Scala analysis: john20110212
john 2011 02 12 best
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 8/7 231.174094 septimal whole tone 3: 7/6 266.870906 septimal minor third 4: 6/5 315.641287 minor third 5: 5/4 386.313714 major third 6: 9/7 435.084095 septimal major third, BP third 7: 4/3 498.044999 perfect fourth 8: 11/8 551.317942 undecimal semi-augmented fourth 9: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 10: 10/7 617.487807 Euler's tritone 11: 3/2 701.955001 perfect fifth 12: 11/7 782.492036 undecimal augmented fifth 13: 8/5 813.686286 minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 12/7 933.129094 septimal major sixth 16: 7/4 968.825906 harmonic seventh 17: 9/5 1017.596288 just minor seventh, BP seventh 18: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 19: 13/7 1071.701755 16/3-tone 20: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 14/13 128.2982 2/3-tone 1: 9/8 203.9100 major whole tone 2: 64/63 27.2641 septimal comma, Archytas' comma 3: 49/48 35.6968 slendro diesis, septimal 1/6-tone 4: 36/35 48.7704 septimal diesis, 1/4-tone 5: 25/24 70.6724 classic chromatic semitone, minor chroma 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 28/27 62.9609 Archytas' 1/3-tone 8: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 9: 56/55 31.1943 undecimal diesis, konbini comma 10: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 11: 21/20 84.4672 minor semitone 12: 22/21 80.5370 undecimal minor semitone 13: 56/55 31.1943 undecimal diesis, konbini comma 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 36/35 48.7704 septimal diesis, 1/4-tone 16: 49/48 35.6968 slendro diesis, septimal 1/6-tone 17: 36/35 48.7704 septimal diesis, 1/4-tone 18: 55/54 31.7667 telepathma 19: 78/77 22.3388 tridecimal minor third comma 20: 14/13 128.2982 2/3-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 78/77 22.339 cents tridecimal minor third comma 1: 1 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 55/54 31.767 cents telepathma 1: 1 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 4 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 28/27 62.961 cents Archytas' 1/3-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 22/21 80.537 cents undecimal minor semitone 1: 1 21/20 84.467 cents minor semitone 1: 1 14/13 128.298 cents 2/3-tone 1: 1 9/8 203.910 cents major whole tone 2: 1 65/63 54.105 cents 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 1 80/77 66.170 cents 2: 1 22/21 80.537 cents undecimal minor semitone 2: 4 21/20 84.467 cents minor semitone 2: 1 35/33 101.867 cents 2: 2 16/15 111.731 cents minor diatonic semitone 2: 1 77/72 116.234 cents undecimal secor 2: 4 15/14 119.443 cents major diatonic semitone 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 2: 1 8/7 231.174 cents septimal whole tone 2: 1 63/52 332.208 cents 3: 1 52/49 102.876 cents 3: 1 16/15 111.731 cents minor diatonic semitone 3: 1 77/72 116.234 cents undecimal secor 3: 1 15/14 119.443 cents major diatonic semitone 3: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 3: 1 49/45 147.428 cents BP minor semitone 3: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 2 35/32 155.140 cents septimal neutral second 3: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 3: 1 54/49 168.213 cents Zalzal's mujannab 3: 3 10/9 182.404 cents minor whole tone 3: 1 28/25 196.198 cents middle second 3: 1 55/49 199.980 cents quasi-equal major second 3: 1 7/6 266.871 cents septimal minor third 3: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 3: 1 16/13 359.472 cents tridecimal neutral third 4: 1 13/12 138.573 cents tridecimal 2/3-tone 4: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 4: 2 10/9 182.404 cents minor whole tone 4: 1 49/44 186.334 cents undecimal minor whole tone 4: 1 28/25 196.198 cents middle second 4: 3 9/8 203.910 cents major whole tone 4: 5 8/7 231.174 cents septimal whole tone 4: 1 55/48 235.677 cents undecimal semi-augmented whole tone 4: 1 7/6 266.871 cents septimal minor third 4: 1 6/5 315.641 cents minor third 4: 1 96/77 381.811 cents 4: 1 5/4 386.314 cents major third 4: 1 49/39 395.169 cents 5: 1 39/35 187.343 cents 5: 2 8/7 231.174 cents septimal whole tone 5: 1 63/55 235.104 cents 5: 1 55/48 235.677 cents undecimal semi-augmented whole tone 5: 1 64/55 262.368 cents 5: 5 7/6 266.871 cents septimal minor third 5: 2 33/28 284.447 cents undecimal minor third 5: 1 25/21 301.847 cents BP second, quasi-equal minor third 5: 1 6/5 315.641 cents minor third 5: 1 5/4 386.314 cents major third 5: 1 80/63 413.578 cents wide major third 5: 1 14/11 417.508 cents undecimal diminished fourth or major third 5: 1 9/7 435.084 cents septimal major third, BP third 5: 1 84/65 443.940 cents 6: 1 65/56 258.015 cents 6: 1 7/6 266.871 cents septimal minor third 6: 1 32/27 294.135 cents Pythagorean minor third 6: 1 25/21 301.847 cents BP second, quasi-equal minor third 6: 5 6/5 315.641 cents minor third 6: 1 77/64 320.144 cents Keemun minor third 6: 1 40/33 333.041 cents 6: 1 11/9 347.408 cents undecimal neutral third 6: 1 60/49 350.617 cents smaller approximation to neutral third 6: 1 49/40 351.338 cents larger approximation to neutral third 6: 1 9/7 435.084 cents septimal major third, BP third 6: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 6: 1 64/49 462.348 cents 2 septatones or septatonic major third 6: 1 72/55 466.278 cents undecimal semi-diminished fourth 6: 1 21/16 470.781 cents narrow fourth 6: 1 35/26 514.612 cents 7: 1 13/11 289.210 cents tridecimal minor third 7: 2 11/9 347.408 cents undecimal neutral third 7: 1 60/49 350.617 cents smaller approximation to neutral third 7: 1 49/40 351.338 cents larger approximation to neutral third 7: 1 56/45 378.602 cents septimal narrow major third 7: 1 96/77 381.811 cents 7: 4 5/4 386.314 cents major third 7: 1 44/35 396.178 cents 7: 1 63/50 400.108 cents quasi-equal major third 7: 4 4/3 498.045 cents perfect fourth 7: 1 27/20 519.551 cents acute fourth 7: 1 15/11 536.951 cents undecimal augmented fourth 7: 1 18/13 563.382 cents tridecimal augmented fourth 8: 1 26/21 369.747 cents 8: 1 56/45 378.602 cents septimal narrow major third 8: 1 5/4 386.314 cents major third 8: 2 14/11 417.508 cents undecimal diminished fourth or major third 8: 1 32/25 427.373 cents classic diminished fourth 8: 1 77/60 431.875 cents 8: 3 9/7 435.084 cents septimal major third, BP third 8: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 8: 1 55/42 466.851 cents 8: 1 49/36 533.742 cents Arabic lute acute fourth 8: 2 48/35 546.815 cents septimal semi-augmented fourth 8: 1 11/8 551.318 cents undecimal semi-augmented fourth 8: 1 25/18 568.717 cents classic augmented fourth 8: 1 108/77 585.721 cents 8: 1 45/32 590.224 cents diatonic tritone 8: 1 56/39 626.343 cents 9: 1 80/63 413.578 cents wide major third 9: 1 13/10 454.214 cents tridecimal semi-diminished fourth 9: 1 72/55 466.278 cents undecimal semi-diminished fourth 9: 1 55/42 466.851 cents 9: 2 21/16 470.781 cents narrow fourth 9: 4 4/3 498.045 cents perfect fourth 9: 1 66/49 515.621 cents 9: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 9: 3 10/7 617.488 cents Euler's tritone 9: 1 63/44 621.418 cents 9: 1 16/11 648.682 cents undecimal semi-diminished fifth 9: 1 77/52 679.616 cents 10: 1 65/49 489.190 cents 10: 2 4/3 498.045 cents perfect fourth 10: 1 27/20 519.551 cents acute fourth 10: 1 49/36 533.742 cents Arabic lute acute fourth 10: 2 48/35 546.815 cents septimal semi-augmented fourth 10: 1 11/8 551.318 cents undecimal semi-augmented fourth 10: 1 25/18 568.717 cents classic augmented fourth 10: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 10: 1 10/7 617.488 cents Euler's tritone 10: 1 36/25 631.283 cents classic diminished fifth 10: 1 16/11 648.682 cents undecimal semi-diminished fifth 10: 2 35/24 653.185 cents septimal semi-diminished fifth 10: 1 72/49 666.258 cents Arabic lute grave fifth 10: 1 40/27 680.449 cents grave fifth 10: 2 3/2 701.955 cents perfect fifth 10: 1 98/65 710.810 cents 11: 1 104/77 520.384 cents 11: 1 11/8 551.318 cents undecimal semi-augmented fourth 11: 1 88/63 578.582 cents 11: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 11: 3 10/7 617.488 cents Euler's tritone 11: 1 49/33 684.379 cents 11: 4 3/2 701.955 cents perfect fifth 11: 2 32/21 729.219 cents wide fifth 11: 1 84/55 733.149 cents 11: 1 55/36 733.722 cents undecimal semi-augmented fifth 11: 1 20/13 745.786 cents tridecimal semi-augmented fifth 11: 1 63/40 786.422 cents narrow minor sixth 12: 1 39/28 573.657 cents 12: 1 64/45 609.776 cents 2nd tritone 12: 1 77/54 614.279 cents 12: 1 36/25 631.283 cents classic diminished fifth 12: 1 16/11 648.682 cents undecimal semi-diminished fifth 12: 2 35/24 653.185 cents septimal semi-diminished fifth 12: 1 72/49 666.258 cents Arabic lute grave fifth 12: 1 84/55 733.149 cents 12: 1 54/35 750.725 cents septimal semi-augmented fifth 12: 3 14/9 764.916 cents septimal minor sixth 12: 1 120/77 768.125 cents 12: 1 25/16 772.627 cents classic augmented fifth 12: 2 11/7 782.492 cents undecimal augmented fifth 12: 1 8/5 813.686 cents minor sixth 12: 1 45/28 821.398 cents septimale wide minor sixth 12: 1 21/13 830.253 cents 13: 1 13/9 636.618 cents tridecimal diminished fifth 13: 1 22/15 663.049 cents undecimal diminished fifth 13: 1 40/27 680.449 cents grave fifth 13: 4 3/2 701.955 cents perfect fifth 13: 1 100/63 799.892 cents quasi-equal minor sixth 13: 1 35/22 803.822 cents 13: 4 8/5 813.686 cents minor sixth 13: 1 77/48 818.189 cents 13: 1 45/28 821.398 cents septimale wide minor sixth 13: 1 80/49 848.662 cents smaller approximation to neutral sixth 13: 1 49/30 849.383 cents larger approximation to neutral sixth 13: 2 18/11 852.592 cents undecimal neutral sixth 13: 1 22/13 910.790 cents tridecimal major sixth 14: 1 52/35 685.388 cents 14: 1 32/21 729.219 cents wide fifth 14: 1 55/36 733.722 cents undecimal semi-augmented fifth 14: 1 49/32 737.652 cents 14: 1 54/35 750.725 cents septimal semi-augmented fifth 14: 1 14/9 764.916 cents septimal minor sixth 14: 1 80/49 848.662 cents smaller approximation to neutral sixth 14: 1 49/30 849.383 cents larger approximation to neutral sixth 14: 1 18/11 852.592 cents undecimal neutral sixth 14: 1 33/20 866.959 cents 14: 1 128/77 879.856 cents 14: 5 5/3 884.359 cents major sixth, BP sixth 14: 1 42/25 898.153 cents quasi-equal major sixth 14: 1 27/16 905.865 cents Pythagorean major sixth 14: 1 12/7 933.129 cents septimal major sixth 14: 1 112/65 941.985 cents 15: 1 65/42 756.060 cents 15: 1 14/9 764.916 cents septimal minor sixth 15: 1 11/7 782.492 cents undecimal augmented fifth 15: 1 63/40 786.422 cents narrow minor sixth 15: 1 8/5 813.686 cents minor sixth 15: 1 5/3 884.359 cents major sixth, BP sixth 15: 1 42/25 898.153 cents quasi-equal major sixth 15: 2 56/33 915.553 cents 15: 5 12/7 933.129 cents septimal major sixth 15: 1 55/32 937.632 cents 15: 1 96/55 964.323 cents 15: 1 110/63 964.896 cents 15: 2 7/4 968.826 cents harmonic seventh 15: 1 70/39 1012.657 cents 16: 1 78/49 804.831 cents 16: 1 8/5 813.686 cents minor sixth 16: 1 77/48 818.189 cents 16: 1 5/3 884.359 cents major sixth, BP sixth 16: 1 12/7 933.129 cents septimal major sixth 16: 1 96/55 964.323 cents 16: 5 7/4 968.826 cents harmonic seventh 16: 3 16/9 996.090 cents Pythagorean minor seventh 16: 1 25/14 1003.802 cents middle minor seventh 16: 1 88/49 1013.666 cents undecimal minor seventh 16: 2 9/5 1017.596 cents just minor seventh, BP seventh 16: 1 20/11 1034.996 cents large minor seventh 16: 1 24/13 1061.427 cents tridecimal neutral seventh 17: 1 13/8 840.528 cents tridecimal neutral sixth 17: 1 44/27 845.453 cents neutral sixth 17: 1 12/7 933.129 cents septimal major sixth 17: 1 98/55 1000.020 cents quasi-equal minor seventh 17: 1 25/14 1003.802 cents middle minor seventh 17: 3 9/5 1017.596 cents just minor seventh, BP seventh 17: 1 49/27 1031.787 cents 17: 1 20/11 1034.996 cents large minor seventh 17: 2 64/35 1044.860 cents septimal neutral seventh 17: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 17: 1 90/49 1052.572 cents 17: 1 50/27 1066.762 cents grave major seventh 17: 1 28/15 1080.557 cents grave major seventh 17: 1 144/77 1083.766 cents 17: 1 15/8 1088.269 cents classic major seventh 17: 1 49/26 1097.124 cents 18: 1 104/63 867.792 cents 18: 1 7/4 968.826 cents harmonic seventh 18: 1 20/11 1034.996 cents large minor seventh 18: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 18: 4 28/15 1080.557 cents grave major seventh 18: 1 144/77 1083.766 cents 18: 2 15/8 1088.269 cents classic major seventh 18: 1 66/35 1098.133 cents 18: 4 40/21 1115.533 cents acute major seventh 18: 1 21/11 1119.463 cents undecimal major seventh 18: 1 77/40 1133.830 cents 18: 1 27/14 1137.039 cents septimal major seventh 18: 1 126/65 1145.895 cents 19: 1 16/9 996.090 cents Pythagorean minor seventh 19: 1 13/7 1071.702 cents 16/3-tone 19: 1 40/21 1115.533 cents acute major seventh 19: 1 21/11 1119.463 cents undecimal major seventh 19: 2 48/25 1129.328 cents classic diminished octave 19: 1 27/14 1137.039 cents septimal major seventh 19: 1 64/33 1146.727 cents 33rd subharmonic 19: 4 35/18 1151.230 cents septimal semi-diminished octave 19: 2 96/49 1164.303 cents 19: 1 49/25 1165.024 cents BP eighth 19: 1 108/55 1168.233 cents 19: 2 55/28 1168.806 cents 19: 1 63/32 1172.736 cents octave - septimal comma 19: 1 77/39 1177.661 cents Highest number of different intervals for one interval class: 16 Average number of different intervals per interval class: 14.21053 = 270/19
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 0.0 : 203.9 231.2 266.9 315.6 386.3 435.1 498.0 551.3 582.5 617.5 702.0 782.5 813.7 884.4 933.1 968.8 1017.6 1049.4 1071.7 1200.0 203.9 : 27.3 63.0 111.7 182.4 231.2 294.1 347.4 378.6 413.6 498.0 578.6 609.8 680.4 729.2 764.9 813.7 845.5 867.8 996.1 1200.0 231.2 : 35.7 84.5 155.1 203.9 266.9 320.1 351.3 386.3 470.8 551.3 582.5 653.2 702.0 737.7 786.4 818.2 840.5 968.8 1172.7 1200.0 266.9 : 48.8 119.4 168.2 231.2 284.4 315.6 350.6 435.1 515.6 546.8 617.5 666.3 702.0 750.7 782.5 804.8 933.1 1137.0 1164.3 1200.0 315.6 : 70.7 119.4 182.4 235.7 266.9 301.8 386.3 466.9 498.0 568.7 617.5 653.2 702.0 733.7 756.1 884.4 1088.3 1115.5 1151.2 1200.0 386.3 : 48.8 111.7 165.0 196.2 231.2 315.6 396.2 427.4 498.0 546.8 582.5 631.3 663.0 685.4 813.7 1017.6 1044.9 1080.6 1129.3 1200.0 435.1 : 63.0 116.2 147.4 182.4 266.9 347.4 378.6 449.3 498.0 533.7 582.5 614.3 636.6 764.9 968.8 996.1 1031.8 1080.6 1151.2 1200.0 498.0 : 53.3 84.5 119.4 203.9 284.4 315.6 386.3 435.1 470.8 519.6 551.3 573.7 702.0 905.9 933.1 968.8 1017.6 1088.3 1137.0 1200.0 551.3 : 31.2 66.2 150.6 231.2 262.4 333.0 381.8 417.5 466.3 498.0 520.4 648.7 852.6 879.9 915.6 964.3 1035.0 1083.8 1146.7 1200.0 582.5 : 35.0 119.4 200.0 231.2 301.8 350.6 386.3 435.1 466.9 489.2 617.5 821.4 848.7 884.4 933.1 1003.8 1052.6 1115.5 1168.8 1200.0 617.5 : 84.5 165.0 196.2 266.9 315.6 351.3 400.1 431.9 454.2 582.5 786.4 813.7 849.4 898.2 968.8 1017.6 1080.6 1133.8 1165.0 1200.0 702.0 : 80.5 111.7 182.4 231.2 266.9 315.6 347.4 369.7 498.0 702.0 729.2 764.9 813.7 884.4 933.1 996.1 1049.4 1080.6 1115.5 1200.0 782.5 : 31.2 101.9 150.6 186.3 235.1 266.9 289.2 417.5 621.4 648.7 684.4 733.1 803.8 852.6 915.6 968.8 1000.0 1035.0 1119.5 1200.0 813.7 : 70.7 119.4 155.1 203.9 235.7 258.0 386.3 590.2 617.5 653.2 702.0 772.6 821.4 884.4 937.6 968.8 1003.8 1088.3 1168.8 1200.0 884.4 : 48.8 84.5 133.2 165.0 187.3 315.6 519.6 546.8 582.5 631.3 702.0 750.7 813.7 867.0 898.2 933.1 1017.6 1098.1 1129.3 1200.0 933.1 : 35.7 84.5 116.2 138.6 266.9 470.8 498.0 533.7 582.5 653.2 702.0 764.9 818.2 849.4 884.4 968.8 1049.4 1080.6 1151.2 1200.0 968.8 : 48.8 80.5 102.9 231.2 435.1 462.3 498.0 546.8 617.5 666.3 729.2 782.5 813.7 848.7 933.1 1013.7 1044.9 1115.5 1164.3 1200.0 1017.6: 31.8 54.1 182.4 386.3 413.6 449.3 498.0 568.7 617.5 680.4 733.7 764.9 799.9 884.4 964.9 996.1 1066.8 1115.5 1151.2 1200.0 1049.4: 22.3 150.6 354.5 381.8 417.5 466.3 537.0 585.7 648.7 702.0 733.1 768.1 852.6 933.1 964.3 1035.0 1083.8 1119.5 1168.2 1200.0 1071.7: 128.3 332.2 359.5 395.2 443.9 514.6 563.4 626.3 679.6 710.8 745.8 830.3 910.8 942.0 1012.7 1061.4 1097.1 1145.9 1177.7 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 22.3388 .. 203.9100 cents 231/208, 181.5712 cents 78/77, 22.3388 cents 2: 54.1055 .. 332.2082 cents 3969/3380, 278.1028 cents 520/567,-149.8045 cents 3: 102.8758 .. 359.4723 cents 196/169, 256.5965 cents 2704/3087,-229.3324 cents 4: 138.5727 .. 395.1692 cents 196/169, 256.5965 cents 169/192,-220.8997 cents 5: 187.3430 .. 443.9395 cents 196/169, 256.5965 cents 1521/1715,-207.8261 cents 6: 258.0155 .. 514.6120 cents 196/169, 256.5965 cents 4225/4704,-185.9241 cents 7: 289.2097 .. 563.3823 cents 198/169, 274.1726 cents 338/385,-225.4022 cents 8: 369.7468 .. 626.3432 cents 196/169, 256.5965 cents 169/189,-193.6356 cents 9: 413.5778 .. 679.6162 cents 4851/4160, 266.0384 cents 130/147,-212.7654 cents 10: 489.1896 .. 710.8104 cents 4802/4225, 221.6209 cents 3380/3773,-190.4266 cents 11: 520.3838 .. 786.4222 cents 4851/4160, 266.0384 cents 3380/3773,-190.4266 cents 12: 573.6568 .. 830.2532 cents 196/169, 256.5965 cents 130/147,-212.7654 cents 13: 636.6177 .. 910.7903 cents 198/169, 274.1726 cents 169/189,-193.6356 cents 14: 685.3880 .. 941.9845 cents 196/169, 256.5965 cents 338/385,-225.4022 cents 15: 756.0605 .. 1012.6570 cents 196/169, 256.5965 cents 4225/4704,-185.9241 cents 16: 804.8308 .. 1061.4273 cents 196/169, 256.5965 cents 1521/1715,-207.8261 cents 17: 840.5277 .. 1097.1242 cents 196/169, 256.5965 cents 169/192,-220.8997 cents 18: 867.7918 .. 1145.8945 cents 3969/3380, 278.1028 cents 2704/3087,-229.3324 cents 19: 996.0900 .. 1177.6612 cents 231/208, 181.5712 cents 520/567,-149.8045 cents
SHOW DATA
Number of notes : 20 -- Interval properties -- Smallest interval : 78/77, 22.3388 cents, class 1 Average step (divided formal octave): 60.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 2.685908 Largest / Average step : 3.398500 Largest / Smallest step : 9.128059 Median interval of one step : 36/35, 48.7704 cents, amount: 4 Most common interval of one step : 36/35, 48.7704 cents, amount: 4 Least squares average step : 61.56946 cents, oct.: 1231.38929 cents Scale is not proper Step pattern alph. order: ABCDEDFGHIJKHEDCDLMN Step pattern size order : NBFGJGIHCELKCJGFGDAM Scale is not a Constant Structure Scale diversity : 1.560804 Lumma stability : 0.037231 Lumma impropriety factor : 0.909824 Number of different interval sizes : 176 = 9.26316 / class Number of one step interval sizes : 14 Highest interval variety : 16 Mean interval variety : 14.21053 = 270/19 Median interval variety : 12 Lowest interval variety : 12 Smallest interval difference : 3025/3024, 0.5724 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Number of recognisable fifths : 11, average 702.7600 cents Scale contains a complete diamond : 1 3 5 7 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 10 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 13 = 65.0000% Scale is differentially coherent in interval class 1 Scale is 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 6 and 7 combined -- Rational properties -- Prime limit : 13 Odd number limit : 77 (O: 77 U: 77) Highest odd numerator or denominator: 13 Scale harmonicity : 0.011402 Average absolute harmonicity : 0.138097 Specific harmonicity : 0.094631 Fundamental : 1/840, -9.7142 octaves, 0.3115 Hz. Guide tone : 360360, 18.4591 octaves, 94279388.712 Hz. Exponens Consonantiae : 3.027024E+08, 28.17332 octaves Euler's gradus suavitatis : 55 Sum of Mann's harmonic distance : 132.0, average 6.60000 Mersenne's string divisions : 232792560 Sum of van Prooijen's expressibility: 15.92156, average 0.79608 Sum of Tenney's harmonic distance : 30.76615, average 1.53831 Vogel's harmonic complexity : 19.75000 Wille's k value : 577 Wilson's harmonic complexity : 57 Rectangular lattice diameter : 9 Triangular lattice diameter : 3 Lattice compactness : 603.92961, average 2.87586 Lattice compactness (without 2's) : 380.16073, average 1.81029 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -3 .. 3 0.00000 26 1 3: -1 .. 2 0.25000 13 3 5: -1 .. 1 -0.05000 7 5 7: -1 .. 1 -0.15000 9 7 11: 0 .. 1 0.15000 3 3 13: 0 .. 1 0.05000 1 1 Average exponent except 2's : 5 / 20 = 0.25000 Average absolute exponent except 2's: 33 / 20 = 1.65000
FIT/MODE
20: 3 1 0 1 1 1 1 1 0 1 1 2 0 1 1 1 1 0 1 2 N SD: 24.5807 c. M: 44.3587 c. 22: 4 0 1 1 1 1 1 1 1 0 2 1 1 1 1 1 1 0 1 2 N SD: 12.0748 c. M:-19.2073 c. 26: 4 1 1 1 1 1 2 1 1 0 2 2 1 1 1 1 1 1 0 3 N SD: 11.6664 c. M: 19.6995 c. 27: 5 0 1 1 2 1 1 1 1 1 2 2 0 2 1 1 1 1 0 3 N SD: 10.4586 c. M:-18.3122 c. 31: 5 1 1 1 2 1 2 1 1 1 2 2 1 2 1 1 1 1 1 3 N SD: 6.3609 c. M:-12.1692 c. 41: 7 1 1 2 2 2 2 2 1 1 3 3 1 2 2 1 2 1 1 4 N SD: 4.9792 c. M:-11.2251 c. 46: 8 1 1 2 3 2 2 2 1 2 3 3 1 3 2 1 2 1 1 5 N SD: 4.8246 c. M:-8.5991 c. 57: 10 1 2 2 3 3 3 2 2 1 4 4 2 3 2 2 2 2 1 6 N SD: 5.4254 c. M: 7.3663 c. 58: 10 1 2 2 4 2 3 3 1 2 4 4 1 4 2 2 2 2 1 6 N SD: 4.1816 c. M:-7.3027 c. 66: 11 2 2 2 4 3 3 3 2 2 5 4 2 4 2 2 3 2 1 7 N SD: 4.6449 c. M:-7.1359 c. 68: 12 1 2 3 4 3 3 3 2 2 5 4 2 4 3 2 3 1 2 7 N SD: 4.1236 c. M: 8.1865 c. 72: 12 2 2 3 4 3 4 3 2 2 5 5 2 4 3 2 3 2 1 8 N SD: 2.0699 c. M: 5.0351 c. 94: 16 2 3 4 5 4 5 4 3 2 7 6 3 5 4 3 4 2 2 10 N SD: 2.6444 c. M:-4.7218 c. 99: 17 2 3 4 6 4 5 4 3 3 7 7 2 6 4 3 4 3 1 11 N SD: 2.5736 c. M: 5.8634 c. 103: 17 3 3 4 6 4 6 4 3 3 7 7 3 6 4 3 4 3 2 11 N SD: 2.4511 c. M: 5.8517 c. 111: 19 2 4 4 7 4 6 5 3 3 8 7 3 7 4 4 4 3 2 12 N SD: 2.4301 c. M:-4.1471 c. 113: 19 3 3 5 6 5 6 5 3 3 8 8 3 6 5 3 5 3 2 12 N SD: 2.2063 c. M: 4.0128 c. 118: 20 3 3 5 7 5 6 5 3 4 8 8 3 7 5 3 5 3 2 13 N SD: 1.9123 c. M: 3.9051 c. 130: 22 3 4 5 8 5 7 6 3 4 9 9 3 8 5 4 5 4 2 14 N SD: 1.4444 c. M:-2.9448 c. 152: 26 3 5 6 9 6 8 7 4 4 11 10 4 9 6 5 6 4 3 16 N SD: 1.2684 c. M: 2.2267 c. 171: 29 4 5 7 10 7 9 8 4 5 12 12 4 10 7 5 7 5 3 18 N SD: 1.3608 c. M:-3.4729 c. 193: 33 4 6 8 11 8 10 9 5 5 14 13 5 11 8 6 8 5 3 21 N SD: 1.3266 c. M: 2.2717 c. 198: 34 4 6 8 12 8 10 9 5 6 14 13 5 12 8 6 8 5 4 21 N SD: 0.9792 c. M:-2.1506 c. 224: 38 5 7 9 13 9 12 10 6 6 16 15 6 13 9 7 9 6 4 24 N SD: 0.7341 c. M:-1.4164 c. 270: 46 6 8 11 16 11 14 12 7 8 19 18 7 16 11 8 11 7 5 29 N SD: 0.3079 c. M: 0.5906 c. 494: 84 11 15 20 29 20 26 22 13 14 35 33 13 29 20 15 20 13 9 53 N SD: 0.2764 c. M:-0.4838 c. 612: 104 14 18 25 36 25 32 27 16 18 43 41 16 36 25 18 25 16 12 65 N SD: 0.2486 c. M:-0.8473 c. 653: 111 15 19 27 38 27 34 29 17 19 46 44 17 38 27 19 27 17 12 70 N SD: 0.3159 c. M:-0.4742 c. 684: 116 16 20 28 40 28 36 30 18 20 48 46 18 40 28 20 28 18 13 73 N SD: 0.2504 c. M: 0.4407 c. 711: 121 16 21 29 42 29 37 32 18 21 50 48 18 42 29 21 29 19 13 76 N SD: 0.2713 c. M:-0.6303 c. 742: 126 17 22 30 44 30 39 33 19 22 52 50 19 44 30 22 30 20 14 79 N SD: 0.2265 c. M:-0.5354 c. 764: 130 17 23 31 45 31 40 34 20 22 54 51 20 45 31 23 31 20 14 82 N SD: 0.2031 c. M: 0.4976 c. 836: 142 19 25 34 49 34 44 37 22 24 59 56 22 49 34 25 34 22 16 89 N SD: 0.1865 c. M:-0.5470 c. 882: 150 20 26 36 52 36 46 39 23 26 62 59 23 52 36 26 36 23 17 94 N SD: 0.1967 c. M:-0.4071 c. 954: 162 22 28 39 56 39 50 42 25 28 67 64 25 56 39 28 39 25 18 102 N SD: 0.1749 c. M: 0.3745 c. 966: 164 22 29 39 57 39 51 43 25 28 68 65 25 57 39 29 39 26 18 103 N SD: 0.1790 c. M:-0.3479 c. 1012: 172 23 30 41 60 41 53 45 26 30 71 68 26 60 41 30 41 27 19 108 N SD: 0.1655 c. M: 0.2988 c. 1084: 184 25 32 44 64 44 57 48 28 32 76 73 28 64 44 32 44 29 20 116 N SD: 0.1442 c. M: 0.2531 c. 1106: 188 25 33 45 65 45 58 49 29 32 78 74 29 65 45 33 45 29 21 118 N SD: 0.1142 c. M:-0.2693 c. 1178: 200 27 35 48 69 48 62 52 31 34 83 79 31 69 48 35 48 31 22 126 N SD: 0.1363 c. M: 0.2356 c. 1236: 210 28 37 50 73 50 65 55 32 36 87 83 32 73 50 37 50 33 23 132 N SD: 0.0972 c. M:-0.1516 c. 1506: 256 34 45 61 89 61 79 67 39 44 106 101 39 89 61 45 61 40 28 161 N SD: 0.0750 c. M: 0.1405 c. 1578: 268 36 47 64 93 64 83 70 41 46 111 106 41 93 64 47 64 42 29 169 N SD: 0.0715 c. M: 0.2189 c. 1848: 314 42 55 75 109 75 97 82 48 54 130 124 48 109 75 55 75 49 34 198 N SD: 0.0694 c. M: 0.2732 c. 1889: 321 43 56 77 111 77 99 84 49 55 133 127 49 111 77 56 77 50 35 202 N SD: 0.0663 c. M:-0.1443 c. 2159: 367 49 64 88 127 88 113 96 56 63 152 145 56 127 88 64 88 57 40 231 N SD: 0.0622 c. M:-0.1174 c. 2190: 372 50 65 89 129 89 115 97 57 64 154 147 57 129 89 65 89 58 41 234 N SD: 0.0461 c. M: 0.0851 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: 0.0000 cents 7 .. 14 match: 7 H SD: 0.0000 cents 8 .. 16 match: 8 H SD: 3.9428 cents 9 .. 18 match: 9 H SD: 6.5453 cents 10 .. 20 match: 10 H SD: 6.0412 cents 11 .. 22 match: 10 S SD: 8.3930 cents 12 .. 24 match: 10 S SD: 1.9509 cents 13 .. 26 match: 11 SD: 7.1269 cents 14 .. 28 match: 12 S SD: 3.4788 cents 15 .. 30 match: 12 SD: 4.1581 cents 16 .. 32 match: 14 S SD: 3.8377 cents 17 .. 34 match: 14 SD: 4.7169 cents 18 .. 36 match: 15 S SD: 3.7248 cents 19 .. 38 match: 14 SD: 4.5123 cents 20 .. 40 match: 16 SD: 3.2664 cents 21 .. 42 match: 16 S SD: 2.7279 cents 22 .. 44 match: 14 SD: 3.8360 cents 23 .. 46 match: 18 SD: 3.5549 cents 24 .. 48 match: 17 S SD: 1.8258 cents 25 .. 50 match: 18 SD: 2.6702 cents 26 .. 52 match: 16 SD: 3.3454 cents 27 .. 54 match: 18 SD: 3.0866 cents 28 .. 56 match: 18 SD: 2.2062 cents 29 .. 58 match: 17 SD: 2.7028 cents 30 .. 60 match: 19 SD: 2.2231 cents 31 .. 62 match: 18 SD: 2.4727 cents 32 .. 64 match: 18 SD: 2.1404 cents 33 .. 66 match: 19 SD: 2.6389 cents 34 .. 68 match: 20 SD: 2.5270 cents 35 .. 70 match: 20 SD: 1.6060 cents 36 .. 72 match: 18 SD: 1.7884 cents 37 .. 74 match: 19 SD: 2.1824 cents 38 .. 76 match: 19 SD: 2.2498 cents 39 .. 78 match: 19 SD: 2.2256 cents 40 .. 80 match: 20 SD: 1.5229 cents 42 .. 84 match: 20 SD: 1.4852 cents 44 .. 88 match: 19 SD: 1.8642 cents 45 .. 90 match: 19 SD: 1.6827 cents 48 .. 96 match: 20 SD: 1.2215 cents 52 .. 104 match: 19 SD: 1.5987 cents 53 .. 106 match: 20 SD: 1.5512 cents 54 .. 108 match: 20 SD: 1.4200 cents 55 .. 110 match: 20 SD: 1.2701 cents 56 .. 112 match: 20 SD: 0.9798 cents 70 .. 140 match: 20 SD: 0.9086 cents 72 .. 144 match: 20 SD: 0.8284 cents 80 .. 160 match: 20 SD: 0.7682 cents 84 .. 168 match: 20 SD: 0.7376 cents 90 .. 180 match: 20 SD: 0.7363 cents 96 .. 192 match: 20 SD: 0.6132 cents 105 .. 210 match: 20 SD: 0.5918 cents 112 .. 224 match: 20 SD: 0.4972 cents 120 .. 240 match: 20 SD: 0.3701 cents 168 .. 336 match: 20 SD: 0.2283 cents 240 .. 480 match: 20 SD: 0.1902 cents 280 .. 560 match: 20 SD: 0.1441 cents 336 .. 672 match: 20 SD: 0.1106 cents 480 .. 960 match: 20 SD: 0.0965 cents 504 .. 1008 match: 20 SD: 0.0737 cents 560 .. 1120 match: 20 SD: 0.0720 cents