Scala analysis: xen05-walker-golden
Scale used in the composition 'The Golden Net'
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 16/15 111.731285 minor diatonic semitone 2: 10/9 182.403712 minor whole tone 3: 9/8 203.910002 major whole tone 4: 7/6 266.870906 septimal minor third 5: 32/27 294.134997 Pythagorean minor third 6: 11/9 347.407941 undecimal neutral third 7: 5/4 386.313714 major third 8: 4/3 498.044999 perfect fourth 9: 11/8 551.317942 undecimal semi-augmented fourth 10: 10/7 617.487807 Euler's tritone 11: 40/27 680.448711 grave fifth 12: 3/2 701.955001 perfect fifth 13: 14/9 764.915905 septimal minor sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 27/16 905.865003 Pythagorean major sixth 16: 7/4 968.825906 harmonic seventh 17: 16/9 996.089998 Pythagorean minor seventh 18: 20/11 1034.995772 large minor seventh 19: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 20: 40/21 1115.532807 acute major seventh 21: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 21/20 84.4672 minor semitone 1: 16/15 111.7313 minor diatonic semitone 2: 25/24 70.6724 classic chromatic semitone, minor chroma 3: 81/80 21.5063 syntonic comma, Didymus comma 4: 28/27 62.9609 Archytas' 1/3-tone 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 7: 45/44 38.9058 1/5-tone 8: 16/15 111.7313 minor diatonic semitone 9: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 10: 80/77 66.1699 11: 28/27 62.9609 Archytas' 1/3-tone 12: 81/80 21.5063 syntonic comma, Didymus comma 13: 28/27 62.9609 Archytas' 1/3-tone 14: 15/14 119.4428 major diatonic semitone 15: 81/80 21.5063 syntonic comma, Didymus comma 16: 28/27 62.9609 Archytas' 1/3-tone 17: 64/63 27.2641 septimal comma, Archytas' comma 18: 45/44 38.9058 1/5-tone 19: 121/120 14.3672 undecimal seconds comma, biyatisma 20: 80/77 66.1699 21: 21/20 84.4672 minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 121/120 14.367 cents undecimal seconds comma, biyatisma 1: 3 81/80 21.506 cents syntonic comma, Didymus comma 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 45/44 38.906 cents 1/5-tone 1: 2 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 4 28/27 62.961 cents Archytas' 1/3-tone 1: 2 80/77 66.170 cents 1: 1 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 1 21/20 84.467 cents minor semitone 1: 2 16/15 111.731 cents minor diatonic semitone 1: 1 15/14 119.443 cents major diatonic semitone 2: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 2: 1 80/77 66.170 cents 2: 2 22/21 80.537 cents undecimal minor semitone 2: 4 21/20 84.467 cents minor semitone 2: 2 256/243 90.225 cents limma, Pythagorean minor second 2: 2 135/128 92.179 cents major chroma, major limma 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 320/297 129.131 cents 2: 1 243/224 140.949 cents Archytas' 2/3-tone 2: 2 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: 2 10/9 182.404 cents minor whole tone 2: 1 28/25 196.198 cents middle second 3: 1 22/21 80.537 cents undecimal minor semitone 3: 2 16/15 111.731 cents minor diatonic semitone 3: 2 15/14 119.443 cents major diatonic semitone 3: 1 320/297 129.131 cents 3: 1 88/81 143.498 cents 2nd undecimal neutral second 3: 1 49/45 147.428 cents BP minor semitone 3: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 1 35/32 155.140 cents septimal neutral second 3: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 3: 1 10/9 182.404 cents minor whole tone 3: 6 9/8 203.910 cents major whole tone 3: 1 8/7 231.174 cents septimal whole tone 3: 1 64/55 262.368 cents 3: 1 7/6 266.871 cents septimal minor third 4: 1 88/81 143.498 cents 2nd undecimal neutral second 4: 1 160/147 146.707 cents 4: 1 12/11 150.637 cents undecimal neutral second, 3/4-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: 2 9/8 203.910 cents major whole tone 4: 1 112/99 213.598 cents 4: 1 729/640 225.416 cents acute major second 4: 2 8/7 231.174 cents septimal whole tone 4: 1 297/256 257.183 cents 4: 3 7/6 266.871 cents septimal minor third 4: 1 90/77 270.080 cents 4: 1 88/75 276.736 cents 4: 1 189/160 288.377 cents 4: 1 32/27 294.135 cents Pythagorean minor third 4: 1 40/33 333.041 cents 5: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 5: 1 9/8 203.910 cents major whole tone 5: 1 640/567 209.668 cents 5: 1 8/7 231.174 cents septimal whole tone 5: 1 55/48 235.677 cents undecimal semi-augmented whole tone 5: 1 7/6 266.871 cents septimal minor third 5: 1 90/77 270.080 cents 5: 1 33/28 284.447 cents undecimal minor third 5: 2 189/160 288.377 cents 5: 3 32/27 294.135 cents Pythagorean minor third 5: 2 6/5 315.641 cents minor third 5: 1 135/112 323.353 cents septimal wide minor third 5: 2 40/33 333.041 cents 5: 1 11/9 347.408 cents undecimal neutral third 5: 1 49/40 351.338 cents larger approximation to neutral third 5: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 6: 1 8/7 231.174 cents septimal whole tone 6: 1 75/64 274.582 cents classic augmented second 6: 1 33/28 284.447 cents undecimal minor third 6: 1 32/27 294.135 cents Pythagorean minor third 6: 2 6/5 315.641 cents minor third 6: 1 40/33 333.041 cents 6: 1 128/105 342.905 cents septimal neutral third 6: 2 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: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 6: 1 99/80 368.914 cents 6: 2 56/45 378.602 cents septimal narrow major third 6: 3 5/4 386.314 cents major third 6: 1 14/11 417.508 cents undecimal diminished fourth or major third 7: 1 6/5 315.641 cents minor third 7: 1 11/9 347.408 cents undecimal neutral third 7: 1 60/49 350.617 cents smaller approximation to neutral third 7: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 7: 1 99/80 368.914 cents 7: 1 56/45 378.602 cents septimal narrow major third 7: 2 5/4 386.314 cents major third 7: 1 512/405 405.866 cents narrow diminished fourth 7: 3 81/64 407.820 cents Pythagorean major third 7: 3 80/63 413.578 cents wide major third 7: 2 14/11 417.508 cents undecimal diminished fourth or major third 7: 2 77/60 431.875 cents 7: 1 128/99 444.772 cents 7: 1 4/3 498.045 cents perfect fourth 8: 1 99/80 368.914 cents 8: 1 80/63 413.578 cents wide major third 8: 1 14/11 417.508 cents undecimal diminished fourth or major third 8: 1 32/25 427.373 cents classic diminished fourth 8: 4 9/7 435.084 cents septimal major third, BP third 8: 1 165/128 439.587 cents 8: 1 128/99 444.772 cents 8: 1 176/135 459.139 cents 8: 4 21/16 470.781 cents narrow fourth 8: 2 320/243 476.539 cents grave fourth 8: 2 4/3 498.045 cents perfect fourth 8: 1 27/20 519.551 cents acute fourth 8: 1 15/11 536.951 cents undecimal augmented fourth 9: 1 77/60 431.875 cents 9: 1 9/7 435.084 cents septimal major third, BP third 9: 1 160/121 483.678 cents 9: 9 4/3 498.045 cents perfect fourth 9: 1 75/56 505.757 cents marvelous fourth 9: 1 121/90 512.412 cents 9: 1 15/11 536.951 cents undecimal augmented fourth 9: 1 48/35 546.815 cents septimal semi-augmented fourth 9: 1 11/8 551.318 cents undecimal semi-augmented fourth 9: 1 243/176 558.457 cents 9: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 9: 1 45/32 590.224 cents diatonic tritone 10: 2 4/3 498.045 cents perfect fourth 10: 3 27/20 519.551 cents acute fourth 10: 1 256/189 525.309 cents 10: 1 15/11 536.951 cents undecimal augmented fourth 10: 2 11/8 551.318 cents undecimal semi-augmented fourth 10: 2 112/81 561.006 cents 10: 1 25/18 568.717 cents classic augmented fourth 10: 2 64/45 609.776 cents 2nd tritone 10: 1 729/512 611.730 cents Pythagorean tritone 10: 3 10/7 617.488 cents Euler's tritone 10: 1 63/44 621.418 cents 10: 1 231/160 635.785 cents 10: 1 16/11 648.682 cents undecimal semi-diminished fifth 11: 1 11/8 551.318 cents undecimal semi-augmented fourth 11: 1 320/231 564.215 cents 11: 1 88/63 578.582 cents 11: 3 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 11: 1 1024/729 588.270 cents Pythagorean diminished fifth 11: 2 45/32 590.224 cents diatonic tritone 11: 1 36/25 631.283 cents classic diminished fifth 11: 2 81/56 638.994 cents 11: 2 16/11 648.682 cents undecimal semi-diminished fifth 11: 1 22/15 663.049 cents undecimal diminished fifth 11: 1 189/128 674.691 cents 11: 3 40/27 680.449 cents grave fifth 11: 2 3/2 701.955 cents perfect fifth 12: 1 64/45 609.776 cents 2nd tritone 12: 2 10/7 617.488 cents Euler's tritone 12: 1 352/243 641.543 cents 12: 1 16/11 648.682 cents undecimal semi-diminished fifth 12: 1 35/24 653.185 cents septimal semi-diminished fifth 12: 1 22/15 663.049 cents undecimal diminished fifth 12: 1 180/121 687.588 cents 12: 1 112/75 694.243 cents marvelous fifth 12: 9 3/2 701.955 cents perfect fifth 12: 1 121/80 716.322 cents 12: 1 14/9 764.916 cents septimal minor sixth 12: 1 120/77 768.125 cents 13: 1 22/15 663.049 cents undecimal diminished fifth 13: 1 40/27 680.449 cents grave fifth 13: 2 3/2 701.955 cents perfect fifth 13: 2 243/160 723.461 cents acute fifth 13: 4 32/21 729.219 cents wide fifth 13: 1 135/88 740.861 cents 13: 1 99/64 755.228 cents 13: 1 256/165 760.413 cents 13: 4 14/9 764.916 cents septimal minor sixth 13: 1 25/16 772.627 cents classic augmented fifth 13: 1 11/7 782.492 cents undecimal augmented fifth 13: 1 63/40 786.422 cents narrow minor sixth 13: 1 160/99 831.086 cents 14: 1 3/2 701.955 cents perfect fifth 14: 1 99/64 755.228 cents 14: 2 120/77 768.125 cents 14: 2 11/7 782.492 cents undecimal augmented fifth 14: 3 63/40 786.422 cents narrow minor sixth 14: 3 128/81 792.180 cents Pythagorean minor sixth 14: 1 405/256 794.134 cents wide augmented fifth 14: 2 8/5 813.686 cents minor sixth 14: 1 45/28 821.398 cents septimale wide minor sixth 14: 1 160/99 831.086 cents 14: 1 44/27 845.453 cents 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 5/3 884.359 cents major sixth, BP sixth 15: 1 11/7 782.492 cents undecimal augmented fifth 15: 3 8/5 813.686 cents minor sixth 15: 2 45/28 821.398 cents septimale wide minor sixth 15: 1 160/99 831.086 cents 15: 2 44/27 845.453 cents neutral sixth 15: 1 80/49 848.662 cents smaller approximation to neutral sixth 15: 1 49/30 849.383 cents larger approximation to neutral sixth 15: 2 18/11 852.592 cents undecimal neutral sixth 15: 1 105/64 857.095 cents septimal neutral sixth 15: 1 33/20 866.959 cents 15: 2 5/3 884.359 cents major sixth, BP sixth 15: 1 27/16 905.865 cents Pythagorean major sixth 15: 1 56/33 915.553 cents 15: 1 128/75 925.418 cents diminished seventh 15: 1 7/4 968.826 cents harmonic seventh 16: 1 44/27 845.453 cents neutral sixth 16: 1 80/49 848.662 cents smaller approximation to neutral sixth 16: 1 18/11 852.592 cents undecimal neutral sixth 16: 2 33/20 866.959 cents 16: 1 224/135 876.647 cents narrow septimal major sixth 16: 2 5/3 884.359 cents major sixth, BP sixth 16: 3 27/16 905.865 cents Pythagorean major sixth 16: 2 320/189 911.623 cents 16: 1 56/33 915.553 cents 16: 1 77/45 929.920 cents 16: 1 12/7 933.129 cents septimal major sixth 16: 1 96/55 964.323 cents 16: 1 7/4 968.826 cents harmonic seventh 16: 1 567/320 990.332 cents 16: 1 16/9 996.090 cents Pythagorean minor seventh 16: 1 20/11 1034.996 cents large minor seventh 17: 1 33/20 866.959 cents 17: 1 27/16 905.865 cents Pythagorean major sixth 17: 1 320/189 911.623 cents 17: 1 75/44 923.264 cents 17: 1 77/45 929.920 cents 17: 3 12/7 933.129 cents septimal major sixth 17: 1 512/297 942.817 cents 17: 2 7/4 968.826 cents harmonic seventh 17: 1 1280/729 974.584 cents grave minor seventh 17: 1 99/56 986.402 cents 17: 2 16/9 996.090 cents Pythagorean minor seventh 17: 2 9/5 1017.596 cents just minor seventh, BP seventh 17: 1 20/11 1034.996 cents large minor seventh 17: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 17: 1 147/80 1053.293 cents 17: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 18: 1 12/7 933.129 cents septimal major sixth 18: 1 55/32 937.632 cents 18: 1 7/4 968.826 cents harmonic seventh 18: 6 16/9 996.090 cents Pythagorean minor seventh 18: 1 9/5 1017.596 cents just minor seventh, BP seventh 18: 1 20/11 1034.996 cents large minor seventh 18: 1 64/35 1044.860 cents septimal neutral seventh 18: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 18: 1 90/49 1052.572 cents 18: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 18: 1 297/160 1070.869 cents 18: 2 28/15 1080.557 cents grave major seventh 18: 2 15/8 1088.269 cents classic major seventh 18: 1 21/11 1119.463 cents undecimal major seventh 19: 1 25/14 1003.802 cents middle minor seventh 19: 2 9/5 1017.596 cents just minor seventh, BP seventh 19: 1 20/11 1034.996 cents large minor seventh 19: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 19: 1 448/243 1059.051 cents 19: 1 297/160 1070.869 cents 19: 1 28/15 1080.557 cents grave major seventh 19: 2 256/135 1107.821 cents octave - major chroma 19: 2 243/128 1109.775 cents Pythagorean major seventh 19: 4 40/21 1115.533 cents acute major seventh 19: 2 21/11 1119.463 cents undecimal major seventh 19: 1 77/40 1133.830 cents 19: 1 64/33 1146.727 cents 33rd subharmonic 20: 1 28/15 1080.557 cents grave major seventh 20: 2 15/8 1088.269 cents classic major seventh 20: 1 40/21 1115.533 cents acute major seventh 20: 1 48/25 1129.328 cents classic diminished octave 20: 2 77/40 1133.830 cents 20: 4 27/14 1137.039 cents septimal major seventh 20: 2 64/33 1146.727 cents 33rd subharmonic 20: 2 88/45 1161.094 cents 20: 2 63/32 1172.736 cents octave - septimal comma 20: 3 160/81 1178.494 cents octave - syntonic comma 20: 1 240/121 1185.633 cents Highest number of different intervals for one interval class: 16 Average number of different intervals per interval class: 13.70000 = 137/10
SHOW/LINE/CENTS INTERVALS
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 0.0 : 111.7 182.4 203.9 266.9 294.1 347.4 386.3 498.0 551.3 617.5 680.4 702.0 764.9 884.4 905.9 968.8 996.1 1035.0 1049.4 1115.5 1200.0 111.7 : 70.7 92.2 155.1 182.4 235.7 274.6 386.3 439.6 505.8 568.7 590.2 653.2 772.6 794.1 857.1 884.4 923.3 937.6 1003.8 1088.3 1200.0 182.4 : 21.5 84.5 111.7 165.0 203.9 315.6 368.9 435.1 498.0 519.6 582.5 702.0 723.5 786.4 813.7 852.6 867.0 933.1 1017.6 1129.3 1200.0 203.9 : 63.0 90.2 143.5 182.4 294.1 347.4 413.6 476.5 498.0 561.0 680.4 702.0 764.9 792.2 831.1 845.5 911.6 996.1 1107.8 1178.5 1200.0 266.9 : 27.3 80.5 119.4 231.2 284.4 350.6 413.6 435.1 498.0 617.5 639.0 702.0 729.2 768.1 782.5 848.7 933.1 1044.9 1115.5 1137.0 1200.0 294.1 : 53.3 92.2 203.9 257.2 323.4 386.3 407.8 470.8 590.2 611.7 674.7 702.0 740.9 755.2 821.4 905.9 1017.6 1088.3 1109.8 1172.7 1200.0 347.4 : 38.9 150.6 203.9 270.1 333.0 354.5 417.5 537.0 558.5 621.4 648.7 687.6 702.0 768.1 852.6 964.3 1035.0 1056.5 1119.5 1146.7 1200.0 386.3 : 111.7 165.0 231.2 294.1 315.6 378.6 498.0 519.6 582.5 609.8 648.7 663.0 729.2 813.7 925.4 996.1 1017.6 1080.6 1107.8 1161.1 1200.0 498.0 : 53.3 119.4 182.4 203.9 266.9 386.3 407.8 470.8 498.0 537.0 551.3 617.5 702.0 813.7 884.4 905.9 968.8 996.1 1049.4 1088.3 1200.0 551.3 : 66.2 129.1 150.6 213.6 333.0 354.5 417.5 444.8 483.7 498.0 564.2 648.7 760.4 831.1 852.6 915.6 942.8 996.1 1035.0 1146.7 1200.0 617.5 : 63.0 84.5 147.4 266.9 288.4 351.3 378.6 417.5 431.9 498.0 582.5 694.2 764.9 786.4 849.4 876.6 929.9 968.8 1080.6 1133.8 1200.0 680.4 : 21.5 84.5 203.9 225.4 288.4 315.6 354.5 368.9 435.1 519.6 631.3 702.0 723.5 786.4 813.7 867.0 905.9 1017.6 1070.9 1137.0 1200.0 702.0 : 63.0 182.4 203.9 266.9 294.1 333.0 347.4 413.6 498.0 609.8 680.4 702.0 764.9 792.2 845.5 884.4 996.1 1049.4 1115.5 1178.5 1200.0 764.9 : 119.4 140.9 203.9 231.2 270.1 284.4 350.6 435.1 546.8 617.5 639.0 702.0 729.2 782.5 821.4 933.1 986.4 1052.6 1115.5 1137.0 1200.0 884.4 : 21.5 84.5 111.7 150.6 165.0 231.2 315.6 427.4 498.0 519.6 582.5 609.8 663.0 702.0 813.7 867.0 933.1 996.1 1017.6 1080.6 1200.0 905.9 : 63.0 90.2 129.1 143.5 209.7 294.1 405.9 476.5 498.0 561.0 588.3 641.5 680.4 792.2 845.5 911.6 974.6 996.1 1059.1 1178.5 1200.0 968.8 : 27.3 66.2 80.5 146.7 231.2 342.9 413.6 435.1 498.0 525.3 578.6 617.5 729.2 782.5 848.7 911.6 933.1 996.1 1115.5 1137.0 1200.0 996.1 : 38.9 53.3 119.4 203.9 315.6 386.3 407.8 470.8 498.0 551.3 590.2 702.0 755.2 821.4 884.4 905.9 968.8 1088.3 1109.8 1172.7 1200.0 1035.0: 14.4 80.5 165.0 276.7 347.4 368.9 431.9 459.1 512.4 551.3 663.0 716.3 782.5 845.5 867.0 929.9 1049.4 1070.9 1133.8 1161.1 1200.0 1049.4: 66.2 150.6 262.4 333.0 354.5 417.5 444.8 498.0 537.0 648.7 702.0 768.1 831.1 852.6 915.6 1035.0 1056.5 1119.5 1146.7 1185.6 1200.0 1115.5: 84.5 196.2 266.9 288.4 351.3 378.6 431.9 470.8 582.5 635.8 702.0 764.9 786.4 849.4 968.8 990.3 1053.3 1080.6 1119.5 1133.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.3672 .. 119.4428 cents 900/847, 105.0756 cents 121/120, 14.3672 cents 2: 53.2729 .. 196.1985 cents 896/825, 142.9255 cents 77/80,-66.1699 cents 3: 80.5370 .. 266.8709 cents 49/44, 186.3339 cents 275/294,-115.6614 cents 4: 143.4979 .. 333.0408 cents 135/121, 189.5428 cents 176/189,-123.3730 cents 5: 165.0042 .. 354.5471 cents 135/121, 189.5428 cents 363/400,-168.0365 cents 6: 231.1741 .. 417.5080 cents 49/44, 186.3339 cents 176/189,-123.3730 cents 7: 315.6413 .. 498.0450 cents 10/9, 182.4037 cents 33/35,-101.8667 cents 8: 368.9142 .. 536.9508 cents 400/363, 168.0365 cents 297/320,-129.1308 cents 9: 431.8751 .. 590.2237 cents 675/616, 158.3486 cents 847/900,-105.0756 cents 10: 498.0450 .. 648.6821 cents 12/11, 150.6371 cents 128/135,-92.1787 cents 11: 551.3179 .. 701.9550 cents 12/11, 150.6371 cents 121/128,-97.3641 cents 12: 609.7763 .. 768.1249 cents 675/616, 158.3486 cents 128/135,-92.1787 cents 13: 663.0492 .. 831.0858 cents 400/363, 168.0365 cents 847/900,-105.0756 cents 14: 701.9550 .. 884.3587 cents 10/9, 182.4037 cents 297/320,-129.1308 cents 15: 782.4920 .. 968.8259 cents 49/44, 186.3339 cents 33/35,-101.8667 cents 16: 845.4529 .. 1034.9958 cents 135/121, 189.5428 cents 176/189,-123.3730 cents 17: 866.9592 .. 1056.5021 cents 135/121, 189.5428 cents 363/400,-168.0365 cents 18: 933.1291 .. 1119.4630 cents 49/44, 186.3339 cents 176/189,-123.3730 cents 19: 1003.8015 .. 1146.7271 cents 896/825, 142.9255 cents 275/294,-115.6614 cents 20: 1080.5572 .. 1185.6328 cents 900/847, 105.0756 cents 77/80,-66.1699 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 121/120, 14.3672 cents, class 1 Average step (divided formal octave): 57.1429 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 3.977322 Largest / Average step : 2.090249 Largest / Smallest step : 8.313593 Median interval of one step : 28/27, 62.9609 cents, amount: 4 Most common interval of one step : 28/27, 62.9609 cents, amount: 4 Least squares average step : 58.55352 cents, oct.: 1229.62383 cents Scale is not proper Step pattern alph. order: ABCDEFGAFHDCDICDEGJHK Step pattern size order : JHBFCEDJEGFBFKBFCDAGI Scale is not a Constant Structure Scale diversity : 1.551259 Lumma stability : 0.023945 Lumma impropriety factor : 0.911212 Number of different interval sizes : 158 = 7.90000 / class Number of one step interval sizes : 11 Highest interval variety : 16 Mean interval variety : 13.70000 = 137/10 Median interval variety : 11.5 Lowest interval variety : 11 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 14 Most common triad is 0.0 498.045 701.955 cents, amount: 9 Number of recognisable fifths : 17, average 701.5014 cents Number of appreciable fifths : 15, average 701.4409 cents Scale contains a complete diamond : 1 3 9 27 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 7 = 33.3333% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is differentially coherent in interval classes 3 and 4 combined -- Rational properties -- Prime limit : 11 Odd number limit : 729 (O: 729 U: 729) Highest odd numerator or denominator: 27 Scale harmonicity : 0.010556 Average absolute harmonicity : 0.133520 Specific harmonicity : 0.099106 Fundamental : 1/166320, -17.3436 octaves, 0.0016 Hz. Guide tone : 332640, 18.3436 octaves, 87027128.042 Hz. Exponens Consonantiae : 5.532468E+10, 35.68720 octaves Euler's gradus suavitatis : 62 Sum of Mann's harmonic distance : 252.5, average 12.02381 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 19.66242, average 0.93631 Sum of Tenney's harmonic distance : 39.63329, average 1.88730 Vogel's harmonic complexity : 37.28571 Wille's k value : 140332 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 12 Triangular lattice diameter : 6 Lattice compactness : 871.25730, average 3.77168 Lattice compactness (without 2's) : 500.15648, average 2.16518 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.47619 44 1 3: -3 .. 3 -0.66667 26 6 5: -1 .. 1 0.28571 8 5 7: -1 .. 1 0.04762 5 5 11: -1 .. 1 0.09524 4 4 Average exponent except 2's :-5 / 21 =-0.23810 Average absolute exponent except 2's: 43 / 21 = 2.04762
FIT/MODE
21: 2 1 1 1 0 1 1 2 1 1 1 0 1 2 1 1 0 1 0 2 1 N SD: 16.3081 c. M:-27.3243 c. 22: 2 1 1 1 0 1 1 2 1 1 1 1 1 2 0 2 0 1 0 1 2 N SD: 15.3976 c. M: 33.1377 c. 24: 2 2 0 1 1 1 1 2 1 1 2 0 1 3 0 1 1 1 0 1 2 N SD: 11.9744 c. M:-19.5513 c. 28: 3 1 1 1 1 1 1 3 1 1 2 0 2 3 0 2 0 1 0 2 2 N SD: 11.4356 c. M: 20.7915 c. 29: 2 2 1 1 1 1 1 3 1 2 1 1 1 3 1 1 1 1 0 2 2 N SD: 13.2358 c. M: 28.9727 c. 30: 3 2 0 2 0 2 1 2 2 1 2 1 1 3 1 1 1 1 0 2 2 N SD: 11.1543 c. M:-18.0450 c. 31: 3 2 0 2 1 1 1 3 1 2 2 0 2 3 0 2 1 1 0 2 2 N SD: 8.6326 c. M:-16.3255 c. 37: 3 3 0 2 1 2 1 3 2 2 2 1 2 3 1 2 1 1 0 2 3 N SD: 8.5628 c. M: 14.4340 c. 41: 4 2 1 2 1 2 1 4 2 2 2 1 2 4 1 2 1 1 1 2 3 N SD: 4.5349 c. M: 10.6055 c. 46: 4 3 1 2 1 2 2 4 2 3 2 1 2 5 1 2 1 2 0 3 3 N SD: 5.6508 c. M:-8.5991 c. 53: 5 3 1 3 1 2 2 5 2 3 3 1 3 5 1 3 1 2 0 3 4 N SD: 4.2637 c. M: 7.9217 c. 58: 5 4 1 3 1 3 2 5 3 3 3 1 3 6 1 3 1 2 1 3 4 N SD: 4.1505 c. M: 8.2830 c. 66: 6 4 1 4 1 3 2 6 3 4 3 2 3 7 1 3 2 2 1 3 5 N SD: 4.6550 c. M: 7.7214 c. 72: 7 4 1 4 2 3 2 7 3 4 4 1 4 7 1 4 2 2 1 4 5 N SD: 2.8606 c. M:-5.8650 c. 87: 8 5 2 4 2 4 3 8 4 5 4 2 4 9 2 4 2 3 1 5 6 N SD: 3.0285 c. M: 6.2952 c. 89: 8 6 1 5 2 4 3 8 4 5 5 1 5 9 1 5 2 3 1 5 6 N SD: 3.4638 c. M:-7.1917 c. 90: 8 6 1 5 2 4 3 8 4 5 5 2 4 9 2 5 2 3 1 5 6 N SD: 3.6784 c. M: 5.0646 c. 93: 9 5 2 5 2 4 3 9 4 5 5 1 5 10 1 5 2 3 1 5 7 N SD: 3.5067 c. M:-5.9639 c. 94: 9 5 2 5 2 4 3 9 4 5 5 2 5 9 2 5 2 3 1 5 7 N SD: 2.5254 c. M: 4.8945 c. 111: 10 7 2 6 2 5 4 10 5 6 6 2 6 11 2 6 2 4 1 6 8 N SD: 2.1391 c. M:-4.1471 c. 114: 11 6 2 6 3 5 4 10 5 7 6 2 6 11 2 6 3 3 2 6 8 N SD: 2.9498 c. M:-4.0582 c. 117: 11 7 2 6 3 5 4 11 5 6 6 2 7 11 2 6 3 4 1 7 8 N SD: 2.8590 c. M: 4.7233 c. 118: 11 7 2 6 3 5 4 11 5 7 6 2 6 12 2 6 3 4 1 7 8 N SD: 1.6295 c. M:-3.1113 c. 130: 12 8 2 7 3 6 4 12 6 7 7 2 7 13 2 7 3 4 2 7 9 N SD: 1.6278 c. M:-3.3613 c. 152: 14 9 3 8 3 7 5 14 7 8 8 3 8 15 3 8 3 5 2 8 11 N SD: 1.3256 c. M: 2.3749 c. 159: 15 9 3 8 4 7 5 15 7 9 8 3 8 16 3 8 4 5 2 9 11 N SD: 1.3223 c. M: 2.7882 c. 183: 17 11 3 10 4 8 6 17 8 10 10 3 10 18 3 10 4 6 2 10 13 N SD: 1.0454 c. M:-2.2972 c. 212: 20 12 4 11 5 9 7 20 9 12 11 4 11 21 4 11 5 7 2 12 15 N SD: 1.1310 c. M: 2.2613 c. 217: 20 13 4 11 5 10 7 20 10 12 11 4 11 22 4 11 5 7 3 12 15 N SD: 1.0714 c. M:-1.8670 c. 224: 21 13 4 12 5 10 7 21 10 12 12 4 12 22 4 12 5 7 3 12 16 N SD: 0.7226 c. M: 1.4164 c. 270: 25 16 5 14 6 12 9 25 12 15 14 5 14 27 5 14 6 9 3 15 19 N SD: 0.4490 c. M:-0.8017 c. 342: 32 20 6 18 8 15 11 32 15 19 18 6 18 34 6 18 8 11 4 19 24 N SD: 0.3219 c. M: 0.6018 c. 494: 46 29 9 26 11 22 16 46 22 27 26 9 26 49 9 26 11 16 6 27 35 N SD: 0.2414 c. M: 0.5530 c. 612: 57 36 11 32 14 27 20 57 27 34 32 11 32 61 11 32 14 20 7 34 43 N SD: 0.1730 c. M: 0.3491 c. 836: 78 49 15 44 19 37 27 78 37 46 44 15 44 83 15 44 19 27 10 46 59 N SD: 0.1314 c. M: 0.2629 c. 1053: 98 62 19 55 24 47 34 98 47 58 55 19 55 105 19 55 24 34 13 58 74 N SD: 0.1435 c. M:-0.2490 c. 1106: 103 65 20 58 25 49 36 103 49 61 58 20 58 110 20 58 25 36 13 61 78 N SD: 0.1065 c. M: 0.2108 c. 1236: 115 73 22 65 28 55 40 115 55 68 65 22 65 123 22 65 28 40 15 68 87 N SD: 0.0923 c. M:-0.1649 c. 1506: 140 89 27 79 34 67 49 140 67 83 79 27 79 150 27 79 34 49 18 83 106 N SD: 0.0796 c. M: 0.1775 c. 1578: 147 93 28 83 36 70 51 147 70 87 83 28 83 157 28 83 36 51 19 87 111 N SD: 0.0871 c. M:-0.1616 c. 1848: 172 109 33 97 42 82 60 172 82 102 97 33 97 184 33 97 42 60 22 102 130 N SD: 0.0369 c. M:-0.0708 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: 12.8326 cents 6 .. 12 match: 6 H SD: 0.0000 cents 7 .. 14 match: 7 H SD: 9.7658 cents 8 .. 16 match: 8 H SD: 6.4523 cents 9 .. 18 match: 9 H SD: 2.6663 cents 10 .. 20 match: 10 H SD: 8.0764 cents 11 .. 22 match: 11 H SD: 6.3310 cents 12 .. 24 match: 12 H SD: 3.7134 cents 13 .. 26 match: 12 S SD: 4.9244 cents 14 .. 28 match: 14 H SD: 5.7652 cents 15 .. 30 match: 14 SD: 5.1817 cents 16 .. 32 match: 14 SD: 2.9874 cents 17 .. 34 match: 14 SD: 4.6467 cents 18 .. 36 match: 15 S SD: 3.4352 cents 19 .. 38 match: 17 S SD: 3.8051 cents 20 .. 40 match: 17 SD: 4.2826 cents 21 .. 42 match: 17 SD: 3.9558 cents 22 .. 44 match: 16 SD: 4.3899 cents 23 .. 46 match: 18 SD: 3.3487 cents 24 .. 48 match: 17 SD: 2.8284 cents 25 .. 50 match: 17 SD: 3.4161 cents 26 .. 52 match: 18 SD: 3.1719 cents 27 .. 54 match: 19 SD: 2.3766 cents 28 .. 56 match: 18 SD: 2.9350 cents 29 .. 58 match: 19 SD: 2.7627 cents 30 .. 60 match: 19 SD: 2.6827 cents 31 .. 62 match: 20 SD: 2.3566 cents 32 .. 64 match: 20 SD: 1.7029 cents 33 .. 66 match: 19 SD: 2.1162 cents 34 .. 68 match: 16 SD: 2.9098 cents 35 .. 70 match: 18 SD: 2.1120 cents 36 .. 72 match: 21 SD: 2.0780 cents 37 .. 74 match: 20 SD: 2.1954 cents 39 .. 78 match: 20 SD: 2.0466 cents 40 .. 80 match: 19 SD: 1.8156 cents 41 .. 82 match: 19 SD: 1.9059 cents 42 .. 84 match: 20 SD: 1.6181 cents 43 .. 86 match: 20 SD: 1.7727 cents 44 .. 88 match: 21 SD: 1.6356 cents 45 .. 90 match: 20 SD: 1.4487 cents 46 .. 92 match: 20 SD: 1.8679 cents 47 .. 94 match: 21 SD: 1.6988 cents 48 .. 96 match: 21 SD: 1.1625 cents 50 .. 100 match: 20 SD: 1.6236 cents 51 .. 102 match: 19 SD: 1.7049 cents 52 .. 104 match: 20 SD: 1.7747 cents 53 .. 106 match: 21 SD: 1.5775 cents 54 .. 108 match: 21 SD: 1.0721 cents 59 .. 118 match: 20 SD: 1.2344 cents 60 .. 120 match: 21 SD: 1.1282 cents 64 .. 128 match: 21 SD: 0.9844 cents 72 .. 144 match: 21 SD: 0.5955 cents 108 .. 216 match: 21 SD: 0.5334 cents 120 .. 240 match: 21 SD: 0.5055 cents 135 .. 270 match: 21 SD: 0.4752 cents 144 .. 288 match: 21 SD: 0.3350 cents 168 .. 336 match: 21 SD: 0.3274 cents 192 .. 384 match: 21 SD: 0.3259 cents 198 .. 396 match: 21 SD: 0.2972 cents 216 .. 432 match: 21 SD: 0.2388 cents 252 .. 504 match: 21 SD: 0.2373 cents 264 .. 528 match: 21 SD: 0.2216 cents 270 .. 540 match: 21 SD: 0.2021 cents 288 .. 576 match: 21 SD: 0.1683 cents 336 .. 672 match: 21 SD: 0.1639 cents 360 .. 720 match: 21 SD: 0.1340 cents 432 .. 864 match: 21 SD: 0.0642 cents