Scala analysis: lumma_wauchope-major
Two 8:10:12:15 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: 5/4 386.313714 major third 3: 21/16 470.780907 narrow fourth 4: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 5: 3/2 701.955001 perfect fifth 6: 7/4 968.825906 harmonic seventh 7: 15/8 1088.268715 classic major seventh 8: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 21/20 84.4672 minor semitone 2: 25/21 301.8465 BP second, quasi-equal minor third 3: 21/20 84.4672 minor semitone 4: 16/15 111.7313 minor diatonic semitone 5: 15/14 119.4428 major diatonic semitone 6: 7/6 266.8709 septimal minor third 7: 15/14 119.4428 major diatonic semitone 8: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 2 15/14 119.443 cents major diatonic semitone 1: 1 7/6 266.871 cents septimal minor third 1: 1 25/21 301.847 cents BP second, quasi-equal minor third 2: 2 28/25 196.198 cents middle second 2: 2 8/7 231.174 cents septimal whole tone 2: 4 5/4 386.314 cents major third 3: 2 6/5 315.641 cents minor third 3: 1 21/16 470.781 cents narrow fourth 3: 4 4/3 498.045 cents perfect fourth 3: 1 75/56 505.757 cents marvelous 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: 1 112/75 694.243 cents marvelous fifth 5: 4 3/2 701.955 cents perfect fifth 5: 1 32/21 729.219 cents wide fifth 5: 2 5/3 884.359 cents major sixth, BP sixth 6: 4 8/5 813.686 cents minor sixth 6: 2 7/4 968.826 cents harmonic seventh 6: 2 25/14 1003.802 cents middle minor seventh 7: 1 42/25 898.153 cents quasi-equal major sixth 7: 1 12/7 933.129 cents septimal major sixth 7: 2 28/15 1080.557 cents grave major seventh 7: 2 15/8 1088.269 cents classic 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 : 84.5 386.3 470.8 582.5 702.0 968.8 1088.3 1200.0 84.5 : 301.8 386.3 498.0 617.5 884.4 1003.8 1115.5 1200.0 386.3 : 84.5 196.2 315.6 582.5 702.0 813.7 898.2 1200.0 470.8 : 111.7 231.2 498.0 617.5 729.2 813.7 1115.5 1200.0 582.5 : 119.4 386.3 505.8 617.5 702.0 1003.8 1088.3 1200.0 702.0 : 266.9 386.3 498.0 582.5 884.4 968.8 1080.6 1200.0 968.8 : 119.4 231.2 315.6 617.5 702.0 813.7 933.1 1200.0 1088.3: 111.7 196.2 498.0 582.5 694.2 813.7 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 84.4672 .. 301.8465 cents 500/441, 217.3793 cents 21/20, 84.4672 cents 2: 196.1985 .. 386.3137 cents 125/112, 190.1152 cents 588/625,-105.6480 cents 3: 315.6413 .. 505.7565 cents 125/112, 190.1152 cents 24/25,-70.6724 cents 4: 582.5122 .. 617.4878 cents 50/49, 34.9756 cents 392/375, 76.7557 cents 5: 694.2435 .. 884.3587 cents 125/112, 190.1152 cents 392/375, 76.7557 cents 6: 813.6863 .. 1003.8015 cents 125/112, 190.1152 cents 24/25,-70.6724 cents 7: 898.1535 .. 1115.5328 cents 500/441, 217.3793 cents 588/625,-105.6480 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 : 25/21, 301.8465 cents Average / Smallest step : 1.775837 Largest / Average step : 2.012310 Largest / Smallest step : 3.573536 Median interval of one step : 115.58705 cents, amount: 0 Least squares average step : 152.64754 cents, oct.: 1221.18030 cents Scale is not proper Step pattern alph. order: ABACDEDC Step pattern size order : AEABCDCB Scale is a Constant Structure, by a margin of 13.79477 cents Scale diversity : 1.425194 Lumma stability : 0.268705 Lumma impropriety factor : 0.293867 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 : 225/224, 7.7115 cents Number of recognisable fifths : 5, average 700.4127 cents Length of longest harmonic part : 2 at degree 6 Length of longest subharmonic part : 2 at degree 3 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 class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Limited inverse transpositions : 3 Inversional symmetry on intervals : 1-2 5-6 -- Rational properties -- Prime limit : 7 Odd number limit : 75 (O: 75 U: 75) Highest odd numerator or denominator: 21 Scale harmonicity : 0.032518 Average absolute harmonicity : 0.215224 Specific harmonicity : 0.160000 Fundamental : 1/80, -6.3219 octaves, 3.2703 Hz. Guide tone : 210, 7.7142 octaves, 54941.369 Hz. Exponens Consonantiae : 1.680000E+04, 14.03617 octaves Euler's gradus suavitatis : 22 Sum of Mann's harmonic distance : 70.5, average 8.81250 Mersenne's string divisions : 69084180 Sum of van Prooijen's expressibility: 6.68682, average 0.83585 Sum of Tenney's harmonic distance : 12.60021, average 1.57503 Vogel's harmonic complexity : 12.37500 Wille's k value : 52 Wilson's harmonic complexity : 20 Rectangular lattice diameter : 4 Triangular lattice diameter : 3 Lattice compactness : 89.87496, average 2.49653 Lattice compactness (without 2's) : 49.41615, average 1.37267 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 1 -1.62500 15 1 3: 0 .. 1 0.50000 4 1 5: -1 .. 1 0.00000 4 2 7: 0 .. 1 0.50000 4 4 Average exponent except 2's : 8 / 8 = 1.00000 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 JI-epimorphic with val: <8 13 18 22| Scale is weakly epimorphic with val: <8 13 20 22| Scale is weakly epimorphic with val: <8 14 17 21| Scale is weakly epimorphic with val: <8 14 19 23| Scale is weakly epimorphic with val: <8 14 20 21| Scale is weakly epimorphic with val: <8 14 20 23|
FIT/MODE
8: 0 2 1 0 1 2 1 1 N T3 SD: 78.3999 c. M: 132.5122 c. 9: 0 3 0 1 1 2 1 1 N SD: 47.0666 c. M: 84.4672 c. 10: 1 2 1 1 1 2 1 1 P B ME SD: 18.7673 c. M:-35.5328 c. 12: 1 3 1 1 1 3 1 1 N B DE SD: 18.3760 c. M:-31.1741 c. Tcherepnin Octatonic mode 1 15: 1 4 1 1 2 3 2 1 N SD: 16.6187 c. M:-31.7313 c. 19: 1 5 1 2 2 4 2 2 N SD: 16.7870 c. M: 28.6756 c. 20: 1 5 2 2 2 4 2 2 N SD: 16.4079 c. M: 26.3137 c. 21: 1 6 1 2 2 5 2 2 N SD: 13.7833 c. M: 27.3243 c. 22: 2 5 2 2 2 5 2 2 N B DE SD: 13.9830 c. M:-24.6237 c. 24: 2 6 1 3 2 5 3 2 N SD: 14.4140 c. M: 20.7809 c. 25: 2 6 2 2 3 5 3 2 N SD: 10.7049 c. M:-18.0450 c. 27: 2 7 2 2 3 6 3 2 N SD: 12.4646 c. M:-22.8424 c. 28: 2 7 2 3 2 7 2 3 N B D3 SD: 11.9411 c. M:-17.4878 c. 29: 2 7 2 3 3 6 3 3 N SD: 10.5985 c. M: 17.1018 c. 31: 2 8 2 3 3 7 3 3 N SD: 4.1889 c. M: 7.0478 c. 41: 3 10 3 4 4 9 4 4 N SD: 3.4825 c. M: 5.8259 c. 56: 4 14 4 5 6 12 6 5 N SD: 3.2872 c. M:-5.1879 c. 68: 5 17 5 6 7 15 7 6 N SD: 3.5887 c. M:-5.8489 c. 72: 5 18 5 7 7 16 7 7 N SD: 2.7525 c. M: 4.9354 c. 74: 5 19 5 7 7 17 7 7 N SD: 2.8214 c. M: 4.6577 c. 84: 6 21 6 8 8 19 8 8 N SD: 1.9271 c. M:-3.2021 c. 87: 6 22 6 8 9 19 9 8 N SD: 1.9868 c. M: 3.3087 c. 99: 7 25 7 9 10 22 10 9 N SD: 1.4032 c. M:-2.6404 c. 130: 9 33 9 12 13 29 13 12 N SD: 0.8692 c. M: 1.3903 c. 140: 10 35 10 13 14 31 14 13 N SD: 0.6541 c. M:-1.2471 c. 171: 12 43 12 16 17 38 17 16 N SD: 0.3646 c. M: 0.6055 c. 270: 19 68 19 25 27 60 27 25 N SD: 0.3119 c. M:-0.6202 c. 311: 22 78 22 29 31 69 31 29 N SD: 0.2819 c. M: 0.4616 c. 441: 31 111 31 41 44 98 44 41 N SD: 0.1169 c. M: 0.1993 c. 612: 43 154 43 57 61 136 61 57 N SD: 0.1265 c. M: 0.1985 c. 752: 53 189 53 70 75 167 75 70 N SD: 0.1183 c. M: 0.2089 c. 966: 68 243 68 90 96 215 96 90 N SD: 0.0687 c. M:-0.1182 c. 1236: 87 311 87 115 123 275 123 115 N SD: 0.0667 c. M:-0.1061 c. 1277: 90 321 90 119 127 284 127 119 N SD: 0.0707 c. M:-0.1060 c. 1407: 99 354 99 131 140 313 140 131 N SD: 0.0274 c. M:-0.0440 c. 2159: 152 543 152 201 215 480 215 201 N SD: 0.0244 c. M: 0.0441 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 4 x x 5 x 6 S SD: 29.5861 cents 4 x 5 x x 6:7 x 8 S SD: 0.0000 cents 5 x 6 x 7:8:9 x 10 S SD: 28.1830 cents 6 x x 8 x 9 x 11:12 SD: 11.8769 cents 7:8 x 9:10:11:12:13:14 S SD: 25.5772 cents 8:9:10 x 11:12:14:15:16 S SD: 17.6356 cents 9:10:11:12:13:14:16:17:18 S SD: 17.5208 cents 10:11 x 13:14:15:18:19:20 SD: 14.0444 cents 11:12:14 x 15:17:19:21:22 SD: 15.3754 cents 12:13:15:16:17:18:21:23:24 SD: 9.3025 cents 14:15 x 18:20:21:25:26:28 SD: 10.3200 cents 15:16:19:20:21:23:26:28:30 SD: 7.6997 cents 16:17:20:21:22:24:28:30:32 SD: 4.6651 cents 20:21:25:26:28:30:35:38:40 SD: 3.5361 cents 32:34:40:42:45:48:56:60:64 SD: 2.7364 cents 40:42:50:53:56:60:70:75:80 SD: 2.0512 cents 48:50:60:63:67:72:84:90:96 SD: 1.8410 cents 60:63:75:79:84:90:105:113:120 SD: 1.1796 cents 64:67:80:84:90:96:112:120:128 SD: 1.1598 cents 80:84:100:105:112:120:140:150:160 SD: 0.0000 cents