Scala analysis: xen11-chalmers-tetrachordal-10-03
Prime-Prime and Inverted-Inverted Heptatonic Diamonds, 27 Tones
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 36/35 48.770381 septimal diesis, 1/4-tone 2: 28/27 62.960904 Archytas' 1/3-tone 3: 16/15 111.731285 minor diatonic semitone 4: 9/8 203.910002 major whole tone 5: 7/6 266.870906 septimal minor third 6: 6/5 315.641287 minor third 7: 5/4 386.313714 major third 8: 9/7 435.084095 septimal major third, BP third 9: 35/27 449.274618 septimal semi-diminished fourth, 9/4-tone 10: 4/3 498.044999 perfect fourth 11: 48/35 546.815381 septimal semi-augmented fourth 12: 112/81 561.005903 13: 45/32 590.223716 diatonic tritone 14: 64/45 609.776284 2nd tritone 15: 81/56 638.994097 16: 35/24 653.184619 septimal semi-diminished fifth 17: 3/2 701.955001 perfect fifth 18: 54/35 750.725382 septimal semi-augmented fifth 19: 14/9 764.915905 septimal minor sixth 20: 8/5 813.686286 minor sixth 21: 5/3 884.358713 major sixth, BP sixth 22: 12/7 933.129094 septimal major sixth 23: 16/9 996.089998 Pythagorean minor seventh 24: 15/8 1088.268715 classic major seventh 25: 27/14 1137.039096 septimal major seventh 26: 35/18 1151.229619 septimal semi-diminished octave 27: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 36/35 48.7704 septimal diesis, 1/4-tone 2: 245/243 14.1905 minor BP diesis, Sensamagic comma 3: 36/35 48.7704 septimal diesis, 1/4-tone 4: 135/128 92.1787 major chroma, major limma 5: 28/27 62.9609 Archytas' 1/3-tone 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 25/24 70.6724 classic chromatic semitone, minor chroma 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 245/243 14.1905 minor BP diesis, Sensamagic comma 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 245/243 14.1905 minor BP diesis, Sensamagic comma 13: 3645/3584 29.2178 14: 2048/2025 19.5526 diaschisma 15: 3645/3584 29.2178 16: 245/243 14.1905 minor BP diesis, Sensamagic comma 17: 36/35 48.7704 septimal diesis, 1/4-tone 18: 36/35 48.7704 septimal diesis, 1/4-tone 19: 245/243 14.1905 minor BP diesis, Sensamagic comma 20: 36/35 48.7704 septimal diesis, 1/4-tone 21: 25/24 70.6724 classic chromatic semitone, minor chroma 22: 36/35 48.7704 septimal diesis, 1/4-tone 23: 28/27 62.9609 Archytas' 1/3-tone 24: 135/128 92.1787 major chroma, major limma 25: 36/35 48.7704 septimal diesis, 1/4-tone 26: 245/243 14.1905 minor BP diesis, Sensamagic comma 27: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 1 2048/2025 19.553 cents diaschisma 1: 2 3645/3584 29.218 cents 1: 12 36/35 48.770 cents septimal diesis, 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 1: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 1: 2 135/128 92.179 cents major chroma, major limma 2: 2 525/512 43.408 cents Avicenna enharmonic diesis 2: 2 36/35 48.770 cents septimal diesis, 1/4-tone 2: 10 28/27 62.961 cents Archytas' 1/3-tone 2: 3 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 16/15 111.731 cents minor diatonic semitone 2: 4 15/14 119.443 cents major diatonic semitone 2: 2 243/224 140.949 cents Archytas' 2/3-tone 2: 2 35/32 155.140 cents septimal neutral second 3: 2 28/27 62.961 cents Archytas' 1/3-tone 3: 1 6561/6272 77.988 cents 3: 2 135/128 92.179 cents major chroma, major limma 3: 10 16/15 111.731 cents minor diatonic semitone 3: 2 175/162 133.633 cents 3: 2 35/32 155.140 cents septimal neutral second 3: 2 54/49 168.213 cents Zalzal's mujannab 3: 2 10/9 182.404 cents minor whole tone 3: 4 9/8 203.910 cents major whole tone 4: 2 135/128 92.179 cents major chroma, major limma 4: 2 16/15 111.731 cents minor diatonic semitone 4: 3 784/729 125.922 cents two (Archytas' 1/3-tone) 4: 2 243/224 140.949 cents Archytas' 2/3-tone 4: 4 192/175 160.502 cents septimal 4/5-tone 4: 4 10/9 182.404 cents minor whole tone 4: 2 9/8 203.910 cents major whole tone 4: 2 245/216 218.101 cents 4: 2 8/7 231.174 cents septimal whole tone 4: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 4: 2 75/64 274.582 cents classic augmented second 5: 1 1225/1152 106.369 cents 5: 2 243/224 140.949 cents Archytas' 2/3-tone 5: 2 35/32 155.140 cents septimal neutral second 5: 2 192/175 160.502 cents septimal 4/5-tone 5: 4 448/405 174.692 cents 5: 4 8/7 231.174 cents septimal whole tone 5: 2 280/243 245.365 cents 5: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 5: 4 7/6 266.871 cents septimal minor third 5: 4 135/112 323.353 cents septimal wide minor third 6: 2 35/32 155.140 cents septimal neutral second 6: 2 448/405 174.692 cents 6: 2 2187/1960 189.719 cents 6: 2 9/8 203.910 cents major whole tone 6: 1 256/225 223.463 cents Neapolitan diminished third 6: 2 280/243 245.365 cents 6: 2 7/6 266.871 cents septimal minor third 6: 2 288/245 279.944 cents 6: 2 32/27 294.135 cents Pythagorean minor third 6: 4 6/5 315.641 cents minor third 6: 4 175/144 337.543 cents 6: 2 243/196 372.123 cents 7: 5 9/8 203.910 cents major whole tone 7: 2 256/225 223.463 cents Neapolitan diminished third 7: 2 75/64 274.582 cents classic augmented second 7: 2 32/27 294.135 cents Pythagorean minor third 7: 2 6/5 315.641 cents minor third 7: 2 98/81 329.832 cents 7: 2 128/105 342.905 cents septimal neutral third 7: 2 216/175 364.412 cents 7: 8 5/4 386.314 cents major third 8: 2 245/216 218.101 cents 8: 4 81/70 252.680 cents Al-Hwarizmi's lute middle finger 8: 2 32/27 294.135 cents Pythagorean minor third 8: 2 135/112 323.353 cents septimal wide minor third 8: 2 896/729 357.096 cents 8: 4 56/45 378.602 cents septimal narrow major third 8: 2 1225/972 400.504 cents 8: 1 81/64 407.820 cents Pythagorean major third 8: 8 9/7 435.084 cents septimal major third, BP third 9: 4 7/6 266.871 cents septimal minor third 9: 1 1458/1225 301.451 cents 9: 2 135/112 323.353 cents septimal wide minor third 9: 2 128/105 342.905 cents septimal neutral third 9: 2 5/4 386.314 cents major third 9: 2 32/25 427.373 cents classic diminished fourth 9: 8 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 9: 2 21/16 470.781 cents narrow fourth 9: 4 324/245 483.854 cents 10: 4 6/5 315.641 cents minor third 10: 2 175/144 337.543 cents 10: 2 243/196 372.123 cents 10: 2 512/405 405.866 cents narrow diminished fourth 10: 2 675/512 478.492 cents wide augmented third 10: 12 4/3 498.045 cents perfect fourth 10: 2 27/20 519.551 cents acute fourth 10: 1 49/36 533.742 cents Arabic lute acute fourth 11: 1 98/81 329.832 cents 11: 2 216/175 364.412 cents 11: 4 5/4 386.314 cents major third 11: 2 9/7 435.084 cents septimal major third, BP third 11: 2 4/3 498.045 cents perfect fourth 11: 4 980/729 512.236 cents 11: 2 1215/896 527.263 cents 11: 6 48/35 546.815 cents septimal semi-augmented fourth 11: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 11: 2 45/32 590.224 cents diatonic tritone 12: 2 56/45 378.602 cents septimal narrow major third 12: 4 9/7 435.084 cents septimal major third, BP third 12: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 12: 2 1215/896 527.263 cents 12: 2 175/128 541.453 cents 12: 2 48/35 546.815 cents septimal semi-augmented fourth 12: 6 112/81 561.006 cents 12: 2 1728/1225 595.586 cents 12: 1 36/25 631.283 cents classic diminished fifth 12: 2 81/56 638.994 cents 12: 2 35/24 653.185 cents septimal semi-diminished fifth 13: 1 32/25 427.373 cents classic diminished fourth 13: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 13: 2 324/245 483.854 cents 13: 2 4/3 498.045 cents perfect fourth 13: 2 175/128 541.453 cents 13: 2 112/81 561.006 cents 13: 2 2187/1568 576.033 cents 13: 2 45/32 590.224 cents diatonic tritone 13: 6 64/45 609.776 cents 2nd tritone 13: 2 35/24 653.185 cents septimal semi-diminished fifth 13: 4 3/2 701.955 cents perfect fifth 14: 4 4/3 498.045 cents perfect fourth 14: 2 48/35 546.815 cents septimal semi-augmented fourth 14: 6 45/32 590.224 cents diatonic tritone 14: 2 64/45 609.776 cents 2nd tritone 14: 2 3136/2187 623.967 cents 14: 2 81/56 638.994 cents 14: 2 256/175 658.547 cents 14: 2 3/2 701.955 cents perfect fifth 14: 2 245/162 716.146 cents 14: 2 54/35 750.725 cents septimal semi-augmented fifth 14: 1 25/16 772.627 cents classic augmented fifth 15: 2 48/35 546.815 cents septimal semi-augmented fourth 15: 2 112/81 561.006 cents 15: 1 25/18 568.717 cents classic augmented fourth 15: 2 1225/864 604.414 cents 15: 6 81/56 638.994 cents 15: 2 35/24 653.185 cents septimal semi-diminished fifth 15: 2 256/175 658.547 cents 15: 2 1792/1215 672.737 cents 15: 2 54/35 750.725 cents septimal semi-augmented fifth 15: 4 14/9 764.916 cents septimal minor sixth 15: 2 45/28 821.398 cents septimale wide minor sixth 16: 2 64/45 609.776 cents 2nd tritone 16: 2 10/7 617.488 cents Euler's tritone 16: 6 35/24 653.185 cents septimal semi-diminished fifth 16: 2 1792/1215 672.737 cents 16: 4 729/490 687.764 cents 16: 2 3/2 701.955 cents perfect fifth 16: 2 14/9 764.916 cents septimal minor sixth 16: 4 8/5 813.686 cents minor sixth 16: 2 175/108 835.588 cents 16: 1 81/49 870.168 cents two (septimal major third, BP third) 17: 1 72/49 666.258 cents Arabic lute grave fifth 17: 2 40/27 680.449 cents grave fifth 17: 12 3/2 701.955 cents perfect fifth 17: 2 1024/675 721.508 cents narrow diminished sixth 17: 2 405/256 794.134 cents wide augmented fifth 17: 2 392/243 827.877 cents 17: 2 288/175 862.457 cents 17: 4 5/3 884.359 cents major sixth, BP sixth 18: 4 245/162 716.146 cents 18: 2 32/21 729.219 cents wide fifth 18: 8 54/35 750.725 cents septimal semi-augmented fifth 18: 2 25/16 772.627 cents classic augmented fifth 18: 2 8/5 813.686 cents minor sixth 18: 2 105/64 857.095 cents septimal neutral sixth 18: 2 224/135 876.647 cents narrow septimal major sixth 18: 1 1225/729 898.549 cents two (septimal semi-diminished fourth, 9/4-tone) 18: 4 12/7 933.129 cents septimal major sixth 19: 8 14/9 764.916 cents septimal minor sixth 19: 1 128/81 792.180 cents Pythagorean minor sixth 19: 2 1944/1225 799.496 cents 19: 4 45/28 821.398 cents septimale wide minor sixth 19: 2 729/448 842.904 cents 19: 2 224/135 876.647 cents narrow septimal major sixth 19: 2 27/16 905.865 cents Pythagorean major sixth 19: 4 140/81 947.320 cents 19: 2 432/245 981.899 cents 20: 8 8/5 813.686 cents minor sixth 20: 2 175/108 835.588 cents 20: 2 105/64 857.095 cents septimal neutral sixth 20: 2 81/49 870.168 cents two (septimal major third, BP third) 20: 2 5/3 884.359 cents major sixth, BP sixth 20: 2 27/16 905.865 cents Pythagorean major sixth 20: 2 128/75 925.418 cents diminished seventh 20: 2 225/128 976.537 cents augmented sixth 20: 5 16/9 996.090 cents Pythagorean minor seventh 21: 2 392/243 827.877 cents 21: 4 288/175 862.457 cents 21: 4 5/3 884.359 cents major sixth, BP sixth 21: 2 27/16 905.865 cents Pythagorean major sixth 21: 2 245/144 920.056 cents 21: 2 12/7 933.129 cents septimal major sixth 21: 2 243/140 954.635 cents 21: 1 225/128 976.537 cents augmented sixth 21: 2 16/9 996.090 cents Pythagorean minor seventh 21: 2 3920/2187 1010.281 cents 21: 2 405/224 1025.308 cents 21: 2 64/35 1044.860 cents septimal neutral seventh 22: 4 224/135 876.647 cents narrow septimal major sixth 22: 4 12/7 933.129 cents septimal major sixth 22: 2 140/81 947.320 cents 22: 2 243/140 954.635 cents 22: 4 7/4 968.826 cents harmonic seventh 22: 4 405/224 1025.308 cents 22: 2 175/96 1039.498 cents 22: 2 64/35 1044.860 cents septimal neutral seventh 22: 2 448/243 1059.051 cents 22: 1 2304/1225 1093.631 cents two (septimal semi-augmented fourth) 23: 2 128/75 925.418 cents diminished seventh 23: 2 140/81 947.320 cents 23: 2 7/4 968.826 cents harmonic seventh 23: 2 432/245 981.899 cents 23: 2 16/9 996.090 cents Pythagorean minor seventh 23: 4 9/5 1017.596 cents just minor seventh, BP seventh 23: 4 175/96 1039.498 cents 23: 2 448/243 1059.051 cents 23: 3 729/392 1074.078 cents 23: 2 15/8 1088.269 cents classic major seventh 23: 2 256/135 1107.821 cents octave - major chroma 24: 4 16/9 996.090 cents Pythagorean minor seventh 24: 2 9/5 1017.596 cents just minor seventh, BP seventh 24: 2 49/27 1031.787 cents 24: 2 64/35 1044.860 cents septimal neutral seventh 24: 2 324/175 1066.367 cents 24: 10 15/8 1088.269 cents classic major seventh 24: 2 256/135 1107.821 cents octave - major chroma 24: 1 12544/6561 1122.012 cents 24: 2 27/14 1137.039 cents septimal major seventh 25: 2 64/35 1044.860 cents septimal neutral seventh 25: 2 448/243 1059.051 cents 25: 4 28/15 1080.557 cents grave major seventh 25: 2 15/8 1088.269 cents classic major seventh 25: 3 1225/648 1102.459 cents 25: 10 27/14 1137.039 cents septimal major seventh 25: 2 35/18 1151.230 cents septimal semi-diminished octave 25: 2 1024/525 1156.592 cents 26: 2 256/135 1107.821 cents octave - major chroma 26: 2 48/25 1129.328 cents classic diminished octave 26: 2 27/14 1137.039 cents septimal major seventh 26: 12 35/18 1151.230 cents septimal semi-diminished octave 26: 2 7168/3645 1170.782 cents 26: 1 2025/1024 1180.447 cents 2 tritones 26: 6 486/245 1185.809 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 9.53846 = 124/13
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 22 23 24 25 26 27 0.0 : 48.8 63.0 111.7 203.9 266.9 315.6 386.3 435.1 449.3 498.0 546.8 561.0 590.2 609.8 639.0 653.2 702.0 750.7 764.9 813.7 884.4 933.1 996.1 1088.3 1137.0 1151.2 1200.0 48.8 : 14.2 63.0 155.1 218.1 266.9 337.5 386.3 400.5 449.3 498.0 512.2 541.5 561.0 590.2 604.4 653.2 702.0 716.1 764.9 835.6 884.4 947.3 1039.5 1088.3 1102.5 1151.2 1200.0 63.0 : 48.8 140.9 203.9 252.7 323.4 372.1 386.3 435.1 483.9 498.0 527.3 546.8 576.0 590.2 639.0 687.8 702.0 750.7 821.4 870.2 933.1 1025.3 1074.1 1088.3 1137.0 1185.8 1200.0 111.7 : 92.2 155.1 203.9 274.6 323.4 337.5 386.3 435.1 449.3 478.5 498.0 527.3 541.5 590.2 639.0 653.2 702.0 772.6 821.4 884.4 976.5 1025.3 1039.5 1088.3 1137.0 1151.2 1200.0 203.9 : 63.0 111.7 182.4 231.2 245.4 294.1 342.9 357.1 386.3 405.9 435.1 449.3 498.0 546.8 561.0 609.8 680.4 729.2 792.2 884.4 933.1 947.3 996.1 1044.9 1059.1 1107.8 1200.0 266.9 : 48.8 119.4 168.2 182.4 231.2 279.9 294.1 323.4 342.9 372.1 386.3 435.1 483.9 498.0 546.8 617.5 666.3 729.2 821.4 870.2 884.4 933.1 981.9 996.1 1044.9 1137.0 1200.0 315.6 : 70.7 119.4 133.6 182.4 231.2 245.4 274.6 294.1 323.4 337.5 386.3 435.1 449.3 498.0 568.7 617.5 680.4 772.6 821.4 835.6 884.4 933.1 947.3 996.1 1088.3 1151.2 1200.0 386.3 : 48.8 63.0 111.7 160.5 174.7 203.9 223.5 252.7 266.9 315.6 364.4 378.6 427.4 498.0 546.8 609.8 702.0 750.7 764.9 813.7 862.5 876.6 925.4 1017.6 1080.6 1129.3 1200.0 435.1 : 14.2 63.0 111.7 125.9 155.1 174.7 203.9 218.1 266.9 315.6 329.8 378.6 449.3 498.0 561.0 653.2 702.0 716.1 764.9 813.7 827.9 876.6 968.8 1031.8 1080.6 1151.2 1200.0 449.3 : 48.8 97.5 111.7 140.9 160.5 189.7 203.9 252.7 301.5 315.6 364.4 435.1 483.9 546.8 639.0 687.8 702.0 750.7 799.5 813.7 862.5 954.6 1017.6 1066.4 1137.0 1185.8 1200.0 498.0 : 48.8 63.0 92.2 111.7 140.9 155.1 203.9 252.7 266.9 315.6 386.3 435.1 498.0 590.2 639.0 653.2 702.0 750.7 764.9 813.7 905.9 968.8 1017.6 1088.3 1137.0 1151.2 1200.0 546.8 : 14.2 43.4 63.0 92.2 106.4 155.1 203.9 218.1 266.9 337.5 386.3 449.3 541.5 590.2 604.4 653.2 702.0 716.1 764.9 857.1 920.1 968.8 1039.5 1088.3 1102.5 1151.2 1200.0 561.0 : 29.2 48.8 78.0 92.2 140.9 189.7 203.9 252.7 323.4 372.1 435.1 527.3 576.0 590.2 639.0 687.8 702.0 750.7 842.9 905.9 954.6 1025.3 1074.1 1088.3 1137.0 1185.8 1200.0 590.2 : 19.6 48.8 63.0 111.7 160.5 174.7 223.5 294.1 342.9 405.9 498.0 546.8 561.0 609.8 658.5 672.7 721.5 813.7 876.6 925.4 996.1 1044.9 1059.1 1107.8 1156.6 1170.8 1200.0 609.8 : 29.2 43.4 92.2 140.9 155.1 203.9 274.6 323.4 386.3 478.5 527.3 541.5 590.2 639.0 653.2 702.0 794.1 857.1 905.9 976.5 1025.3 1039.5 1088.3 1137.0 1151.2 1180.4 1200.0 639.0 : 14.2 63.0 111.7 125.9 174.7 245.4 294.1 357.1 449.3 498.0 512.2 561.0 609.8 624.0 672.7 764.9 827.9 876.6 947.3 996.1 1010.3 1059.1 1107.8 1122.0 1151.2 1170.8 1200.0 653.2 : 48.8 97.5 111.7 160.5 231.2 279.9 342.9 435.1 483.9 498.0 546.8 595.6 609.8 658.5 750.7 813.7 862.5 933.1 981.9 996.1 1044.9 1093.6 1107.8 1137.0 1156.6 1185.8 1200.0 702.0 : 48.8 63.0 111.7 182.4 231.2 294.1 386.3 435.1 449.3 498.0 546.8 561.0 609.8 702.0 764.9 813.7 884.4 933.1 947.3 996.1 1044.9 1059.1 1088.3 1107.8 1137.0 1151.2 1200.0 750.7 : 14.2 63.0 133.6 182.4 245.4 337.5 386.3 400.5 449.3 498.0 512.2 561.0 653.2 716.1 764.9 835.6 884.4 898.5 947.3 996.1 1010.3 1039.5 1059.1 1088.3 1102.5 1151.2 1200.0 764.9 : 48.8 119.4 168.2 231.2 323.4 372.1 386.3 435.1 483.9 498.0 546.8 639.0 702.0 750.7 821.4 870.2 884.4 933.1 981.9 996.1 1025.3 1044.9 1074.1 1088.3 1137.0 1185.8 1200.0 813.7 : 70.7 119.4 182.4 274.6 323.4 337.5 386.3 435.1 449.3 498.0 590.2 653.2 702.0 772.6 821.4 835.6 884.4 933.1 947.3 976.5 996.1 1025.3 1039.5 1088.3 1137.0 1151.2 1200.0 884.4 : 48.8 111.7 203.9 252.7 266.9 315.6 364.4 378.6 427.4 519.6 582.5 631.3 702.0 750.7 764.9 813.7 862.5 876.6 905.9 925.4 954.6 968.8 1017.6 1066.4 1080.6 1129.3 1200.0 933.1 : 63.0 155.1 203.9 218.1 266.9 315.6 329.8 378.6 470.8 533.7 582.5 653.2 702.0 716.1 764.9 813.7 827.9 857.1 876.6 905.9 920.1 968.8 1017.6 1031.8 1080.6 1151.2 1200.0 996.1 : 92.2 140.9 155.1 203.9 252.7 266.9 315.6 407.8 470.8 519.6 590.2 639.0 653.2 702.0 750.7 764.9 794.1 813.7 842.9 857.1 905.9 954.6 968.8 1017.6 1088.3 1137.0 1200.0 1088.3: 48.8 63.0 111.7 160.5 174.7 223.5 315.6 378.6 427.4 498.0 546.8 561.0 609.8 658.5 672.7 702.0 721.5 750.7 764.9 813.7 862.5 876.6 925.4 996.1 1044.9 1107.8 1200.0 1137.0: 14.2 63.0 111.7 125.9 174.7 266.9 329.8 378.6 449.3 498.0 512.2 561.0 609.8 624.0 653.2 672.7 702.0 716.1 764.9 813.7 827.9 876.6 947.3 996.1 1059.1 1151.2 1200.0 1151.2: 48.8 97.5 111.7 160.5 252.7 315.6 364.4 435.1 483.9 498.0 546.8 595.6 609.8 639.0 658.5 687.8 702.0 750.7 799.5 813.7 862.5 933.1 981.9 1044.9 1137.0 1185.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1905 .. 92.1787 cents 6561/6272, 77.9882 cents 245/243, 14.1905 cents 2: 43.4083 .. 155.1396 cents 16/15, 111.7313 cents 35/36,-48.7704 cents 3: 62.9609 .. 203.9100 cents 243/224, 140.9491 cents 128/135,-92.1787 cents 4: 92.1787 .. 274.5824 cents 10/9, 182.4037 cents 15/16,-111.7313 cents 5: 106.3692 .. 323.3528 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 6: 155.1396 .. 372.1232 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 7: 203.9100 .. 386.3137 cents 10/9, 182.4037 cents 49/54,-168.2132 cents 8: 218.1005 .. 435.0841 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 9: 266.8709 .. 483.8545 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 10: 315.6413 .. 533.7418 cents 245/216, 218.1005 cents 49/54,-168.2132 cents 11: 329.8318 .. 590.2237 cents 3645/3136, 260.3919 cents 8/9,-203.9100 cents 12: 378.6022 .. 653.1846 cents 75/64, 274.5824 cents 1792/2025,-211.6215 cents 13: 427.3726 .. 701.9550 cents 75/64, 274.5824 cents 768/875,-225.8120 cents 14: 498.0450 .. 772.6274 cents 75/64, 274.5824 cents 8/9,-203.9100 cents 15: 546.8154 .. 821.3978 cents 75/64, 274.5824 cents 768/875,-225.8120 cents 16: 609.7763 .. 870.1682 cents 3645/3136, 260.3919 cents 1792/2025,-211.6215 cents 17: 666.2582 .. 884.3587 cents 245/216, 218.1005 cents 8/9,-203.9100 cents 18: 716.1455 .. 933.1291 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 19: 764.9159 .. 981.8995 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 20: 813.6863 .. 996.0900 cents 10/9, 182.4037 cents 49/54,-168.2132 cents 21: 827.8768 .. 1044.8604 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 22: 876.6472 .. 1093.6308 cents 1944/1715, 216.9836 cents 49/54,-168.2132 cents 23: 925.4176 .. 1107.8213 cents 10/9, 182.4037 cents 49/54,-168.2132 cents 24: 996.0900 .. 1137.0391 cents 243/224, 140.9491 cents 15/16,-111.7313 cents 25: 1044.8604 .. 1156.5917 cents 16/15, 111.7313 cents 128/135,-92.1787 cents 26: 1107.8213 .. 1185.8095 cents 6561/6272, 77.9882 cents 35/36,-48.7704 cents
SHOW DATA
Number of notes : 27 -- Interval properties -- Smallest interval : 245/243, 14.1905 cents, class 1 Average step (divided formal octave): 44.4444 cents Largest one step interval : 135/128, 92.1787 cents Average / Smallest step : 3.131981 Largest / Average step : 2.074021 Largest / Smallest step : 6.495794 Median interval of one step : 36/35, 48.7704 cents, amount: 12 Most common interval of one step : 36/35, 48.7704 cents, amount: 12 Least squares average step : 43.85216 cents, oct.: 1184.00828 cents Scale is not proper Step pattern alph. order: ABACDAEABAABFGFBAABAEADCABA Step pattern size order : DADGEDFDADDACBCADDADFDEGDAD Scale is not a Constant Structure Scale diversity : 1.427450 Lumma stability : 0.023651 Lumma impropriety factor : 0.927653 Number of different interval sizes : 130 = 5.00000 / class Number of one step interval sizes : 7 Highest interval variety : 12 Mean interval variety : 9.53846 = 124/13 Median interval variety : 11 Lowest interval variety : 7 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 20 Most common triad is 0.0 498.045 701.955 cents, amount: 13 Number of recognisable fifths : 30, average 702.9010 cents Number of appreciable fifths : 20, average 701.9550 cents Scale contains a complete diamond : 1 3 5 15 45 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 27 = 100.0000% Scale is n-1 differentially coherent in interval classes 2 and 3 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 13-14 -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.015220 Average absolute harmonicity : 0.115650 Specific harmonicity : 0.093160 Fundamental : 1/90720, -16.4691 octaves, 0.0029 Hz. Guide tone : 181440, 17.4691 octaves, 47469342.568 Hz. Exponens Consonantiae : 1.646024E+10, 33.93827 octaves Euler's gradus suavitatis : 48 Sum of Mann's harmonic distance : 626.0, average 23.18519 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 30.86000, average 1.14296 Sum of Tenney's harmonic distance : 61.62633, average 2.28246 Vogel's harmonic complexity : 29.51852 Wille's k value : 63787 Wilson's harmonic complexity : 48 Rectangular lattice diameter : 12 Triangular lattice diameter : 8 Lattice compactness : 1692.55446, average 4.47766 Lattice compactness (without 2's) : 1066.22437, average 2.82070 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.51852 60 1 3: -4 .. 4 0.00000 46 4 5: -1 .. 1 0.00000 14 8 7: -1 .. 1 0.00000 14 14 Average exponent except 2's : 0 / 27 = 0.00000 Average absolute exponent except 2's: 74 / 27 = 2.74074 Scale is weakly epimorphic with val: <27 40 60 76| Scale is weakly epimorphic with val: <27 46 64 77|
FIT/MODE
27: 1 0 2 2 1 1 2 1 0 1 1 1 0 1 0 1 1 1 0 1 2 1 1 2 2 0 1 N I SD: 12.7197 c. M:-21.6020 c. 28: 1 0 2 2 1 1 2 1 0 2 1 0 1 0 1 0 1 2 0 1 2 1 1 2 2 0 1 N I SD: 12.5373 c. M: 20.7032 c. 30: 1 1 1 2 2 1 2 1 0 1 2 0 1 0 1 0 2 1 0 1 2 1 2 2 1 1 1 N I SD: 10.6661 c. M:-18.0450 c. 31: 1 1 1 2 2 1 2 1 1 1 1 0 1 1 0 1 1 1 1 1 2 1 2 2 1 1 1 N SD: 9.9085 c. M: 19.6393 c. 32: 1 1 1 2 2 1 2 2 0 1 2 0 1 0 1 0 2 1 0 2 2 1 2 2 1 1 1 N I SD: 10.9261 c. M:-16.4100 c. 34: 1 1 1 3 2 1 2 1 1 1 1 1 1 0 1 1 1 1 1 1 2 1 2 3 1 1 1 N I SD: 9.5660 c. M:-17.4036 c. 35: 1 1 1 3 2 1 2 2 0 2 1 0 1 1 1 0 1 2 0 2 2 1 2 3 1 1 1 N I SD: 9.0830 c. M:-16.2407 c. 36: 1 1 1 3 2 1 3 1 0 2 1 1 1 0 1 1 1 2 0 1 3 1 2 3 1 1 1 N I SD: 10.2102 c. M: 15.9413 c. 38: 2 0 2 2 2 2 2 2 0 2 1 1 1 0 1 1 1 2 0 2 2 2 2 2 2 0 2 N I SD: 9.7678 c. M: 14.5845 c. 39: 2 0 2 3 2 1 3 1 1 1 2 0 1 1 1 0 2 1 1 1 3 1 2 3 2 0 2 N I SD: 9.0720 c. M: 13.6863 c. 41: 2 0 2 3 2 2 2 2 0 2 2 0 1 1 1 0 2 2 0 2 2 2 2 3 2 0 2 N I SD: 5.9926 c. M: 10.2502 c. 53: 2 1 2 4 3 2 3 2 1 2 2 1 1 1 1 1 2 2 1 2 3 2 3 4 2 1 2 N I SD: 3.2442 c. M:-5.0318 c. 75: 3 1 3 6 4 3 4 3 1 3 3 1 2 1 2 1 3 3 1 3 4 3 4 6 3 1 3 N I SD: 2.6742 c. M:-5.1291 c. 77: 3 1 3 6 4 3 5 3 1 3 3 1 2 1 2 1 3 3 1 3 5 3 4 6 3 1 3 N I SD: 2.0799 c. M:-3.9530 c. 94: 4 1 4 7 5 4 5 4 1 4 4 1 2 2 2 1 4 4 1 4 5 4 5 7 4 1 4 N I SD: 2.1456 c. M:-3.5076 c. 99: 4 1 4 8 5 4 6 4 1 4 4 1 3 1 3 1 4 4 1 4 6 4 5 8 4 1 4 N I SD: 1.9398 c. M:-3.7157 c. 118: 5 1 5 9 6 5 7 5 1 5 5 1 3 2 3 1 5 5 1 5 7 5 6 9 5 1 5 N I SD: 1.5226 c. M: 2.4641 c. 152: 6 2 6 12 8 6 9 6 2 6 6 2 4 2 4 2 6 6 2 6 9 6 8 12 6 2 6 N I SD: 1.1492 c. M:-2.0785 c. 171: 7 2 7 13 9 7 10 7 2 7 7 2 4 3 4 2 7 7 2 7 10 7 9 13 7 2 7 N I SD: 0.3753 c. M: 0.7500 c. 323: 13 4 13 25 17 13 19 13 4 13 13 4 8 5 8 4 13 13 4 13 19 13 17 25 13 4 13 N I SD: 0.3771 c. M:-0.6853 c. 419: 17 5 17 32 22 17 25 17 5 17 17 5 10 7 10 5 17 17 5 17 25 17 22 32 17 5 17 N I SD: 0.3400 c. M: 0.6055 c. 441: 18 5 18 34 23 18 26 18 5 18 18 5 11 7 11 5 18 18 5 18 26 18 23 34 18 5 18 N I SD: 0.2375 c. M:-0.4617 c. 494: 20 6 20 38 26 20 29 20 6 20 20 6 12 8 12 6 20 20 6 20 29 20 26 38 20 6 20 N I SD: 0.1741 c. M: 0.3356 c. 612: 25 7 25 47 32 25 36 25 7 25 25 7 15 10 15 7 25 25 7 25 36 25 32 47 25 7 25 N I SD: 0.1663 c. M: 0.2550 c. 665: 27 8 27 51 35 27 39 27 8 27 27 8 16 11 16 8 27 27 8 27 39 27 35 51 27 8 27 N I SD: 0.1362 c. M:-0.1971 c. 913: 37 11 37 70 48 37 54 37 11 37 37 11 22 15 22 11 37 37 11 37 54 37 48 70 37 11 37 N I SD: 0.1348 c. M: 0.2325 c. 935: 38 11 38 72 49 38 55 38 11 38 38 11 23 15 23 11 38 38 11 38 55 38 49 72 38 11 38 N I SD: 0.0906 c. M:-0.1542 c. 1106: 45 13 45 85 58 45 65 45 13 45 45 13 27 18 27 13 45 45 13 45 65 45 58 85 45 13 45 N I SD: 0.0515 c. M: 0.0911 c. 1848: 75 22 75 142 97 75 109 75 22 75 75 22 45 30 45 22 75 75 22 75 109 75 97 142 75 22 75 N I SD: 0.0437 c. M: 0.0760 c. 2019: 82 24 82 155 106 82 119 82 24 82 82 24 49 33 49 24 82 82 24 82 119 82 106 155 82 24 82 N I SD: 0.0345 c. M:-0.0639 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: 6.8160 cents 5 .. 10 match: 5 H SD: 4.5694 cents 6 .. 12 match: 6 H SD: 6.4843 cents 7 .. 14 match: 7 H SD: 5.3188 cents 8 .. 16 match: 8 H SD: 4.8154 cents 9 .. 18 match: 9 H SD: 4.5004 cents 10 .. 20 match: 10 H SD: 5.2875 cents 11 .. 22 match: 11 H SD: 6.7113 cents 12 .. 24 match: 11 SD: 4.0178 cents 13 .. 26 match: 13 H SD: 4.3670 cents 14 .. 28 match: 14 H SD: 3.8293 cents 15 .. 30 match: 15 H SD: 2.8805 cents 16 .. 32 match: 15 S SD: 3.6493 cents 17 .. 34 match: 16 S SD: 3.3312 cents 18 .. 36 match: 17 S SD: 2.8522 cents 19 .. 38 match: 17 S SD: 4.2592 cents 20 .. 40 match: 17 SD: 3.3335 cents 21 .. 42 match: 18 SD: 3.4165 cents 22 .. 44 match: 18 SD: 2.9784 cents 23 .. 46 match: 21 SD: 3.4516 cents 24 .. 48 match: 21 SD: 2.0443 cents 25 .. 50 match: 21 SD: 2.5540 cents 26 .. 52 match: 21 SD: 2.6808 cents 27 .. 54 match: 20 SD: 2.4032 cents 28 .. 56 match: 22 SD: 2.6067 cents 29 .. 58 match: 21 SD: 2.5372 cents 30 .. 60 match: 22 SD: 1.9277 cents 31 .. 62 match: 20 SD: 1.9132 cents 32 .. 64 match: 22 SD: 1.8209 cents 33 .. 66 match: 22 SD: 2.2336 cents 34 .. 68 match: 22 SD: 2.1572 cents 35 .. 70 match: 21 SD: 1.8075 cents 36 .. 72 match: 24 SD: 1.9319 cents 37 .. 74 match: 23 SD: 2.0667 cents 38 .. 76 match: 22 SD: 2.0180 cents 39 .. 78 match: 25 SD: 1.8366 cents 40 .. 80 match: 23 SD: 1.4436 cents 41 .. 82 match: 25 SD: 1.6789 cents 42 .. 84 match: 23 SD: 1.5610 cents 43 .. 86 match: 26 SD: 1.7157 cents 44 .. 88 match: 24 SD: 1.6892 cents 45 .. 90 match: 25 SD: 1.5185 cents 46 .. 92 match: 24 SD: 1.5956 cents 47 .. 94 match: 25 SD: 1.5539 cents 48 .. 96 match: 23 SD: 1.2611 cents 49 .. 98 match: 24 SD: 1.4139 cents 50 .. 100 match: 26 SD: 1.3421 cents 51 .. 102 match: 24 SD: 1.6792 cents 52 .. 104 match: 26 SD: 1.4244 cents 53 .. 106 match: 22 SD: 1.4969 cents 54 .. 108 match: 26 SD: 1.0982 cents 55 .. 110 match: 24 SD: 1.1565 cents 56 .. 112 match: 25 SD: 1.0675 cents 57 .. 114 match: 26 SD: 1.0774 cents 58 .. 116 match: 23 SD: 1.2987 cents 59 .. 118 match: 25 SD: 1.0390 cents 60 .. 120 match: 25 SD: 1.0346 cents 61 .. 122 match: 25 SD: 1.1620 cents 62 .. 124 match: 23 SD: 1.1941 cents 63 .. 126 match: 25 SD: 1.0802 cents 64 .. 128 match: 24 SD: 0.9760 cents 65 .. 130 match: 25 SD: 1.0152 cents 66 .. 132 match: 25 SD: 1.0205 cents 67 .. 134 match: 26 SD: 1.0341 cents 69 .. 138 match: 25 SD: 1.1527 cents 70 .. 140 match: 27 SD: 0.9262 cents 71 .. 142 match: 26 SD: 0.9341 cents 72 .. 144 match: 26 SD: 0.7540 cents 73 .. 146 match: 26 SD: 0.8907 cents 74 .. 148 match: 27 SD: 0.8324 cents 77 .. 154 match: 26 SD: 0.9169 cents 78 .. 156 match: 27 SD: 0.7582 cents 79 .. 158 match: 26 SD: 0.8572 cents 80 .. 160 match: 27 SD: 0.8183 cents 81 .. 162 match: 27 SD: 0.7174 cents 84 .. 168 match: 26 SD: 0.8359 cents 85 .. 170 match: 27 SD: 0.8264 cents 86 .. 172 match: 26 SD: 0.8700 cents 87 .. 174 match: 27 SD: 0.7963 cents 88 .. 176 match: 26 SD: 0.6627 cents 89 .. 178 match: 26 SD: 0.7685 cents 90 .. 180 match: 26 SD: 0.6916 cents 91 .. 182 match: 26 SD: 0.7719 cents 92 .. 184 match: 26 SD: 0.7594 cents 93 .. 186 match: 26 SD: 0.9343 cents 94 .. 188 match: 26 SD: 0.6423 cents 102 .. 204 match: 27 SD: 0.6028 cents 104 .. 208 match: 27 SD: 0.5655 cents 105 .. 210 match: 27 SD: 0.5007 cents 133 .. 266 match: 27 SD: 0.4990 cents 135 .. 270 match: 27 SD: 0.4251 cents 144 .. 288 match: 27 SD: 0.3941 cents 162 .. 324 match: 27 SD: 0.3624 cents 168 .. 336 match: 27 SD: 0.2874 cents 210 .. 420 match: 27 SD: 0.2458 cents 216 .. 432 match: 27 SD: 0.2372 cents 240 .. 480 match: 27 SD: 0.2026 cents 270 .. 540 match: 27 SD: 0.1995 cents 280 .. 560 match: 27 SD: 0.1890 cents 318 .. 636 match: 27 SD: 0.1822 cents 320 .. 640 match: 27 SD: 0.1778 cents 344 .. 688 match: 27 SD: 0.1757 cents 345 .. 690 match: 27 SD: 0.1726 cents 350 .. 700 match: 27 SD: 0.1706 cents 360 .. 720 match: 27 SD: 0.1266 cents 450 .. 900 match: 27 SD: 0.1208 cents 455 .. 910 match: 27 SD: 0.1158 cents 480 .. 960 match: 27 SD: 0.1004 cents 560 .. 1120 match: 27 SD: 0.0991 cents 600 .. 1200 match: 27 SD: 0.0826 cents