Scala analysis: Newton_ext_mixolydian
kernel of the 8 pitch-classes core from N's 14 tones out of 53
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 10/9 182.403712 minor whole tone 2: 5/4 386.313714 major third 3: 4/3 498.044999 perfect fourth 4: 3/2 701.955001 perfect fifth 5: 5/3 884.358713 major sixth, BP sixth 6: 16/9 996.089998 Pythagorean minor 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: 10/9 182.4037 minor whole tone 2: 9/8 203.9100 major whole tone 3: 16/15 111.7313 minor diatonic semitone 4: 9/8 203.9100 major whole tone 5: 10/9 182.4037 minor whole tone 6: 16/15 111.7313 minor diatonic semitone 7: 135/128 92.1787 major chroma, major limma 8: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 135/128 92.179 cents major chroma, major limma 1: 3 16/15 111.731 cents minor diatonic semitone 1: 2 10/9 182.404 cents minor whole tone 1: 2 9/8 203.910 cents major whole tone 2: 2 9/8 203.910 cents major whole tone 2: 2 32/27 294.135 cents Pythagorean minor third 2: 2 6/5 315.641 cents minor third 2: 2 5/4 386.314 cents major third 3: 1 6/5 315.641 cents minor third 3: 2 5/4 386.314 cents major third 3: 4 4/3 498.045 cents perfect fourth 3: 1 27/20 519.551 cents acute fourth 4: 2 4/3 498.045 cents perfect fourth 4: 2 45/32 590.224 cents diatonic tritone 4: 2 64/45 609.776 cents 2nd tritone 4: 2 3/2 701.955 cents perfect fifth 5: 1 40/27 680.449 cents grave fifth 5: 4 3/2 701.955 cents perfect fifth 5: 2 8/5 813.686 cents minor sixth 5: 1 5/3 884.359 cents major sixth, BP sixth 6: 2 8/5 813.686 cents minor sixth 6: 2 5/3 884.359 cents major sixth, BP sixth 6: 2 27/16 905.865 cents Pythagorean major sixth 6: 2 16/9 996.090 cents Pythagorean minor seventh 7: 2 16/9 996.090 cents Pythagorean minor seventh 7: 2 9/5 1017.596 cents just minor seventh, BP seventh 7: 3 15/8 1088.269 cents classic major seventh 7: 1 256/135 1107.821 cents octave - major chroma 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 5 6 7 8 0.0 : 182.4 386.3 498.0 702.0 884.4 996.1 1088.3 1200.0 182.4 : 203.9 315.6 519.6 702.0 813.7 905.9 1017.6 1200.0 386.3 : 111.7 315.6 498.0 609.8 702.0 813.7 996.1 1200.0 498.0 : 203.9 386.3 498.0 590.2 702.0 884.4 1088.3 1200.0 702.0 : 182.4 294.1 386.3 498.0 680.4 884.4 996.1 1200.0 884.4 : 111.7 203.9 315.6 498.0 702.0 813.7 1017.6 1200.0 996.1 : 92.2 203.9 386.3 590.2 702.0 905.9 1088.3 1200.0 1088.3: 111.7 294.1 498.0 609.8 813.7 996.1 1107.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 92.1787 .. 203.9100 cents 16/15, 111.7313 cents 135/128, 92.1787 cents 2: 203.9100 .. 386.3137 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 3: 315.6413 .. 519.5513 cents 9/8, 203.9100 cents 24/25,-70.6724 cents 4: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 80/81,-21.5063 cents 5: 680.4487 .. 884.3587 cents 9/8, 203.9100 cents 80/81,-21.5063 cents 6: 813.6863 .. 996.0900 cents 10/9, 182.4037 cents 24/25,-70.6724 cents 7: 996.0900 .. 1107.8213 cents 16/15, 111.7313 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 8 -- Interval properties -- Smallest interval : 135/128, 92.1787 cents, class 1 Average step (divided formal octave): 150.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 1.627274 Largest / Average step : 1.359400 Largest / Smallest step : 2.212116 Median interval of one step : 147.06750 cents, amount: 0 Most common interval of one step : 16/15, 111.7313 cents, amount: 3 Least squares average step : 161.14314 cents, oct.: 1289.14513 cents Scale is not proper Step pattern alph. order: ABCBACDC Step pattern size order : CDBDCBAB Scale is not a Constant Structure Scale diversity : 1.322073 Lumma stability : 0.153631 Lumma impropriety factor : 0.153631 Rothenberg efficiency : 0.546429 redundancy: 0.453571 Efficiency x scale size : 4.371429 Number of different interval sizes : 20 = 2.85714 / 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 : 2048/2025, 19.5526 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 6 Most common triad is 0.0 498.045 701.955 cents, amount: 4 Number of recognisable fifths : 6, average 701.9550 cents Scale is fully connected 5-limit major-minor triadic Scale is a complete genus musicum : 2^m 3^3 5^1 Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 3 Length of longest subharmonic part : 2 at degree 0 Formal octave complements present : 3 = 37.5000% Scale is n-1 differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval class 2 Scale is n-1 differentially coherent in interval class 3 Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is n-1 differentially coherent in interval classes 5 and 6 combined Limited inverse transpositions : 5 Inversional symmetry on intervals : 2-3 6-7 -- Rational properties -- Prime limit : 5 Odd number limit : 135 (O: 135 U: 135) Highest odd numerator or denominator: 15 Scale harmonicity : 0.046729 Average absolute harmonicity : 0.248113 Specific harmonicity : 0.234104 Fundamental : 1/72, -6.1699 octaves, 3.6337 Hz. Guide tone : 240, 7.9069 octaves, 62790.136 Hz. Exponens Consonantiae : 1.728000E+04, 14.07682 octaves Euler's gradus suavitatis : 18 Sum of Mann's harmonic distance : 49.5, average 6.18750 Mersenne's string divisions : 5506200 Sum of van Prooijen's expressibility: 5.43676, average 0.67959 Sum of Tenney's harmonic distance : 10.82727, average 1.35341 Vogel's harmonic complexity : 10.25000 Wille's k value : 67 Wilson's harmonic complexity : 14 Rectangular lattice diameter : 4 Triangular lattice diameter : 4 Lattice compactness : 111.45229, average 3.09590 Lattice compactness (without 2's) : 57.81860, average 1.60607 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -3 .. 4 0.25000 14 1 3: -2 .. 1 -0.50000 8 3 5: 0 .. 1 0.50000 4 4 Average exponent except 2's : 0 / 8 = 0.00000 Average absolute exponent except 2's: 12 / 8 = 1.50000 Scale is weakly epimorphic with val: <8 13 20| Scale is weakly epimorphic with val: <8 14 17| Scale is weakly epimorphic with val: <8 14 19| Scale is weakly epimorphic with val: <8 14 21|
FIT/MODE
8: 1 1 1 1 1 1 1 1 SP B ME I SD: 79.0200 c. M: 134.3587 c. 9: 1 2 0 2 1 1 1 1 P D3 SD: 55.8735 c. M: 98.0450 c. 10: 1 2 1 2 1 1 1 1 N D3 SD: 32.7422 c. M: 62.4037 c. 12: 2 2 1 2 2 1 1 1 N D3 SD: 10.6193 c. M:-17.5963 c. Genus diatonicum, Dominant Bebop, Raga Khamaj, Alhaiya Bilaval, Bihagara, Desh Malhar (Des), Devagandhari, Lankeshree, Malagunji, Nat Bihag, Nat Malhar, Maqam Shawq Awir, Gregorian nr.6, Chinese Eight-Tone, Rast: Greece, Ionian/Mixolydian mixed 19: 3 3 2 3 3 2 1 2 N G SD: 8.8712 c. M: 14.5845 c. 29: 4 5 3 5 4 3 2 3 N SD: 10.5037 c. M: 16.8865 c. 31: 5 5 3 5 5 3 2 3 N G SD: 6.5266 c. M:-11.1447 c. Genus diatonicum 34: 5 6 3 6 5 3 3 3 N SD: 4.6053 c. M: 7.8547 c. 41: 6 7 4 7 6 4 3 4 N SD: 4.3280 c. M: 6.7940 c. 46: 7 8 4 8 7 4 4 4 N SD: 3.8821 c. M:-7.3835 c. 53: 8 9 5 9 8 5 4 5 N SD: 0.9748 c. M: 1.4763 c. 118: 18 20 11 20 18 11 9 11 N SD: 0.3550 c. M:-0.6471 c. 171: 26 29 16 29 26 16 13 16 N SD: 0.2936 c. M: 0.5494 c. 289: 44 49 27 49 44 27 22 27 N SD: 0.2654 c. M:-0.4498 c. 323: 49 55 30 55 49 30 25 30 N SD: 0.2506 c. M: 0.4244 c. 376: 57 64 35 64 57 35 29 35 N SD: 0.2596 c. M: 0.4888 c. 388: 59 66 36 66 59 36 30 36 N SD: 0.2058 c. M:-0.3911 c. 441: 67 75 41 75 67 41 34 41 N SD: 0.1041 c. M: 0.1716 c. 494: 75 84 46 84 75 46 38 46 N SD: 0.1142 c. M: 0.2175 c. 559: 85 95 52 95 85 52 43 52 N SD: 0.0614 c. M:-0.1034 c. 612: 93 104 57 104 93 57 47 57 N SD: 0.0305 c. M: 0.0508 c. 1171: 178 199 109 199 178 109 90 109 N SD: 0.0167 c. M:-0.0319 c. 1783: 271 303 166 303 271 166 137 166 N SD: 0.0095 c. M: 0.0160 c.
FIT/HARMONIC
1 x x x x x x x 2 S SD: 0.0000 cents 2 x x x 3 x x x 4 S SD: 0.0000 cents 3 x x 4 x 5 x x 6 S SD: 0.0000 cents 4 x 5 x 6 x 7 x 8 S SD: 6.8160 cents 5 x 6:7 x 8:9 x 10 S SD: 26.5228 cents 6:7 x 8:9:10 x 11:12 S SD: 15.4994 cents 7:8:9 x 11:12 x 13:14 SD: 19.6471 cents 8:9:10:11:12:13:14:15:16 H SD: 9.6542 cents 9:10:11:12:14:15:16:17:18 S SD: 9.3883 cents 10:11 x 13:15:17:18:19:20 SD: 9.4627 cents 12:13:15:16:18:20:21:23:24 SD: 8.0159 cents 15:17:19:20:23:25:27:28:30 SD: 7.5736 cents 16:18:20:21:24:27:28:30:32 S SD: 6.1386 cents 18:20:23:24:27:30:32:34:36 SD: 5.0173 cents 24:27:30:32:36:40:43:45:48 SD: 3.1722 cents 36:40:45:48:54:60:64:68:72 S SD: 1.5971 cents 60:67:75:80:90:100:107:113:120 SD: 1.5943 cents 63:70:79:84:95:105:112:118:126 SD: 1.3517 cents 64:71:80:85:96:107:114:120:128 SD: 1.2108 cents 72:80:90:96:108:120:128:135:144 SD: 0.0000 cents