Scala analysis: xen14-polansky-horn
Scale from 'Horn'
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 65/64 26.841376 13th-partial chroma 2: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 3: 17/16 104.955410 17th harmonic 4: 35/32 155.139620 septimal neutral second 5: 9/8 203.910002 major whole tone 6: 75/64 274.582429 classic augmented second 7: 39/32 342.482663 39th harmonic, Zalzal wosta of Ibn Sina 8: 5/4 386.313714 major third 9: 21/16 470.780907 narrow fourth 10: 85/64 491.269123 11: 11/8 551.317942 undecimal semi-augmented fourth 12: 45/32 590.223716 diatonic tritone 13: 3/2 701.955001 perfect fifth 14: 25/16 772.627428 classic augmented fifth 15: 51/32 806.910410 16: 13/8 840.527662 tridecimal neutral sixth 17: 27/16 905.865003 Pythagorean major sixth 18: 55/32 937.631656 19: 7/4 968.825906 harmonic seventh 20: 15/8 1088.268715 classic major seventh 21: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 16/15 111.7313 minor diatonic semitone 1: 65/64 26.8414 13th-partial chroma 2: 66/65 26.4316 Winmeanma 3: 34/33 51.6825 4: 35/34 50.1842 septendecimal 1/4-tone 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 25/24 70.6724 classic chromatic semitone, minor chroma 7: 26/25 67.9002 tridecimal 1/3-tone 8: 40/39 43.8311 tridecimal minor diesis 9: 21/20 84.4672 minor semitone 10: 85/84 20.4882 11: 88/85 60.0488 12: 45/44 38.9058 1/5-tone 13: 16/15 111.7313 minor diatonic semitone 14: 25/24 70.6724 classic chromatic semitone, minor chroma 15: 51/50 34.2830 17th-partial chroma 16: 52/51 33.6173 17: 27/26 65.3373 tridecimal comma 18: 55/54 31.7667 telepathma 19: 56/55 31.1943 undecimal diesis, konbini comma 20: 15/14 119.4428 major diatonic semitone 21: 16/15 111.7313 minor diatonic semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 1 85/84 20.488 cents 1: 1 66/65 26.432 cents Winmeanma 1: 1 65/64 26.841 cents 13th-partial chroma 1: 1 56/55 31.194 cents undecimal diesis, konbini comma 1: 1 55/54 31.767 cents telepathma 1: 1 52/51 33.617 cents 1: 1 51/50 34.283 cents 17th-partial chroma 1: 1 45/44 38.906 cents 1/5-tone 1: 1 40/39 43.831 cents tridecimal minor diesis 1: 1 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 35/34 50.184 cents septendecimal 1/4-tone 1: 1 34/33 51.682 cents 1: 1 88/85 60.049 cents 1: 1 27/26 65.337 cents tridecimal comma 1: 1 26/25 67.900 cents tridecimal 1/3-tone 1: 2 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 28/27 62.961 cents Archytas' 1/3-tone 2: 1 26/25 67.900 cents tridecimal 1/3-tone 2: 1 68/65 78.114 cents Valentine semitone 2: 1 22/21 80.537 cents undecimal minor semitone 2: 1 55/52 97.104 cents 2: 3 18/17 98.955 cents Arabic lute index finger 2: 1 35/33 101.867 cents 2: 2 17/16 104.955 cents 17th harmonic 2: 1 16/15 111.731 cents minor diatonic semitone 2: 1 15/14 119.443 cents major diatonic semitone 2: 1 14/13 128.298 cents 2/3-tone 2: 2 13/12 138.573 cents tridecimal 2/3-tone 2: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 10/9 182.404 cents minor whole tone 2: 1 8/7 231.174 cents septimal whole tone 3: 1 17/16 104.955 cents 17th harmonic 3: 1 15/14 119.443 cents major diatonic semitone 3: 2 14/13 128.298 cents 2/3-tone 3: 1 55/51 130.721 cents 3: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 3: 1 13/12 138.573 cents tridecimal 2/3-tone 3: 1 85/78 148.786 cents 3: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 3: 1 75/68 169.627 cents 3: 2 10/9 182.404 cents minor whole tone 3: 1 39/35 187.343 cents 3: 1 28/25 196.198 cents middle second 3: 1 96/85 210.686 cents 3: 1 17/15 216.687 cents septendecimal whole tone 3: 1 25/22 221.309 cents undecimal acute whole tone 3: 1 65/56 258.015 cents 3: 1 64/55 262.368 cents 4: 1 35/32 155.140 cents septimal neutral second 4: 1 56/51 161.915 cents 4: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 4: 1 72/65 177.069 cents 4: 2 9/8 203.910 cents major whole tone 4: 1 44/39 208.835 cents 4: 2 17/15 216.687 cents septendecimal whole tone 4: 1 25/22 221.309 cents undecimal acute whole tone 4: 2 8/7 231.174 cents septimal whole tone 4: 1 39/34 237.527 cents 4: 1 15/13 247.741 cents tridecimal 5/4-tone 4: 1 52/45 250.304 cents 4: 1 51/44 255.592 cents 4: 1 7/6 266.871 cents septimal minor third 4: 1 20/17 281.358 cents septendecimal augmented second 4: 1 33/28 284.447 cents undecimal minor third 4: 1 13/11 289.210 cents tridecimal minor third 4: 1 32/27 294.135 cents Pythagorean minor third 5: 1 28/25 196.198 cents middle second 5: 1 9/8 203.910 cents major whole tone 5: 1 55/48 235.677 cents undecimal semi-augmented whole tone 5: 2 15/13 247.741 cents tridecimal 5/4-tone 5: 1 7/6 266.871 cents septimal minor third 5: 1 88/75 276.736 cents 5: 2 20/17 281.358 cents septendecimal augmented second 5: 1 85/72 287.359 cents septendecimal minor third 5: 2 13/11 289.210 cents tridecimal minor third 5: 1 25/21 301.847 cents BP second, quasi-equal minor third 5: 5 6/5 315.641 cents minor third 5: 1 65/54 320.976 cents 5: 1 17/14 336.130 cents supraminor third 5: 1 16/13 359.472 cents tridecimal neutral third 6: 1 7/6 266.871 cents septimal minor third 6: 1 75/64 274.582 cents classic augmented second 6: 4 6/5 315.641 cents minor third 6: 1 40/33 333.041 cents 6: 2 17/14 336.130 cents supraminor third 6: 3 11/9 347.408 cents undecimal neutral third 6: 1 104/85 349.259 cents 6: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 6: 1 16/13 359.472 cents tridecimal neutral third 6: 1 21/17 365.825 cents submajor third 6: 1 68/55 367.324 cents 6: 3 5/4 386.314 cents major third 6: 1 64/51 393.090 cents 7: 1 39/32 342.483 cents 39th harmonic, Zalzal wosta of Ibn Sina 7: 1 16/13 359.472 cents tridecimal neutral third 7: 1 26/21 369.747 cents 7: 1 56/45 378.602 cents septimal narrow major third 7: 5 5/4 386.314 cents major third 7: 1 44/35 396.178 cents 7: 1 34/27 399.090 cents septendecimal major third 7: 1 33/26 412.745 cents tridecimal major third 7: 1 108/85 414.596 cents 7: 2 14/11 417.508 cents undecimal diminished fourth or major third 7: 1 65/51 419.931 cents 7: 1 51/40 420.597 cents septendecimal diminished fourth 7: 2 32/25 427.373 cents classic diminished fourth 7: 1 50/39 430.145 cents 7: 1 9/7 435.084 cents septimal major third, BP third 8: 1 5/4 386.314 cents major third 8: 1 14/11 417.508 cents undecimal diminished fourth or major third 8: 2 9/7 435.084 cents septimal major third, BP third 8: 1 85/66 437.996 cents 8: 1 84/65 443.940 cents 8: 3 22/17 446.363 cents 8: 1 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 8: 3 13/10 454.214 cents tridecimal semi-diminished fourth 8: 2 17/13 464.428 cents 8: 1 72/55 466.278 cents undecimal semi-diminished fourth 8: 4 4/3 498.045 cents perfect fourth 8: 1 75/56 505.757 cents marvelous fourth 9: 1 17/13 464.428 cents 9: 1 55/42 466.851 cents 9: 1 21/16 470.781 cents narrow fourth 9: 1 112/85 477.557 cents 9: 1 33/25 480.646 cents 2 pentatones 9: 1 45/34 485.268 cents 9: 5 4/3 498.045 cents perfect fourth 9: 1 35/26 514.612 cents 9: 1 27/20 519.551 cents acute fourth 9: 1 65/48 524.886 cents 9: 1 34/25 532.328 cents 9: 2 15/11 536.951 cents undecimal augmented fourth 9: 1 48/35 546.815 cents septimal semi-augmented fourth 9: 1 25/18 568.717 cents classic augmented fourth 9: 1 39/28 573.657 cents 9: 1 64/45 609.776 cents 2nd tritone 10: 1 85/64 491.269 cents 10: 1 4/3 498.045 cents perfect fourth 10: 1 88/65 524.477 cents 10: 1 34/25 532.328 cents 10: 1 15/11 536.951 cents undecimal augmented fourth 10: 1 70/51 548.229 cents 10: 2 11/8 551.318 cents undecimal semi-augmented fourth 10: 2 18/13 563.382 cents tridecimal augmented fourth 10: 1 104/75 565.945 cents 10: 1 25/18 568.717 cents classic augmented fourth 10: 1 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 10: 2 24/17 597.000 cents 1st septendecimal tritone 10: 1 17/12 603.000 cents 2nd septendecimal tritone 10: 1 78/55 604.851 cents 10: 2 10/7 617.488 cents Euler's tritone 10: 1 13/9 636.618 cents tridecimal diminished fifth 10: 1 16/11 648.682 cents undecimal semi-diminished fifth 11: 1 11/8 551.318 cents undecimal semi-augmented fourth 11: 1 18/13 563.382 cents tridecimal augmented fourth 11: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 11: 1 55/39 595.149 cents 11: 1 24/17 597.000 cents 1st septendecimal tritone 11: 2 17/12 603.000 cents 2nd septendecimal tritone 11: 1 10/7 617.488 cents Euler's tritone 11: 1 36/25 631.283 cents classic diminished fifth 11: 1 75/52 634.055 cents 11: 2 13/9 636.618 cents tridecimal diminished fifth 11: 2 16/11 648.682 cents undecimal semi-diminished fifth 11: 1 51/35 651.771 cents 11: 1 22/15 663.049 cents undecimal diminished fifth 11: 1 25/17 667.672 cents 11: 1 65/44 675.523 cents 11: 1 3/2 701.955 cents perfect fifth 11: 1 128/85 708.731 cents 12: 1 45/32 590.224 cents diatonic tritone 12: 1 56/39 626.343 cents 12: 1 36/25 631.283 cents classic diminished fifth 12: 1 35/24 653.185 cents septimal semi-diminished fifth 12: 2 22/15 663.049 cents undecimal diminished fifth 12: 1 25/17 667.672 cents 12: 1 96/65 675.114 cents 12: 1 40/27 680.449 cents grave fifth 12: 1 52/35 685.388 cents 12: 5 3/2 701.955 cents perfect fifth 12: 1 68/45 714.732 cents 12: 1 50/33 719.354 cents 3 pentatones 12: 1 85/56 722.443 cents 12: 1 32/21 729.219 cents wide fifth 12: 1 84/55 733.149 cents 12: 1 26/17 735.572 cents 13: 1 112/75 694.243 cents marvelous fifth 13: 4 3/2 701.955 cents perfect fifth 13: 1 55/36 733.722 cents undecimal semi-augmented fifth 13: 2 26/17 735.572 cents 13: 3 20/13 745.786 cents tridecimal semi-augmented fifth 13: 1 54/35 750.725 cents septimal semi-augmented fifth 13: 3 17/11 753.637 cents 13: 1 65/42 756.060 cents 13: 1 132/85 762.004 cents 13: 2 14/9 764.916 cents septimal minor sixth 13: 1 11/7 782.492 cents undecimal augmented fifth 13: 1 8/5 813.686 cents minor sixth 14: 1 14/9 764.916 cents septimal minor sixth 14: 1 39/25 769.855 cents 14: 2 25/16 772.627 cents classic augmented fifth 14: 1 80/51 779.403 cents 14: 1 102/65 780.069 cents 14: 2 11/7 782.492 cents undecimal augmented fifth 14: 1 85/54 785.404 cents 14: 1 52/33 787.255 cents tridecimal minor sixth 14: 1 27/17 800.910 cents septendecimal minor sixth 14: 1 35/22 803.822 cents 14: 5 8/5 813.686 cents minor sixth 14: 1 45/28 821.398 cents septimale wide minor sixth 14: 1 21/13 830.253 cents 14: 1 13/8 840.528 cents tridecimal neutral sixth 14: 1 64/39 857.517 cents 39th subharmonic 15: 1 51/32 806.910 cents 15: 3 8/5 813.686 cents minor sixth 15: 1 55/34 832.676 cents 15: 1 34/21 834.175 cents supraminor sixth 15: 1 13/8 840.528 cents tridecimal neutral sixth 15: 1 44/27 845.453 cents neutral sixth 15: 1 85/52 850.741 cents 15: 3 18/11 852.592 cents undecimal neutral sixth 15: 2 28/17 863.870 cents submajor sixth 15: 1 33/20 866.959 cents 15: 4 5/3 884.359 cents major sixth, BP sixth 15: 1 128/75 925.418 cents diminished seventh 15: 1 12/7 933.129 cents septimal major sixth 16: 1 13/8 840.528 cents tridecimal neutral sixth 16: 1 28/17 863.870 cents submajor sixth 16: 1 108/65 879.024 cents 16: 5 5/3 884.359 cents major sixth, BP sixth 16: 1 42/25 898.153 cents quasi-equal major sixth 16: 2 22/13 910.790 cents tridecimal major sixth 16: 1 144/85 912.641 cents 16: 2 17/10 918.642 cents septendecimal diminished seventh 16: 1 75/44 923.264 cents 16: 1 12/7 933.129 cents septimal major sixth 16: 2 26/15 952.259 cents tridecimal semi-augmented sixth 16: 1 96/55 964.323 cents 16: 1 16/9 996.090 cents Pythagorean minor seventh 16: 1 25/14 1003.802 cents middle minor seventh 17: 1 27/16 905.865 cents Pythagorean major sixth 17: 1 22/13 910.790 cents tridecimal major sixth 17: 1 56/33 915.553 cents 17: 1 17/10 918.642 cents septendecimal diminished seventh 17: 1 12/7 933.129 cents septimal major sixth 17: 1 88/51 944.408 cents 17: 1 45/26 949.696 cents 17: 1 26/15 952.259 cents tridecimal semi-augmented sixth 17: 1 68/39 962.473 cents 17: 2 7/4 968.826 cents harmonic seventh 17: 1 44/25 978.691 cents undecimal grave minor seventh 17: 2 30/17 983.313 cents septendecimal minor seventh 17: 1 39/22 991.165 cents 17: 2 16/9 996.090 cents Pythagorean minor seventh 17: 1 65/36 1022.931 cents 17: 1 20/11 1034.996 cents large minor seventh 17: 1 51/28 1038.085 cents 17: 1 64/35 1044.860 cents septimal neutral seventh 18: 1 55/32 937.632 cents 18: 1 112/65 941.985 cents 18: 1 44/25 978.691 cents undecimal grave minor seventh 18: 1 30/17 983.313 cents septendecimal minor seventh 18: 1 85/48 989.314 cents 18: 1 25/14 1003.802 cents middle minor seventh 18: 1 70/39 1012.657 cents 18: 2 9/5 1017.596 cents just minor seventh, BP seventh 18: 1 136/75 1030.373 cents 18: 2 20/11 1034.996 cents large minor seventh 18: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 18: 1 156/85 1051.214 cents 18: 1 24/13 1061.427 cents tridecimal neutral seventh 18: 1 50/27 1066.762 cents grave major seventh 18: 1 102/55 1069.279 cents 18: 2 13/7 1071.702 cents 16/3-tone 18: 1 28/15 1080.557 cents grave major seventh 18: 1 32/17 1095.045 cents 17th subharmonic 19: 1 7/4 968.826 cents harmonic seventh 19: 1 9/5 1017.596 cents just minor seventh, BP seventh 19: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 19: 2 24/13 1061.427 cents tridecimal neutral seventh 19: 1 13/7 1071.702 cents 16/3-tone 19: 1 28/15 1080.557 cents grave major seventh 19: 1 15/8 1088.269 cents classic major seventh 19: 2 32/17 1095.045 cents 17th subharmonic 19: 1 66/35 1098.133 cents 19: 3 17/9 1101.045 cents septendecimal major seventh 19: 1 104/55 1102.896 cents 19: 1 21/11 1119.463 cents undecimal major seventh 19: 1 65/34 1121.886 cents 19: 1 25/13 1132.100 cents 19: 1 27/14 1137.039 cents septimal major seventh 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: 2 48/25 1129.328 cents classic diminished octave 20: 1 25/13 1132.100 cents 20: 1 52/27 1134.663 cents 20: 1 85/44 1139.951 cents 20: 1 33/17 1148.318 cents 20: 1 68/35 1149.816 cents 23/4-tone 20: 1 35/18 1151.230 cents septimal semi-diminished octave 20: 1 39/20 1156.169 cents 20: 1 88/45 1161.094 cents 20: 1 100/51 1165.717 cents 20: 1 51/26 1166.383 cents 20: 1 108/55 1168.233 cents 20: 1 55/28 1168.806 cents 20: 1 128/65 1173.159 cents 20: 1 65/33 1173.568 cents 20: 1 168/85 1179.512 cents Highest number of different intervals for one interval class: 19 Average number of different intervals per interval class: 15.80000 = 79/5
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 : 26.8 53.3 105.0 155.1 203.9 274.6 342.5 386.3 470.8 491.3 551.3 590.2 702.0 772.6 806.9 840.5 905.9 937.6 968.8 1088.3 1200.0 26.8 : 26.4 78.1 128.3 177.1 247.7 315.6 359.5 443.9 464.4 524.5 563.4 675.1 745.8 780.1 813.7 879.0 910.8 942.0 1061.4 1173.2 1200.0 53.3 : 51.7 101.9 150.6 221.3 289.2 333.0 417.5 438.0 498.0 537.0 648.7 719.4 753.6 787.3 852.6 884.4 915.6 1035.0 1146.7 1173.6 1200.0 105.0 : 50.2 99.0 169.6 237.5 281.4 365.8 386.3 446.4 485.3 597.0 667.7 702.0 735.6 800.9 832.7 863.9 983.3 1095.0 1121.9 1148.3 1200.0 155.1 : 48.8 119.4 187.3 231.2 315.6 336.1 396.2 435.1 546.8 617.5 651.8 685.4 750.7 782.5 813.7 933.1 1044.9 1071.7 1098.1 1149.8 1200.0 203.9 : 70.7 138.6 182.4 266.9 287.4 347.4 386.3 498.0 568.7 603.0 636.6 702.0 733.7 764.9 884.4 996.1 1022.9 1049.4 1101.0 1151.2 1200.0 274.6 : 67.9 111.7 196.2 216.7 276.7 315.6 427.4 498.0 532.3 565.9 631.3 663.0 694.2 813.7 925.4 952.3 978.7 1030.4 1080.6 1129.3 1200.0 342.5 : 43.8 128.3 148.8 208.8 247.7 359.5 430.1 464.4 498.0 563.4 595.1 626.3 745.8 857.5 884.4 910.8 962.5 1012.7 1061.4 1132.1 1200.0 386.3 : 84.5 105.0 165.0 203.9 315.6 386.3 420.6 454.2 519.6 551.3 582.5 702.0 813.7 840.5 867.0 918.6 968.8 1017.6 1088.3 1156.2 1200.0 470.8 : 20.5 80.5 119.4 231.2 301.8 336.1 369.7 435.1 466.9 498.0 617.5 729.2 756.1 782.5 834.2 884.4 933.1 1003.8 1071.7 1115.5 1200.0 491.3 : 60.0 99.0 210.7 281.4 315.6 349.3 414.6 446.4 477.6 597.0 708.7 735.6 762.0 813.7 863.9 912.6 983.3 1051.2 1095.0 1179.5 1200.0 551.3 : 38.9 150.6 221.3 255.6 289.2 354.5 386.3 417.5 537.0 648.7 675.5 702.0 753.6 803.8 852.6 923.3 991.2 1035.0 1119.5 1140.0 1200.0 590.2 : 111.7 182.4 216.7 250.3 315.6 347.4 378.6 498.0 609.8 636.6 663.0 714.7 764.9 813.7 884.4 952.3 996.1 1080.6 1101.0 1161.1 1200.0 702.0 : 70.7 105.0 138.6 203.9 235.7 266.9 386.3 498.0 524.9 551.3 603.0 653.2 702.0 772.6 840.5 884.4 968.8 989.3 1049.4 1088.3 1200.0 772.6 : 34.3 67.9 133.2 165.0 196.2 315.6 427.4 454.2 480.6 532.3 582.5 631.3 702.0 769.9 813.7 898.2 918.6 978.7 1017.6 1129.3 1200.0 806.9 : 33.6 99.0 130.7 161.9 281.4 393.1 419.9 446.4 498.0 548.2 597.0 667.7 735.6 779.4 863.9 884.4 944.4 983.3 1095.0 1165.7 1200.0 840.5 : 65.3 97.1 128.3 247.7 359.5 386.3 412.7 464.4 514.6 563.4 634.1 702.0 745.8 830.3 850.7 910.8 949.7 1061.4 1132.1 1166.4 1200.0 905.9 : 31.8 63.0 182.4 294.1 321.0 347.4 399.1 449.3 498.0 568.7 636.6 680.4 764.9 785.4 845.5 884.4 996.1 1066.8 1101.0 1134.7 1200.0 937.6 : 31.2 150.6 262.4 289.2 315.6 367.3 417.5 466.3 537.0 604.9 648.7 733.1 753.6 813.7 852.6 964.3 1035.0 1069.3 1102.9 1168.2 1200.0 968.8 : 119.4 231.2 258.0 284.4 336.1 386.3 435.1 505.8 573.7 617.5 702.0 722.4 782.5 821.4 933.1 1003.8 1038.1 1071.7 1137.0 1168.8 1200.0 1088.3: 111.7 138.6 165.0 216.7 266.9 315.6 386.3 454.2 498.0 582.5 603.0 663.0 702.0 813.7 884.4 918.6 952.3 1017.6 1049.4 1080.6 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 20.4882 .. 119.4428 cents 18/17, 98.9546 cents 85/84, 20.4882 cents 2: 53.2729 .. 231.1741 cents 256/231, 177.9012 cents 77/80,-66.1699 cents 3: 104.9554 .. 262.3683 cents 1024/935, 157.4129 cents 119/128,-126.2187 cents 4: 155.1396 .. 294.1350 cents 1024/945, 138.9954 cents 1925/2048,-107.2287 cents 5: 196.1985 .. 359.4723 cents 100/91, 163.2739 cents 189/200,-97.9365 cents 6: 266.8709 .. 393.0896 cents 128/119, 126.2187 cents 91/96,-92.6014 cents 7: 342.4827 .. 435.0841 cents 96/91, 92.6014 cents 1989/2048,-50.6069 cents 8: 386.3137 .. 505.7565 cents 15/14, 119.4428 cents 35/36,-48.7704 cents 9: 464.4277 .. 609.7763 cents 832/765, 145.3485 cents 952/975,-41.3288 cents 10: 491.2691 .. 648.6821 cents 1024/935, 157.4129 cents 3825/4096,-118.5072 cents 11: 551.3179 .. 708.7309 cents 1024/935, 157.4129 cents 121/128,-97.3641 cents 12: 590.2237 .. 735.5723 cents 832/765, 145.3485 cents 3825/4096,-118.5072 cents 13: 694.2435 .. 813.6863 cents 15/14, 119.4428 cents 952/975,-41.3288 cents 14: 764.9159 .. 857.5173 cents 96/91, 92.6014 cents 35/36,-48.7704 cents 15: 806.9104 .. 933.1291 cents 128/119, 126.2187 cents 1989/2048,-50.6069 cents 16: 840.5277 .. 1003.8015 cents 100/91, 163.2739 cents 91/96,-92.6014 cents 17: 905.8650 .. 1044.8604 cents 1024/945, 138.9954 cents 189/200,-97.9365 cents 18: 937.6317 .. 1095.0446 cents 1024/935, 157.4129 cents 1925/2048,-107.2287 cents 19: 968.8259 .. 1146.7271 cents 256/231, 177.9012 cents 119/128,-126.2187 cents 20: 1080.5572 .. 1179.5118 cents 18/17, 98.9546 cents 77/80,-66.1699 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 85/84, 20.4882 cents, class 1 Average step (divided formal octave): 57.1429 cents Largest one step interval : 15/14, 119.4428 cents Average / Smallest step : 2.789060 Largest / Average step : 2.090249 Largest / Smallest step : 5.829830 Median interval of one step : 35/34, 50.1842 cents, amount: 1 Least squares average step : 52.75297 cents, oct.: 1107.81238 cents Scale is not proper Step pattern alph. order: ABCDEFGHIJKLMFNOPQRSM Step pattern size order : CBLKJPOIQAMHRPGFNEDSR Scale is not a Constant Structure Scale diversity : 1.683802 Lumma stability : 0.034147 Lumma impropriety factor : 0.862306 Number of different interval sizes : 240 = 12.00000 / class Number of one step interval sizes : 19 Highest interval variety : 19 Mean interval variety : 15.80000 = 79/5 Median interval variety : 12.5 Lowest interval variety : 12 Smallest interval difference : 4225/4224, 0.4098 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 10 Number of recognisable fifths : 14, average 704.0436 cents Number of appreciable fifths : 12, average 701.8770 cents Length of longest harmonic part : 3 at degree 2 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 1 = 4.7619% Scale is differentially coherent in interval class 1 Scale is differentially coherent in interval class 2 Scale is differentially coherent in interval class 3 Scale is differentially coherent in interval class 4 Scale is differentially coherent in interval class 5 Scale is n-1 differentially coherent in interval class 6 Scale is n-1 differentially coherent in interval class 7 Scale is differentially coherent in interval classes 8 and 9 combined Scale is n-1 differentially coherent in interval class 9 Scale is differentially coherent in interval classes 10 and 11 combined Scale is differentially coherent in interval classes 11 and 12 combined Scale is differentially coherent in interval classes 12 and 13 combined Scale is differentially coherent in interval classes 13 and 14 combined Scale is differentially coherent in interval classes 14 and 15 combined Scale is differentially coherent in interval classes 15 and 16 combined Scale is differentially coherent in interval classes 16 and 17 combined Scale is n-1 differentially coherent in interval classes 18 and 19 combined Scale is n-1 differentially coherent in interval classes 19 and 20 combined -- Rational properties -- Prime limit : 17 Odd number limit : 85 (O: 85 U: 85) Highest odd numerator or denominator: 85 Scale harmonicity : 0.009213 Average absolute harmonicity : 0.111027 Specific harmonicity : 0.073013 Fundamental : 1/64, -6.0000 octaves, 4.0879 Hz. Guide tone : 22972950, 24.4534 octaves, 6010311030.382 Hz. Exponens Consonantiae : 1.470269E+09, 30.45343 octaves Euler's gradus suavitatis : 66 Sum of Mann's harmonic distance : 564.5, average 26.88095 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 27.06102, average 1.28862 Sum of Tenney's harmonic distance : 51.74548, average 2.46407 Vogel's harmonic complexity : 13.66667 Wille's k value : 42 Wilson's harmonic complexity : 67 Rectangular lattice diameter : 9 Triangular lattice diameter : 3 Lattice compactness : 691.56131, average 2.99377 Lattice compactness (without 2's) : 399.99750, average 1.73159 Number of different primes : 7 Prime exponents' range, average, count, tones@limit: 2: -6 .. 1 -3.80952 82 1 3: 0 .. 3 0.66667 14 3 5: 0 .. 2 0.52381 11 5 7: 0 .. 1 0.14286 3 3 11: 0 .. 1 0.14286 3 3 13: 0 .. 1 0.14286 3 3 17: 0 .. 1 0.14286 3 3 Average exponent except 2's : 37 / 21 = 1.76190 Average absolute exponent except 2's: 37 / 21 = 1.76190
FIT/MODE
21: 1 0 1 1 1 1 1 1 1 1 1 0 2 2 0 1 1 1 0 2 2 N SD: 17.2404 c. M:-33.7969 c. 22: 1 0 1 1 1 1 1 1 2 0 1 1 2 1 1 0 2 0 1 2 2 N SD: 12.6338 c. M:-27.7041 c. 24: 0 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 0 3 2 N SD: 13.0633 c. M: 26.8414 c. 27: 1 0 1 1 2 1 2 1 2 0 1 1 3 1 1 1 1 1 1 2 3 N SD: 13.7692 c. M: 21.8063 c. 28: 1 0 1 2 1 1 2 1 2 0 2 1 2 2 1 1 1 1 1 2 3 N SD: 12.2719 c. M: 19.8406 c. 31: 1 0 2 1 1 2 2 1 2 1 1 1 3 2 1 1 1 1 1 3 3 N SD: 8.5074 c. M: 15.5424 c. 36: 1 1 1 2 1 2 2 2 2 1 2 1 3 2 1 1 2 1 1 4 3 N SD: 8.4128 c. M:-15.3487 c. 37: 1 1 1 2 1 3 2 1 3 0 2 1 4 2 1 1 2 1 1 4 3 N SD: 8.7595 c. M:-17.3095 c. 40: 1 1 1 2 2 2 2 2 3 0 2 2 3 3 1 1 2 1 1 4 4 N SD: 8.2070 c. M: 14.9554 c. 41: 1 1 2 1 2 2 3 1 3 1 2 1 4 2 2 1 2 1 1 4 4 N SD: 6.8643 c. M:-12.6018 c. 43: 1 1 2 2 1 3 2 2 3 1 2 1 4 3 1 1 3 1 1 4 4 N SD: 7.2391 c. M:-15.0652 c. 46: 1 1 2 2 2 3 2 2 3 1 2 2 4 3 1 1 3 1 1 5 4 N SD: 5.3787 c. M:-12.3741 c. 52: 1 1 3 2 2 3 3 2 3 1 3 2 4 3 2 1 3 2 1 5 5 N SD: 6.7182 c. M: 11.0890 c. 53: 1 1 3 2 2 3 3 2 4 1 2 2 5 3 2 1 3 1 2 5 5 N SD: 4.9179 c. M: 9.3298 c. 61: 1 2 2 3 2 4 3 3 4 1 3 2 6 3 2 2 3 2 1 6 6 N SD: 4.9237 c. M: 8.0564 c. 65: 2 1 3 3 2 4 4 2 5 1 3 2 6 4 2 2 3 2 2 6 6 N SD: 5.7925 c. M:-11.0142 c. 69: 2 1 3 3 3 4 4 2 5 1 4 2 6 4 2 2 4 2 2 7 6 N SD: 4.6492 c. M:-7.9412 c. 73: 2 1 3 3 3 5 4 3 5 1 4 2 7 4 2 2 4 2 2 7 7 N SD: 4.5339 c. M:-8.2068 c. 74: 2 1 4 3 3 4 4 3 5 1 4 2 7 5 2 2 4 2 2 7 7 N SD: 4.4287 c. M:-8.5581 c. 77: 2 1 4 3 3 5 4 3 5 2 3 3 7 5 2 2 4 2 2 8 7 N SD: 3.8554 c. M:-7.4322 c. 78: 2 1 4 3 3 5 4 3 6 1 4 2 8 4 2 3 4 2 2 8 7 N SD: 4.0007 c. M: 7.1191 c. 82: 2 2 3 4 3 5 4 3 6 2 4 2 8 5 2 2 5 2 2 8 8 N SD: 4.0381 c. M: 6.3813 c. 83: 2 2 3 4 3 5 5 3 6 1 4 3 8 5 2 2 5 2 2 8 8 N SD: 3.8248 c. M:-8.0955 c. 84: 2 2 3 4 3 5 5 3 6 1 5 2 8 5 2 3 4 3 2 8 8 N SD: 3.7242 c. M: 6.9104 c. 87: 2 2 4 3 4 5 5 3 6 2 4 3 8 5 3 2 5 2 2 9 8 N SD: 2.9601 c. M:-6.8827 c. 91: 2 2 4 4 3 6 5 3 7 1 5 3 8 6 2 3 5 2 2 10 8 N SD: 3.5432 c. M:-6.2368 c. 92: 2 2 4 4 4 5 5 4 6 2 4 3 9 5 3 2 5 3 2 9 9 N SD: 3.3814 c. M: 5.8650 c. 93: 2 2 4 4 4 5 6 3 6 2 5 3 8 6 3 2 5 3 2 9 9 N SD: 3.3807 c. M: 6.2648 c. 94: 2 2 4 4 4 5 6 3 7 1 5 3 9 5 3 3 5 2 3 9 9 N SD: 3.3255 c. M: 6.6700 c. 95: 2 2 4 4 4 6 5 4 6 2 5 3 9 5 3 3 5 2 3 9 9 N SD: 3.3567 c. M:-5.7881 c. 98: 2 2 5 4 4 5 6 4 6 2 5 3 9 6 3 3 5 3 2 10 9 N SD: 3.4632 c. M:-5.5230 c. 100: 2 2 5 4 4 6 5 4 7 2 5 3 9 6 3 3 5 3 3 10 9 N SD: 3.3498 c. M: 6.4827 c. 105: 2 3 4 5 4 6 6 4 7 2 5 4 9 7 3 3 5 3 3 10 10 N SD: 3.1612 c. M:-5.1866 c. 109: 2 3 5 4 5 6 6 4 8 2 5 4 10 6 3 3 6 3 3 11 10 N SD: 2.9212 c. M:-5.2643 c. 110: 2 3 5 4 5 6 6 4 8 2 6 3 10 7 3 3 6 3 3 11 10 N SD: 2.7866 c. M:-5.0457 c. 114: 3 2 5 5 4 7 7 4 8 2 5 4 11 6 4 3 6 3 3 11 11 N SD: 2.9190 c. M:-4.8858 c. 115: 3 2 5 5 5 6 7 4 8 2 6 4 10 7 3 4 6 3 3 11 11 N SD: 2.6410 c. M:-4.7857 c. 117: 3 2 5 5 5 7 6 5 8 2 6 4 10 7 4 3 6 3 3 12 11 N SD: 2.9925 c. M: 4.7233 c. 118: 3 2 5 5 5 7 7 4 8 2 6 4 11 7 3 4 6 3 3 12 11 N SD: 2.2739 c. M:-3.6671 c. 130: 3 3 5 6 5 8 7 5 9 2 7 4 12 8 3 4 7 4 3 13 12 N SD: 1.9580 c. M:-3.9068 c. 137: 3 3 6 6 5 8 8 5 10 2 7 4 13 8 4 4 7 4 4 13 13 N SD: 1.9188 c. M: 3.6752 c. 140: 3 3 6 6 6 8 8 5 10 2 7 5 13 8 4 4 8 3 4 14 13 N SD: 1.5883 c. M: 3.3459 c. 168: 4 3 8 7 7 9 10 6 12 3 8 6 15 10 5 5 9 4 5 16 16 N SD: 2.0043 c. M: 3.2729 c. 171: 4 4 7 7 7 10 10 6 12 3 9 5 16 10 5 5 9 5 4 17 16 N SD: 1.2905 c. M:-3.0680 c. 181: 4 4 8 7 8 10 11 6 13 3 9 6 17 11 5 5 10 4 5 18 17 N SD: 1.6905 c. M:-3.0632 c. 183: 4 4 8 8 7 11 10 7 13 3 9 6 17 11 5 5 10 5 5 18 17 N SD: 0.9446 c. M:-2.2374 c. 207: 5 4 9 9 8 12 12 8 14 4 10 7 19 12 6 6 11 6 5 21 19 N SD: 1.2919 c. M:-2.1441 c. 217: 5 5 9 9 9 13 12 8 15 4 11 7 20 13 6 6 12 6 5 22 20 N SD: 1.1654 c. M:-2.4605 c. 224: 5 5 10 9 9 13 13 8 16 4 11 7 21 13 7 6 12 6 6 22 21 N SD: 0.9466 c. M:-2.1874 c. 266: 6 6 11 11 11 16 15 10 18 5 13 9 25 15 8 7 15 7 7 26 25 N SD: 1.0772 c. M:-1.8044 c. 270: 6 6 12 11 11 16 15 10 19 5 13 9 25 16 8 7 15 7 7 27 25 N SD: 0.8612 c. M:-2.0642 c. 294: 7 6 13 12 12 17 17 11 20 5 15 10 27 17 9 8 16 8 7 30 27 N SD: 1.0619 c. M:-1.7301 c. 298: 7 6 13 13 12 17 17 11 21 5 15 10 27 18 8 9 16 8 8 29 28 N SD: 1.0246 c. M:-1.9074 c. 301: 7 6 13 13 12 18 17 11 21 5 15 10 28 18 8 9 16 8 8 30 28 N SD: 0.7958 c. M: 1.5948 c. 311: 7 7 13 13 13 18 18 11 22 5 16 10 29 18 9 9 17 8 8 31 29 N SD: 0.6128 c. M: 1.2370 c. 354: 8 8 15 15 14 21 20 13 25 6 18 11 33 21 10 10 19 10 9 35 33 N SD: 0.5733 c. M:-1.3514 c. 388: 9 8 17 16 16 23 22 14 27 7 19 13 36 23 11 11 21 10 10 39 36 N SD: 0.5634 c. M:-0.9937 c. 441: 10 10 19 18 18 26 25 16 31 8 22 14 41 26 13 12 24 12 11 44 41 N SD: 0.6515 c. M:-1.2529 c. 460: 10 10 20 19 19 27 26 17 32 8 23 15 43 27 13 13 25 12 12 46 43 N SD: 0.7663 c. M: 1.2266 c. 461: 10 10 20 20 18 27 27 16 33 8 23 15 43 27 13 13 25 12 12 46 43 N SD: 0.7438 c. M: 1.2636 c. 464: 10 11 20 19 19 27 26 17 33 8 23 15 43 28 13 13 25 13 12 46 43 N SD: 0.7234 c. M:-1.1614 c. 466: 10 11 20 19 19 28 26 17 33 8 23 15 44 27 13 13 26 12 12 47 43 N SD: 0.6697 c. M: 1.0903 c. 472: 11 10 20 20 19 28 27 17 33 8 24 15 44 28 13 14 25 13 12 47 44 N SD: 0.5550 c. M:-1.1247 c. 494: 11 11 21 21 20 29 28 18 35 8 25 16 46 29 14 14 27 13 13 49 46 N SD: 0.2616 c. M: 0.5809 c. 718: 16 16 31 30 29 42 41 26 51 12 36 23 67 42 21 20 39 19 19 71 67 N SD: 0.2823 c. M:-0.5334 c. 742: 17 16 32 31 30 44 42 27 52 13 37 24 69 44 21 21 40 20 19 74 69 N SD: 0.2756 c. M:-0.6519 c. 764: 17 17 33 32 31 45 43 28 54 13 38 25 71 45 22 21 42 20 20 76 71 N SD: 0.2591 c. M:-0.4233 c. 882: 20 19 38 37 36 52 50 32 62 15 44 29 82 52 25 25 48 23 23 88 82 N SD: 0.2078 c. M:-0.3745 c. 1019: 23 22 44 43 41 60 58 37 72 17 51 33 95 60 29 29 55 27 27 101 95 N SD: 0.2202 c. M:-0.3596 c. 1065: 24 23 46 45 43 63 60 39 75 18 53 35 99 63 30 30 58 28 28 106 99 N SD: 0.2033 c. M:-0.3533 c. 1075: 24 24 46 45 44 63 61 39 76 18 54 35 100 63 31 30 59 28 28 107 100 N SD: 0.2068 c. M:-0.5536 c. 1084: 24 24 47 45 44 64 61 40 76 19 54 35 101 64 31 30 59 29 28 108 101 N SD: 0.2006 c. M: 0.4162 c. 1106: 25 24 48 46 45 65 63 40 78 19 55 36 103 65 32 31 60 29 29 110 103 N SD: 0.1833 c. M:-0.3745 c. 1224: 27 27 53 51 50 72 69 45 86 21 61 40 114 72 35 34 67 32 32 122 114 N SD: 0.2049 c. M: 0.3768 c. 1236: 28 27 53 52 50 73 70 45 87 21 62 40 115 73 35 35 67 33 32 123 115 N SD: 0.1537 c. M:-0.3431 c. 1289: 29 28 56 54 52 76 73 47 91 22 64 42 120 76 37 36 70 34 34 128 120 N SD: 0.1735 c. M:-0.3297 c. 1371: 31 30 59 57 56 81 77 50 97 23 69 44 128 81 39 38 75 36 36 136 128 N SD: 0.1992 c. M: 0.3181 c. 1376: 31 30 59 58 56 81 78 50 97 23 69 45 128 81 39 39 75 36 36 137 128 N SD: 0.1670 c. M: 0.3042 c. 1395: 31 31 60 58 57 82 79 51 98 24 70 45 130 82 40 39 76 37 36 139 130 N SD: 0.1309 c. M: 0.3009 c. 1460: 33 32 63 61 59 86 83 53 103 25 73 47 136 86 42 41 79 39 38 145 136 N SD: 0.1745 c. M:-0.2943 c. 1506: 34 33 65 63 61 89 85 55 106 26 75 49 140 89 43 42 82 40 39 150 140 N SD: 0.1945 c. M:-0.3643 c. 1517: 34 33 66 63 62 89 86 55 107 26 76 49 141 90 43 43 82 40 40 151 141 N SD: 0.1853 c. M:-0.3425 c. 1547: 35 34 66 65 63 91 88 56 109 26 78 50 144 91 44 44 84 41 40 154 144 N SD: 0.1800 c. M:-0.3745 c. 1556: 35 34 67 65 63 92 88 57 109 27 78 50 145 92 44 44 85 41 40 155 145 N SD: 0.1696 c. M: 0.3439 c. 1578: 35 35 68 66 64 93 89 58 111 27 79 51 147 93 45 44 86 42 41 157 147 N SD: 0.1084 c. M: 0.2773 c. 1600: 36 35 69 67 65 94 91 58 113 27 80 52 149 94 46 45 87 42 42 159 149 N SD: 0.1246 c. M:-0.2673 c. 1730: 39 38 74 73 70 102 98 63 122 29 87 56 161 102 49 49 94 46 45 172 161 N SD: 0.1459 c. M:-0.2361 c. 1783: 40 39 77 75 72 105 101 65 126 30 89 58 166 105 51 50 97 47 47 177 166 N SD: 0.1361 c. M:-0.3352 c. 1817: 41 40 78 76 74 107 103 66 128 31 91 59 169 107 52 51 99 48 47 181 169 N SD: 0.1538 c. M:-0.2801 c. 1826: 41 40 79 76 74 108 103 67 128 32 91 59 170 108 52 51 99 49 47 182 170 N SD: 0.1487 c. M:-0.2971 c. 1848: 41 41 80 77 75 109 104 68 130 32 92 60 172 109 53 51 101 49 48 184 172 N SD: 0.1414 c. M:-0.2893 c. 1889: 42 42 81 79 77 111 107 69 133 32 95 61 176 111 54 53 103 50 49 188 176 N SD: 0.1039 c. M: 0.2157 c. 1966: 44 43 85 82 80 116 111 72 138 34 98 64 183 116 56 55 107 52 51 196 183 N SD: 0.0906 c. M: 0.1807 c. 2159: 48 48 93 90 88 127 122 79 152 37 108 70 201 127 62 60 118 57 56 215 201 N SD: 0.0779 c. M: 0.1624 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: 7.5162 cents 4 .. 8 match: 4 H SD: 0.0000 cents 5 .. 10 match: 5 H SD: 11.3215 cents 6 .. 12 match: 6 H SD: 7.6040 cents 7 .. 14 match: 7 H SD: 8.0216 cents 8 .. 16 match: 8 H SD: 0.0000 cents 9 .. 18 match: 9 H SD: 7.1264 cents 10 .. 20 match: 10 H SD: 6.5309 cents 11 .. 22 match: 9 SD: 6.0515 cents 12 .. 24 match: 11 SD: 4.6197 cents 13 .. 26 match: 11 S SD: 5.5063 cents 14 .. 28 match: 13 S SD: 5.7030 cents 15 .. 30 match: 12 SD: 4.8640 cents 16 .. 32 match: 14 S SD: 3.1733 cents 17 .. 34 match: 14 S SD: 4.6251 cents 18 .. 36 match: 15 SD: 4.2860 cents 19 .. 38 match: 15 SD: 4.0171 cents 20 .. 40 match: 16 SD: 4.4469 cents 21 .. 42 match: 16 SD: 4.4124 cents 22 .. 44 match: 18 SD: 3.3902 cents 23 .. 46 match: 16 SD: 3.4518 cents 24 .. 48 match: 16 SD: 2.2589 cents 25 .. 50 match: 18 SD: 3.2901 cents 26 .. 52 match: 18 SD: 3.8243 cents 27 .. 54 match: 18 SD: 3.0623 cents 28 .. 56 match: 18 SD: 3.0332 cents 29 .. 58 match: 20 SD: 2.5789 cents 30 .. 60 match: 20 SD: 2.5837 cents 31 .. 62 match: 19 SD: 2.5331 cents 32 .. 64 match: 20 S SD: 1.5296 cents 33 .. 66 match: 20 SD: 2.3434 cents 34 .. 68 match: 19 SD: 2.2820 cents 35 .. 70 match: 19 SD: 2.0441 cents 36 .. 72 match: 20 SD: 2.3453 cents 37 .. 74 match: 19 SD: 2.3124 cents 38 .. 76 match: 19 SD: 2.6080 cents 39 .. 78 match: 20 SD: 2.1283 cents 40 .. 80 match: 19 SD: 1.8480 cents 41 .. 82 match: 19 SD: 1.9829 cents 42 .. 84 match: 20 SD: 1.7919 cents 43 .. 86 match: 20 SD: 2.1604 cents 44 .. 88 match: 19 SD: 2.1026 cents 45 .. 90 match: 20 SD: 1.6606 cents 46 .. 92 match: 20 SD: 1.6581 cents 47 .. 94 match: 19 SD: 1.7090 cents 50 .. 100 match: 20 SD: 1.7587 cents 51 .. 102 match: 21 SD: 1.4921 cents 53 .. 106 match: 20 SD: 1.6743 cents 54 .. 108 match: 21 SD: 1.3835 cents 56 .. 112 match: 20 SD: 1.4137 cents 57 .. 114 match: 21 SD: 1.3909 cents 59 .. 118 match: 21 SD: 1.3817 cents 61 .. 122 match: 21 SD: 1.2014 cents 63 .. 126 match: 21 SD: 1.1603 cents 64 .. 128 match: 21 SD: 0.0000 cents