Scala analysis: fractal-03-day-for-night
Sevish: Day for Night, One With the Fractal
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 6/5 315.641287 minor third 2: 4/3 498.044999 perfect fourth 3: 3/2 701.955001 perfect fifth 4: 5/3 884.358713 major sixth, BP sixth 5: 9/5 1017.596288 just minor seventh, BP seventh 6: 2/1 1200.000000 octave 7: 12/5 1515.641287 minor 10th 8: 8/3 1698.044999 perfect 11th 9: 3/1 1901.955001 perfect 12th 10: 10/3 2084.358713 major 13th 11: 18/5 2217.596288 minor 14th 12: 4/1 2400.000000 2 octaves 13: 9/2 2603.910002 perfect 16th 14: 5/1 2786.313714 major 17th
SHOW/INTERVAL
0: 10/9 182.4037 minor whole tone 1: 6/5 315.6413 minor third 2: 10/9 182.4037 minor whole tone 3: 9/8 203.9100 major whole tone 4: 10/9 182.4037 minor whole tone 5: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 6: 10/9 182.4037 minor whole tone 7: 6/5 315.6413 minor third 8: 10/9 182.4037 minor whole tone 9: 9/8 203.9100 major whole tone 10: 10/9 182.4037 minor whole tone 11: 27/25 133.2376 large limma, BP small semitone, Zarlino semitone 12: 10/9 182.4037 minor whole tone 13: 9/8 203.9100 major whole tone 14: 10/9 182.4037 minor whole tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 1: 7 10/9 182.404 cents minor whole tone 1: 3 9/8 203.910 cents major whole tone 1: 2 6/5 315.641 cents minor third 2: 4 6/5 315.641 cents minor third 2: 6 5/4 386.314 cents major third 2: 4 4/3 498.045 cents perfect fourth 3: 2 4/3 498.045 cents perfect fourth 3: 3 27/20 519.551 cents acute fourth 3: 3 25/18 568.717 cents classic augmented fourth 3: 1 36/25 631.283 cents classic diminished fifth 3: 2 40/27 680.449 cents grave fifth 3: 3 3/2 701.955 cents perfect fifth 4: 6 3/2 701.955 cents perfect fifth 4: 2 8/5 813.686 cents minor sixth 4: 6 5/3 884.359 cents major sixth, BP sixth 5: 3 5/3 884.359 cents major sixth, BP sixth 5: 1 27/16 905.865 cents Pythagorean major sixth 5: 1 16/9 996.090 cents Pythagorean minor seventh 5: 5 9/5 1017.596 cents just minor seventh, BP seventh 5: 3 50/27 1066.762 cents grave major seventh 5: 1 15/8 1088.269 cents classic major seventh 6: 2 15/8 1088.269 cents classic major seventh 6: 10 2/1 1200.000 cents octave 6: 2 25/12 1270.672 cents classic augmented octave 7: 1 25/12 1270.672 cents classic augmented octave 7: 1 54/25 1333.238 cents large limma, BP small semitone, Zarlino semitone +1 octave 7: 5 20/9 1382.404 cents small ninth 7: 5 9/4 1403.910 cents major ninth 7: 1 125/54 1453.076 cents semi-augmented whole tone +1 octave 7: 1 12/5 1515.641 cents minor 10th 8: 2 12/5 1515.641 cents minor 10th 8: 10 5/2 1586.314 cents major 10th 8: 2 8/3 1698.045 cents perfect 11th 9: 1 8/3 1698.045 cents perfect 11th 9: 3 27/10 1719.551 cents acute fourth +1 octave 9: 5 25/9 1768.717 cents classic augmented eleventh, BP twelfth 9: 1 45/16 1790.224 cents diatonic tritone +1 octave 9: 1 80/27 1880.449 cents grave fifth +1 octave 9: 3 3/1 1901.955 cents perfect 12th 10: 6 3/1 1901.955 cents perfect 12th 10: 2 25/8 1972.627 cents classic augmented 12th 10: 6 10/3 2084.359 cents major 13th 11: 3 10/3 2084.359 cents major 13th 11: 2 27/8 2105.865 cents Pythagorean major sixth +1 octave 11: 1 125/36 2155.031 cents classic augmented sixth +1 octave 11: 3 18/5 2217.596 cents minor 14th 11: 3 100/27 2266.762 cents grave major seventh +1 octave 11: 2 15/4 2288.269 cents classic major 14th 12: 4 15/4 2288.269 cents classic major 14th 12: 6 4/1 2400.000 cents 2 octaves 12: 4 25/6 2470.672 cents classic chromatic semitone, minor chroma +2 octaves 13: 2 25/6 2470.672 cents classic chromatic semitone, minor chroma +2 octaves 13: 3 40/9 2582.404 cents minor whole tone +2 octaves 13: 7 9/2 2603.910 cents perfect 16th 13: 2 125/27 2653.076 cents semi-augmented whole tone +2 octaves Highest number of different intervals for one interval class: 6 Average number of different intervals per interval class: 4.30769 = 56/13
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.0 : 315.6 498.0 702.0 884.4 1017.6 1200.0 1515.6 1698.0 1902.0 2084.4 2217.6 2400.0 2603.9 2786.3 315.6 : 182.4 386.3 568.7 702.0 884.4 1200.0 1382.4 1586.3 1768.7 1902.0 2084.4 2288.3 2470.7 2786.3 498.0 : 203.9 386.3 519.6 702.0 1017.6 1200.0 1403.9 1586.3 1719.6 1902.0 2105.9 2288.3 2603.9 2786.3 702.0 : 182.4 315.6 498.0 813.7 996.1 1200.0 1382.4 1515.6 1698.0 1902.0 2084.4 2400.0 2582.4 2786.3 884.4 : 133.2 315.6 631.3 813.7 1017.6 1200.0 1333.2 1515.6 1719.6 1902.0 2217.6 2400.0 2603.9 2786.3 1017.6: 182.4 498.0 680.4 884.4 1066.8 1200.0 1382.4 1586.3 1768.7 2084.4 2266.8 2470.7 2653.1 2786.3 1200.0: 315.6 498.0 702.0 884.4 1017.6 1200.0 1403.9 1586.3 1902.0 2084.4 2288.3 2470.7 2603.9 2786.3 1515.6: 182.4 386.3 568.7 702.0 884.4 1088.3 1270.7 1586.3 1768.7 1972.6 2155.0 2288.3 2470.7 2786.3 1698.0: 203.9 386.3 519.6 702.0 905.9 1088.3 1403.9 1586.3 1790.2 1972.6 2105.9 2288.3 2603.9 2786.3 1902.0: 182.4 315.6 498.0 702.0 884.4 1200.0 1382.4 1586.3 1768.7 1902.0 2084.4 2400.0 2582.4 2786.3 2084.4: 133.2 315.6 519.6 702.0 1017.6 1200.0 1403.9 1586.3 1719.6 1902.0 2217.6 2400.0 2603.9 2786.3 2217.6: 182.4 386.3 568.7 884.4 1066.8 1270.7 1453.1 1586.3 1768.7 2084.4 2266.8 2470.7 2653.1 2786.3 2400.0: 203.9 386.3 702.0 884.4 1088.3 1270.7 1403.9 1586.3 1902.0 2084.4 2288.3 2470.7 2603.9 2786.3 2603.9: 182.4 498.0 680.4 884.4 1066.8 1200.0 1382.4 1698.0 1880.4 2084.4 2266.8 2400.0 2582.4 2786.3 2786.3
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 133.2376 .. 315.6413 cents 10/9, 182.4037 cents 27/25, 133.2376 cents 2: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 3: 498.0450 .. 701.9550 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 4: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 5: 884.3587 .. 1088.2687 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 6: 1088.2687 .. 1270.6724 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 7: 1270.6724 .. 1515.6413 cents 144/125, 244.9689 cents 1/1, 0.0000 cents 8: 1515.6413 .. 1698.0450 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 9: 1698.0450 .. 1901.9550 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 10: 1901.9550 .. 2084.3587 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 11: 2084.3587 .. 2288.2687 cents 9/8, 203.9100 cents 1/1, 0.0000 cents 12: 2288.2687 .. 2470.6724 cents 10/9, 182.4037 cents 1/1, 0.0000 cents 13: 2470.6724 .. 2653.0761 cents 10/9, 182.4037 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 14 -- Interval properties -- Smallest interval : 27/25, 133.2376 cents, class 1 Average step (divided formal octave): 199.0224 cents Largest one step interval : 6/5, 315.6413 cents Average / Smallest step : 1.493741 Largest / Average step : 1.585959 Largest / Smallest step : 2.369011 Median interval of one step : 10/9, 182.4037 cents, amount: 7 Most common interval of one step : 10/9, 182.4037 cents, amount: 7 Least squares average step : 204.38505 cents, oct.: 2861.39069 cents Scale is proper Step pattern alph. order: ABCBDBABCBDBCB Step pattern size order : DBCBABDBCBABCB Scale is not a Constant Structure Scale diversity :-0.243855 Rothenberg stability : 0.604396 = 55/91 Lumma stability : 0.095637 Number of different interval sizes : 44 = 3.38462 / class Number of one step interval sizes : 4 Highest interval variety : 6 Mean interval variety : 4.30769 = 56/13 Median interval variety : 3 Lowest interval variety : 3 Smallest interval difference : 81/80, 21.5063 cents Most common intervals : 2/1, 1200.0000 cents & inv., amount: 10 Most common triad is 0.0 1200.000 1586.314 cents, amount: 6 Number of recognisable fifths : 9, average 701.9550 cents Number of recognisable fourths : 6, average 498.0450 cents Scale contains two identical disjunct "tetrachords" of 3 notes Scale contains a complete diamond : 1 3 Length of longest harmonic part : 2 at degree 2 Length of longest subharmonic part : 2 at degree 1 Formal octave complements present : 5 = 35.7143% 2/1 octave complements present : 5 = 35.7143% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval classes 3 and 4 combined Scale is differentially coherent in interval class 4 -- Rational properties -- Prime limit : 5 Odd number limit : 125 (O: 125 U: 27) Highest odd numerator or denominator: 9 Scale harmonicity : 0.040323 Average absolute harmonicity : 0.243980 Specific harmonicity : 0.221747 Fundamental : 1/30, -4.9069 octaves, 8.7209 Hz. Guide tone : 360, 8.4919 octaves, 94185.204 Hz. Exponens Consonantiae : 1.080000E+04, 13.39874 octaves Euler's gradus suavitatis : 19 Sum of Mann's harmonic distance : 69.0, average 4.92857 Mersenne's string divisions : 46966920 Sum of van Prooijen's expressibility: 8.26606, average 0.59043 Sum of Tenney's harmonic distance : 16.08794, average 1.14914 Vogel's harmonic complexity : 10.71429 Wille's k value : 67 Wilson's harmonic complexity : 19 Rectangular lattice diameter : 5 Triangular lattice diameter : 3 Lattice compactness : 242.61738, average 2.31064 Lattice compactness (without 2's) : 172.49229, average 1.64278 Number of different primes : 3 Prime exponents' range, average, count, tones@limit: 2: -1 .. 3 0.78571 15 2 3: -1 .. 2 0.42857 14 5 5: -1 .. 1 -0.07143 7 7 Average exponent except 2's : 5 / 14 = 0.35714 Average absolute exponent except 2's: 21 / 14 = 1.50000
FIT/MODE
14: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 80.8384 c. M: 122.4844 c. 15: 2 1 1 1 0 1 2 1 1 1 1 1 1 1 N D3 SD: 47.1081 c. M: 88.8250 c. 16: 2 1 1 1 1 1 2 1 1 1 1 1 1 1 P D3 SD: 28.5410 c. M:-51.6602 c. 24: 3 1 2 2 1 1 3 2 1 2 1 2 1 2 N SD: 32.1346 c. M: 49.7891 c. 25: 3 1 2 2 1 2 3 1 2 2 1 2 1 2 N SD: 30.9813 c. M: 52.2348 c. 28: 3 2 2 2 1 2 3 2 2 2 1 2 2 2 P T3 SD: 14.4645 c. M: 28.3498 c. 35: 4 2 3 2 2 2 4 2 3 2 2 2 3 2 P SD: 14.2309 c. M: 26.2568 c. 41: 5 2 3 3 2 3 4 3 3 3 2 2 3 3 N SD: 18.1256 c. M:-25.0465 c. 43: 5 3 3 3 2 3 4 3 3 3 2 3 3 3 P SD: 17.4694 c. M:-31.1619 c. 44: 5 3 3 3 2 3 5 3 3 3 2 3 3 3 P SD: 5.5129 c. M:-11.7384 c. 79: 9 5 6 5 4 5 9 5 6 5 4 5 6 5 P SD: 3.5092 c. M:-6.0547 c. 107: 12 7 8 7 5 7 12 7 8 7 5 7 8 7 P SD: 3.0166 c. M: 5.4245 c. 123: 14 8 9 8 6 8 14 8 9 8 6 8 9 8 P SD: 1.2411 c. M:-2.3935 c. 230: 26 15 17 15 11 15 26 15 17 15 11 15 17 15 P SD: 0.9370 c. M: 2.0280 c. 274: 31 18 20 18 13 18 31 18 20 18 13 18 20 18 P SD: 0.4083 c. M: 0.7482 c. 397: 45 26 29 26 19 26 45 26 29 26 19 26 29 26 P SD: 0.2057 c. M:-0.4132 c. 671: 76 44 49 44 32 44 76 44 49 44 32 44 49 44 P SD: 0.1829 c. M:-0.3191 c. 901: 102 59 66 59 43 59 102 59 66 59 43 59 66 59 P SD: 0.1834 c. M: 0.3319 c. 1024: 116 67 75 67 49 67 116 67 75 67 49 67 75 67 P SD: 0.0655 c. M: 0.1351 c. 1298: 147 85 95 85 62 85 147 85 95 85 62 85 95 85 P SD: 0.0726 c. M: 0.1371 c. 1421: 161 93 104 93 68 93 161 93 104 93 68 93 104 93 P SD: 0.0418 c. M:-0.0820 c. 1695: 192 111 124 111 81 111 192 111 124 111 81 111 124 111 P SD: 0.0364 c. M: 0.0628 c.
FIT/HARMONIC
1 x x x x x 2 x x 3 x x 4 x 5 S SD: 0.0000 cents 2 x x 3 x x 4:5 x 6 x 7:8:9:10 S SD: 10.7334 cents 3 x 4 x 5 x 6:7:8:9:10:11:12:14:15 S SD: 7.7948 cents 4:5 x 6 x 7:8:10:11:12:13:14:16:18:20 S SD: 11.6385 cents 5:6:7 x 8:9:10:12:13:15:17:18:20:23:25 SD: 9.9328 cents 6:7:8:9:10:11:12:14:16:18:20:22:24:27:30 S SD: 5.8795 cents 10:12:13:15:17:18:20:24:27:30:33:36:40:45:50 SD: 4.4388 cents 12:14:16:18:20:22:24:29:32:36:40:43:48:54:60 SD: 4.2832 cents 14:17:19:21:23:25:28:34:37:42:47:50:56:63:70 SD: 4.0232 cents 15:18:20:23:25:27:30:36:40:45:50:54:60:68:75 SD: 2.8670 cents 18:22:24:27:30:32:36:43:48:54:60:65:72:81:90 SD: 2.8254 cents 20:24:27:30:33:36:40:48:53:60:67:72:80:90:100 SD: 2.2104 cents 24:29:32:36:40:43:48:58:64:72:80:86:96:108:120 SD: 1.4571 cents 30:36:40:45:50:54:60:72:80:90:100:108:120:135:150 SD: 0.0000 cents