Scala analysis: xen07-chalmers-perrett
Perrett
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: 35/32 155.139620 septimal neutral second 3: 9/8 203.910002 major whole tone 4: 7/6 266.870906 septimal minor third 5: 6/5 315.641287 minor third 6: 5/4 386.313714 major third 7: 21/16 470.780907 narrow fourth 8: 4/3 498.044999 perfect fourth 9: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 10: 35/24 653.184619 septimal semi-diminished fifth 11: 3/2 701.955001 perfect fifth 12: 63/40 786.422194 narrow minor sixth 13: 8/5 813.686286 minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 7/4 968.825906 harmonic seventh 16: 9/5 1017.596288 just minor seventh, BP seventh 17: 15/8 1088.268715 classic major seventh 18: 63/32 1172.735908 octave - septimal comma 19: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 21/20 84.4672 minor semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 28/27 62.9609 Archytas' 1/3-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 21/20 84.4672 minor semitone 8: 64/63 27.2641 septimal comma, Archytas' comma 9: 21/20 84.4672 minor semitone 10: 25/24 70.6724 classic chromatic semitone, minor chroma 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 21/20 84.4672 minor semitone 13: 64/63 27.2641 septimal comma, Archytas' comma 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 21/20 84.4672 minor semitone 16: 36/35 48.7704 septimal diesis, 1/4-tone 17: 25/24 70.6724 classic chromatic semitone, minor chroma 18: 21/20 84.4672 minor semitone 19: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 64/63 27.264 cents septimal comma, Archytas' comma 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 6 21/20 84.467 cents minor semitone 2: 1 200/189 97.937 cents 2: 7 16/15 111.731 cents minor diatonic semitone 2: 4 15/14 119.443 cents major diatonic semitone 2: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 2: 5 35/32 155.140 cents septimal neutral second 3: 2 192/175 160.502 cents septimal 4/5-tone 3: 8 10/9 182.404 cents minor whole tone 3: 2 28/25 196.198 cents middle second 3: 7 9/8 203.910 cents major whole tone 4: 9 8/7 231.174 cents septimal whole tone 4: 7 7/6 266.871 cents septimal minor third 4: 1 75/64 274.582 cents classic augmented second 4: 2 189/160 288.377 cents 5: 2 32/27 294.135 cents Pythagorean minor third 5: 3 25/21 301.847 cents BP second, quasi-equal minor third 5: 11 6/5 315.641 cents minor third 5: 2 175/144 337.543 cents 5: 1 315/256 359.050 cents 6: 3 128/105 342.905 cents septimal neutral third 6: 1 216/175 364.412 cents 6: 2 56/45 378.602 cents septimal narrow major third 6: 11 5/4 386.314 cents major third 6: 2 63/50 400.108 cents quasi-equal major third 7: 4 80/63 413.578 cents wide major third 7: 3 32/25 427.373 cents classic diminished fourth 7: 4 9/7 435.084 cents septimal major third, BP third 7: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 7: 6 21/16 470.781 cents narrow fourth 8: 13 4/3 498.045 cents perfect fourth 8: 1 75/56 505.757 cents marvelous fourth 8: 4 27/20 519.551 cents acute fourth 8: 1 175/128 541.453 cents 9: 1 256/189 525.309 cents 9: 5 48/35 546.815 cents septimal semi-augmented fourth 9: 4 25/18 568.717 cents classic augmented fourth 9: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 9: 3 45/32 590.224 cents diatonic tritone 10: 3 64/45 609.776 cents 2nd tritone 10: 6 10/7 617.488 cents Euler's tritone 10: 4 36/25 631.283 cents classic diminished fifth 10: 5 35/24 653.185 cents septimal semi-diminished fifth 10: 1 189/128 674.691 cents 11: 1 256/175 658.547 cents 11: 4 40/27 680.449 cents grave fifth 11: 1 112/75 694.243 cents marvelous fifth 11: 13 3/2 701.955 cents perfect fifth 12: 6 32/21 729.219 cents wide fifth 12: 2 54/35 750.725 cents septimal semi-augmented fifth 12: 4 14/9 764.916 cents septimal minor sixth 12: 3 25/16 772.627 cents classic augmented fifth 12: 4 63/40 786.422 cents narrow minor sixth 13: 2 100/63 799.892 cents quasi-equal minor sixth 13: 11 8/5 813.686 cents minor sixth 13: 2 45/28 821.398 cents septimale wide minor sixth 13: 1 175/108 835.588 cents 13: 3 105/64 857.095 cents septimal neutral sixth 14: 1 512/315 840.950 cents 14: 2 288/175 862.457 cents 14: 11 5/3 884.359 cents major sixth, BP sixth 14: 3 42/25 898.153 cents quasi-equal major sixth 14: 2 27/16 905.865 cents Pythagorean major sixth 15: 2 320/189 911.623 cents 15: 1 128/75 925.418 cents diminished seventh 15: 7 12/7 933.129 cents septimal major sixth 15: 9 7/4 968.826 cents harmonic seventh 16: 7 16/9 996.090 cents Pythagorean minor seventh 16: 2 25/14 1003.802 cents middle minor seventh 16: 8 9/5 1017.596 cents just minor seventh, BP seventh 16: 2 175/96 1039.498 cents 17: 5 64/35 1044.860 cents septimal neutral seventh 17: 2 50/27 1066.762 cents grave major seventh 17: 4 28/15 1080.557 cents grave major seventh 17: 7 15/8 1088.269 cents classic major seventh 17: 1 189/100 1102.063 cents 18: 6 40/21 1115.533 cents acute major seventh 18: 5 48/25 1129.328 cents classic diminished octave 18: 1 27/14 1137.039 cents septimal major seventh 18: 4 35/18 1151.230 cents septimal semi-diminished octave 18: 3 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 5 Average number of different intervals per interval class: 4.66667 = 14/3
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 0.0 : 84.5 155.1 203.9 266.9 315.6 386.3 470.8 498.0 582.5 653.2 702.0 786.4 813.7 884.4 968.8 1017.6 1088.3 1172.7 1200.0 84.5 : 70.7 119.4 182.4 231.2 301.8 386.3 413.6 498.0 568.7 617.5 702.0 729.2 799.9 884.4 933.1 1003.8 1088.3 1115.5 1200.0 155.1 : 48.8 111.7 160.5 231.2 315.6 342.9 427.4 498.0 546.8 631.3 658.5 729.2 813.7 862.5 933.1 1017.6 1044.9 1129.3 1200.0 203.9 : 63.0 111.7 182.4 266.9 294.1 378.6 449.3 498.0 582.5 609.8 680.4 764.9 813.7 884.4 968.8 996.1 1080.6 1151.2 1200.0 266.9 : 48.8 119.4 203.9 231.2 315.6 386.3 435.1 519.6 546.8 617.5 702.0 750.7 821.4 905.9 933.1 1017.6 1088.3 1137.0 1200.0 315.6 : 70.7 155.1 182.4 266.9 337.5 386.3 470.8 498.0 568.7 653.2 702.0 772.6 857.1 884.4 968.8 1039.5 1088.3 1151.2 1200.0 386.3 : 84.5 111.7 196.2 266.9 315.6 400.1 427.4 498.0 582.5 631.3 702.0 786.4 813.7 898.2 968.8 1017.6 1080.6 1129.3 1200.0 470.8 : 27.3 111.7 182.4 231.2 315.6 342.9 413.6 498.0 546.8 617.5 702.0 729.2 813.7 884.4 933.1 996.1 1044.9 1115.5 1200.0 498.0 : 84.5 155.1 203.9 288.4 315.6 386.3 470.8 519.6 590.2 674.7 702.0 786.4 857.1 905.9 968.8 1017.6 1088.3 1172.7 1200.0 582.5 : 70.7 119.4 203.9 231.2 301.8 386.3 435.1 505.8 590.2 617.5 702.0 772.6 821.4 884.4 933.1 1003.8 1088.3 1115.5 1200.0 653.2 : 48.8 133.2 160.5 231.2 315.6 364.4 435.1 519.6 546.8 631.3 702.0 750.7 813.7 862.5 933.1 1017.6 1044.9 1129.3 1200.0 702.0 : 84.5 111.7 182.4 266.9 315.6 386.3 470.8 498.0 582.5 653.2 702.0 764.9 813.7 884.4 968.8 996.1 1080.6 1151.2 1200.0 786.4 : 27.3 97.9 182.4 231.2 301.8 386.3 413.6 498.0 568.7 617.5 680.4 729.2 799.9 884.4 911.6 996.1 1066.8 1115.5 1200.0 813.7 : 70.7 155.1 203.9 274.6 359.0 386.3 470.8 541.5 590.2 653.2 702.0 772.6 857.1 884.4 968.8 1039.5 1088.3 1172.7 1200.0 884.4 : 84.5 133.2 203.9 288.4 315.6 400.1 470.8 519.6 582.5 631.3 702.0 786.4 813.7 898.2 968.8 1017.6 1102.1 1129.3 1200.0 968.8 : 48.8 119.4 203.9 231.2 315.6 386.3 435.1 498.0 546.8 617.5 702.0 729.2 813.7 884.4 933.1 1017.6 1044.9 1115.5 1200.0 1017.6: 70.7 155.1 182.4 266.9 337.5 386.3 449.3 498.0 568.7 653.2 680.4 764.9 835.6 884.4 968.8 996.1 1066.8 1151.2 1200.0 1088.3: 84.5 111.7 196.2 266.9 315.6 378.6 427.4 498.0 582.5 609.8 694.2 764.9 813.7 898.2 925.4 996.1 1080.6 1129.3 1200.0 1172.7: 27.3 111.7 182.4 231.2 294.1 342.9 413.6 498.0 525.3 609.8 680.4 729.2 813.7 841.0 911.6 996.1 1044.9 1115.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 84.4672 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 2: 97.9365 .. 155.1396 cents 1323/1280, 57.2031 cents 4000/3969, 13.4693 cents 3: 160.5017 .. 203.9100 cents 525/512, 43.4083 cents 6144/6125, 5.3620 cents 4: 231.1741 .. 288.3772 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 5: 294.1350 .. 359.0496 cents 8505/8192, 64.9146 cents 5120/5103, 5.7578 cents 6: 342.9054 .. 400.1085 cents 1323/1280, 57.2031 cents 32768/33075,-16.1442 cents 7: 413.5778 .. 470.7809 cents 1323/1280, 57.2031 cents 4000/3969, 13.4693 cents 8: 498.0450 .. 541.4533 cents 525/512, 43.4083 cents 64/63, 27.2641 cents 9: 525.3091 .. 590.2237 cents 8505/8192, 64.9146 cents 32768/33075,-16.1442 cents 10: 609.7763 .. 674.6909 cents 8505/8192, 64.9146 cents 2048/2025, 19.5526 cents 11: 658.5467 .. 701.9550 cents 525/512, 43.4083 cents 32768/33075,-16.1442 cents 12: 729.2191 .. 786.4222 cents 1323/1280, 57.2031 cents 64/63, 27.2641 cents 13: 799.8915 .. 857.0946 cents 1323/1280, 57.2031 cents 4000/3969, 13.4693 cents 14: 840.9504 .. 905.8650 cents 8505/8192, 64.9146 cents 32768/33075,-16.1442 cents 15: 911.6228 .. 968.8259 cents 1323/1280, 57.2031 cents 5120/5103, 5.7578 cents 16: 996.0900 .. 1039.4983 cents 525/512, 43.4083 cents 64/63, 27.2641 cents 17: 1044.8604 .. 1102.0635 cents 1323/1280, 57.2031 cents 6144/6125, 5.3620 cents 18: 1115.5328 .. 1172.7359 cents 1323/1280, 57.2031 cents 4000/3969, 13.4693 cents
SHOW DATA
Number of notes : 19 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 63.1579 cents Largest one step interval : 21/20, 84.4672 cents Average / Smallest step : 2.316523 Largest / Average step : 1.337397 Largest / Smallest step : 3.098111 Median interval of one step : 25/24, 70.6724 cents, amount: 5 Most common interval of one step : 21/20, 84.4672 cents, amount: 6 Least squares average step : 64.11562 cents, oct.: 1218.19684 cents Scale is not proper Step pattern alph. order: ABCDCBAEABCAEBACBAE Step pattern size order : EDBCBDEAEDBEADEBDEA Scale is a Constant Structure, by a margin of 5.36205 cents Scale diversity : 1.431165 Lumma stability : 0.216045 Lumma impropriety factor : 0.053814 Number of different interval sizes : 84 = 4.66667 / class Number of one step interval sizes : 5 Highest interval variety : 5 Mean interval variety : 4.66667 = 14/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 6144/6125, 5.3620 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 13 Most common triad is 0.0 498.045 701.955 cents, amount: 7 Number of recognisable fifths : 14, average 701.4042 cents Scale contains a complete diamond : 1 3 5 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 36.8421% Scale is differentially coherent in interval class 1 Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 3 and 4 combined Scale is n-1 differentially coherent in interval classes 4 and 5 combined Scale is differentially coherent in interval classes 5 and 6 combined Scale is differentially coherent in interval classes 7 and 8 combined -- Rational properties -- Prime limit : 7 Odd number limit : 315 (O: 315 U: 315) Highest odd numerator or denominator: 63 Scale harmonicity : 0.025585 Average absolute harmonicity : 0.142543 Specific harmonicity : 0.127623 Fundamental : 1/480, -8.9069 octaves, 0.5451 Hz. Guide tone : 2520, 11.2992 octaves, 659296.425 Hz. Exponens Consonantiae : 1.209600E+06, 20.20610 octaves Euler's gradus suavitatis : 29 Sum of Mann's harmonic distance : 274.0, average 14.42105 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 18.70125, average 0.98428 Sum of Tenney's harmonic distance : 35.74784, average 1.88147 Vogel's harmonic complexity : 16.05263 Wille's k value : 472 Wilson's harmonic complexity : 26 Rectangular lattice diameter : 6 Triangular lattice diameter : 4 Lattice compactness : 643.56054, average 3.38716 Lattice compactness (without 2's) : 349.12256, average 1.83749 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -1.42105 41 1 3: -1 .. 2 0.47368 17 3 5: -1 .. 1 -0.05263 11 6 7: 0 .. 1 0.47368 9 9 Average exponent except 2's : 17 / 19 = 0.89474 Average absolute exponent except 2's: 37 / 19 = 1.94737 Scale is JI-epimorphic with val: <19 30 44 53| = patent
FIT/MODE
19: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 18.0959 c. M: 35.8938 c. 20: 1 2 0 1 1 1 2 0 2 1 1 1 1 1 1 1 1 2 0 N D3 SD: 18.3671 c. M:-27.2641 c. 22: 2 1 1 1 1 1 2 0 2 1 1 2 0 1 2 1 1 2 0 N D3 SD: 15.0825 c. M:-31.7596 c. 26: 2 1 1 2 1 1 2 1 2 1 1 2 1 1 2 1 2 1 1 P M ME S SD: 12.3041 c. M:-19.4236 c. 27: 2 2 1 1 1 2 2 0 2 2 1 2 0 2 2 1 2 2 0 N SD: 13.6379 c. M:-27.2641 c. 29: 2 1 2 1 1 2 2 1 2 2 1 2 0 2 2 1 2 2 1 N D3 SD: 15.8315 c. M: 31.0017 c. 30: 2 2 1 1 2 1 2 1 2 2 1 2 1 2 2 1 2 2 1 N D3 SD: 16.9374 c. M: 30.7809 c. 31: 2 2 1 2 1 2 2 1 2 2 1 2 1 2 2 1 2 2 1 P M ME S SD: 6.4554 c. M: 12.2286 c. 41: 3 2 2 2 2 2 3 1 3 2 2 3 1 2 3 2 2 3 1 P D3 SD: 4.8777 c. M: 9.2822 c. 46: 3 3 2 2 2 3 3 1 3 3 2 3 1 3 3 2 3 3 1 N SD: 4.1931 c. M: 8.5991 c. 53: 4 3 2 3 2 3 4 1 4 3 2 4 1 3 4 2 3 4 1 N SD: 3.5185 c. M:-6.1671 c. 72: 5 4 3 4 3 4 5 2 5 4 3 5 2 4 5 3 4 5 2 P SD: 3.0310 c. M: 6.0692 c. 84: 6 5 3 5 3 5 6 2 6 5 3 6 2 5 6 3 5 6 2 N SD: 2.3673 c. M:-4.5577 c. 87: 6 5 4 4 4 5 6 2 6 5 4 6 2 5 6 4 5 6 2 N SD: 2.4751 c. M: 4.9088 c. 99: 7 6 4 5 4 6 7 2 7 6 4 7 2 6 7 4 6 7 2 N SD: 1.5198 c. M:-3.0217 c. 130: 9 8 5 7 5 8 9 3 9 8 5 9 3 8 9 5 8 9 3 N SD: 1.3037 c. M: 2.2117 c. 140: 10 8 6 7 6 8 10 3 10 8 6 10 3 8 10 6 8 10 3 N SD: 1.2631 c. M:-2.4037 c. 171: 12 10 7 9 7 10 12 4 12 10 7 12 4 10 12 7 10 12 4 N SD: 0.4109 c. M: 0.8061 c. 270: 19 16 11 14 11 16 19 6 19 16 11 19 6 16 19 11 16 19 6 N SD: 0.3213 c. M:-0.6202 c. 441: 31 26 18 23 18 26 31 10 31 26 18 31 10 26 31 18 26 31 10 N SD: 0.1083 c. M: 0.2042 c. 1053: 74 62 43 55 43 62 74 24 74 62 43 74 24 62 74 43 62 74 24 N SD: 0.1101 c. M: 0.2042 c. 1106: 78 65 45 58 45 65 78 25 78 65 45 78 25 65 78 45 65 78 25 N SD: 0.0932 c. M:-0.1963 c. 1277: 90 75 52 67 52 75 90 29 90 75 52 90 29 75 90 52 75 90 29 N SD: 0.0751 c. M:-0.1087 c. 1407: 99 83 57 74 57 83 99 32 99 83 57 99 32 83 99 57 83 99 32 N SD: 0.0615 c. M:-0.1203 c. 1547: 109 91 63 81 63 91 109 35 109 91 63 109 35 91 109 63 91 109 35 N SD: 0.0669 c. M:-0.1324 c. 1578: 111 93 64 83 64 93 111 36 111 93 64 111 36 93 111 64 93 111 36 N SD: 0.0621 c. M: 0.1123 c. 1718: 121 101 70 90 70 101 121 39 121 101 70 121 39 101 121 70 101 121 39 N SD: 0.0552 c. M: 0.0996 c. 1848: 130 109 75 97 75 109 130 42 130 109 75 130 42 109 130 75 109 130 42 N SD: 0.0416 c. M: 0.0638 c. 2019: 142 119 82 106 82 119 142 46 142 119 82 142 46 119 142 82 119 142 46 N SD: 0.0436 c. M: 0.0923 c. 2289: 161 135 93 120 93 135 161 52 161 135 93 161 52 135 161 93 135 161 52 N SD: 0.0413 c. M: 0.0744 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 0.0000 cents 4 .. 8 match: 4 H SD: 0.0000 cents 5 .. 10 match: 5 H SD: 0.0000 cents 6 .. 12 match: 6 H SD: 5.2944 cents 7 .. 14 match: 7 H SD: 9.9026 cents 8 .. 16 match: 8 H SD: 5.1441 cents 9 .. 18 match: 9 H SD: 5.9154 cents 10 .. 20 match: 10 H SD: 4.5529 cents 11 .. 22 match: 11 H SD: 7.5505 cents 12 .. 24 match: 12 H SD: 4.7395 cents 13 .. 26 match: 12 S SD: 6.4175 cents 14 .. 28 match: 12 SD: 6.9340 cents 15 .. 30 match: 14 S SD: 4.1104 cents 16 .. 32 match: 15 S SD: 4.1413 cents 17 .. 34 match: 16 S SD: 4.7161 cents 18 .. 36 match: 16 S SD: 4.4905 cents 19 .. 38 match: 16 SD: 4.1005 cents 20 .. 40 match: 17 SD: 3.0317 cents 21 .. 42 match: 17 SD: 3.7751 cents 22 .. 44 match: 16 SD: 3.6794 cents 23 .. 46 match: 19 SD: 3.3252 cents 24 .. 48 match: 17 SD: 2.0884 cents 25 .. 50 match: 18 SD: 2.9664 cents 27 .. 54 match: 16 SD: 3.6239 cents 28 .. 56 match: 18 SD: 3.2613 cents 29 .. 58 match: 18 SD: 3.1516 cents 30 .. 60 match: 19 SD: 2.5339 cents 31 .. 62 match: 18 SD: 2.6135 cents 32 .. 64 match: 19 SD: 2.2820 cents 34 .. 68 match: 17 SD: 2.7882 cents 35 .. 70 match: 19 SD: 1.9817 cents 37 .. 74 match: 18 SD: 2.4458 cents 38 .. 76 match: 19 SD: 2.3537 cents 39 .. 78 match: 19 SD: 2.0456 cents 40 .. 80 match: 18 SD: 1.3264 cents 55 .. 110 match: 19 SD: 1.1777 cents 64 .. 128 match: 19 SD: 0.9790 cents 80 .. 160 match: 19 SD: 0.8122 cents 95 .. 190 match: 19 SD: 0.7344 cents 96 .. 192 match: 19 SD: 0.4618 cents 120 .. 240 match: 19 SD: 0.3506 cents 160 .. 320 match: 19 SD: 0.2769 cents 240 .. 480 match: 19 SD: 0.1984 cents 320 .. 640 match: 19 SD: 0.1384 cents 360 .. 720 match: 19 SD: 0.1169 cents 384 .. 768 match: 19 SD: 0.1154 cents 480 .. 960 match: 19 S SD: 0.0000 cents