, 111.7313 cents 25/24, 70.6724 cents 4: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 21/20, 84.4672 cents 5: 701.9550 .. 813.6863 cents 16/15, 111.7313 cents 21/20, 84.4672 cents 6: 884.3587 .. 933.1291 cents 36/35, 48.7704 cents 25/24, 70.6724 cents 7: 968.8259 .. 1115.5328 cents 160/147, 146.7069 cents 49/48, 35.6968 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 21/20, 84.4672 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 8/7, 231.1741 cents Average / Smallest step : 1.775837 Largest / Average step : 1.541161 Largest / Smallest step : 2.736851 Median interval of one step : 150.92326 cents, amount: 0 Least squares average step : 143.65151 cents, oct.: 1149.21206 cents Scale is strictly proper Step pattern alph. order: ABCDCBAE Step pattern size order : ACBDBCAE Scale is a Constant Structure, by a margin of 35.69681 cents Scale diversity : 1.460523 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.458839 Rothenberg efficiency : 0.421429 redundancy: 0.578571 Efficiency x scale size : 3.371429 Number of different interval sizes : 26 = 3.71429 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 3.71429 = 26/7 Median interval variety : 2 Lowest interval variety : 2 Smallest interval difference : 126/125, 13.7948 cents Number of recognisable fifths : 4, average 701.9550 cents Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 12.5000% Scale is n-1 differentially coherent in interval class 1 Scale is differentially coherent in interval classes 2 and 3 combined Scale is n-1 differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval class 5 Limited inverse transpositions : 7 Inversional symmetry on intervals : 3-4 7-8 -- Rational properties -- Prime limit : 7 Odd number limit : 63 (O: 63 U: 63) Highest odd numerator or denominator: 21 Scale harmonicity : 0.031828 Average absolute harmonicity : 0.220237 Specific harmonicity : 0.160211 Fundamental : 1/60, -5.9069 octaves, 4.3604 Hz. Guide tone : 210, 7.7142 octaves, 54941.369 Hz. Exponens Consonantiae : 1.260000E+04, 13.62114 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 51.0, average 6.37500 Mersenne's string divisions : 2110680 Sum of van Prooijen's expressibility: 5.73257, average 0.71657 Sum of Tenney's harmonic distance : 10.79403, average 1.34925 Vogel's harmonic complexity : 12.62500 Wille's k value : 52 Wilson's harmonic complexity : 23 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 76.92732, average 2.13687 Lattice compactness (without 2's) : 53.88828, average 1.49690 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -2 .. 1 -0.87500 9 1 3: -1 .. 1 0.00000 4 1 5: -1 .. 1 0.00000 4 2 7: 0 .. 1 0.50000 4 4 Average exponent except 2's : 4 / 8 = 0.50000 Average absolute exponent except 2's: 12 / 8 = 1.50000 Scale is weakly epimorphic with val: <8 12 17 23| Scale is weakly epimorphic with val: <8 12 18 21| Scale is weakly epimorphic with val: <8 12 18 23| Scale is weakly epimorphic with val: <8 12 19 21| Scale is weakly epimorphic with val: <8 12 21 23| Scale is weakly epimorphic with val: <8 13 17 23| Scale is JI-epimorphic with val: <8 13 19 23| Scale is weakly epimorphic with val: <8 14 17 21| Scale is weakly epimorphic with val: <8 14 18 21| Scale is weakly epimorphic with val: <8 14 18 23| Scale is weakly epimorphic with val: <8 14 19 23|
FIT/MODE
8: 0 1 1 1 1 1 1 2 N T3 SD: 99.3649 c. M: 134.3587 c. 9: 1 1 1 1 1 2 0 2 P D3 SD: 35.1734 c. M: 49.1789 c. 10: 1 1 1 2 1 1 1 2 P B ME SD: 25.8700 c. M: 44.3587 c. 12: 1 2 1 2 1 2 1 2 SP B ME SD: 19.5328 c. M:-33.1291 c. Octatonic, Messiaen mode 2, Dominant Diminished, Diminished Blues, Half-Whole step scale 15: 1 2 2 2 2 2 1 3 P D3 SD: 15.2423 c. M: 26.8709 c. 19: 1 3 2 3 2 3 1 4 P SD: 13.3333 c. M: 21.4575 c. 22: 2 3 2 4 2 3 2 4 SP B D3 SD: 12.8533 c. M:-24.6237 c. 26: 2 4 2 5 2 4 2 5 SP B D3 SD: 10.6577 c. M:-17.4878 c. 27: 2 4 3 4 3 4 2 5 SP SD: 7.1921 c. M:-13.6863 c. 31: 2 5 3 5 3 5 2 6 SP SD: 4.0948 c. M: 7.0478 c. 41: 3 6 4 7 4 6 3 8 SP SD: 3.7758 c. M: 6.3099 c. 53: 4 8 5 9 5 8 4 10 SP SD: 3.9522 c. M:-6.1671 c. 58: 4 9 6 9 6 9 4 11 SP SD: 3.6540 c. M:-6.7897 c. 68: 5 10 7 11 7 10 5 13 SP SD: 2.3758 c. M:-3.9274 c. 72: 5 11 7 12 7 11 5 14 SP SD: 1.5977 c. M: 2.9804 c. 99: 7 15 10 16 10 15 7 19 SP SD: 0.8119 c. M:-1.5651 c. 140: 10 21 14 23 14 21 10 27 SP SD: 0.9017 c. M: 1.5016 c. 171: 12 26 17 28 17 26 12 33 SP SD: 0.2394 c. M: 0.4049 c. 270: 19 41 27 44 27 41 19 52 SP SD: 0.2042 c. M:-0.3530 c. 441: 31 67 44 72 44 67 31 85 SP SD: 0.1236 c. M: 0.2042 c. 612: 43 93 61 100 61 93 43 118 SP SD: 0.1292 c. M: 0.2042 c. 783: 55 119 78 128 78 119 55 151 SP SD: 0.1450 c. M: 0.2435 c. 935: 66 142 93 153 93 142 66 180 SP SD: 0.1260 c. M:-0.2387 c. 966: 68 147 96 158 96 147 68 186 SP SD: 0.1055 c. M:-0.2098 c. 1065: 75 162 106 174 106 162 75 205 SP SD: 0.1206 c. M:-0.1882 c. 1106: 78 168 110 181 110 168 78 213 SP SD: 0.0879 c. M:-0.1621 c. 1137: 80 173 113 186 113 173 80 219 SP SD: 0.0777 c. M:-0.1476 c. 1236: 87 188 123 202 123 188 87 238 SP SD: 0.0760 c. M:-0.1194 c. 1277: 90 194 127 209 127 194 90 246 SP SD: 0.0716 c. M:-0.1060 c. 1308: 92 199 130 214 130 199 92 252 SP SD: 0.0707 c. M: 0.1201 c. 1376: 97 209 137 225 137 209 97 265 SP SD: 0.0642 c. M:-0.1258 c. 1407: 99 214 140 230 140 214 99 271 SP SD: 0.0476 c. M:-0.0801 c. 1547: 109 235 154 253 154 235 109 298 SP SD: 0.0456 c. M:-0.0835 c. 1578: 111 240 157 258 157 240 111 304 SP SD: 0.0375 c. M: 0.0565 c. 1848: 130 281 184 302 184 281 130 356 SP SD: 0.0364 c. M:-0.0569 c. 2019: 142 307 201 330 201 307 142 389 SP SD: 0.0356 c. M: 0.0690 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x x 3 x x 4 S SD: 0.0000 cents 3 x x x 4 x 5 x 6 S SD: 28.1557 cents 4 x x 5 x 6 x 7:8 S SD: 0.0000 cents 5 x 6 x 7 x 8:9:10 S SD: 19.7501 cents 6 x 7 x 8:9:10:11:12 S SD: 19.4515 cents 7 x 8:9:10:11 x 12:14 S SD: 18.7354 cents 8 x 9:10:11:12:13:14:16 S SD: 11.8307 cents 9 x x 11:13:14:15:16:18 SD: 15.9413 cents 11:12:13:14:15:17:18:19:22 SD: 13.7606 cents 12:13:14:15:17:18:20:21:24 SD: 7.2318 cents 16:17:19:20:22:24:27:28:32 SD: 6.6077 cents 18:19:21:23:25:27:30:32:36 SD: 6.2060 cents 20:21:23:25:28:30:33:35:40 SD: 3.7982 cents 24:25:28:30:34:36:40:42:48 SD: 3.0874 cents 36:38:42:45:50:54:60:63:72 SD: 2.0682 cents 40:42:47:50:56:60:67:70:80 SD: 1.8808 cents 48:50:56:60:67:72:80:84:96 SD: 1.8410 cents 60:63:70:75:84:90:100:105:120 SD: 0.0000 cents