Scala analysis: xen11-chalmers-tetrachordal-10-04
Prime-Inverted Heptatonic Diamond, 25 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: 784/729 125.921808 two (Archytas' 1/3-tone) 5: 448/405 174.692189 6: 9/8 203.910002 major whole tone 7: 256/225 223.462571 Neapolitan diminished third 8: 5/4 386.313714 major third 9: 9/7 435.084095 septimal major third, BP third 10: 4/3 498.044999 perfect fourth 11: 112/81 561.005903 12: 45/32 590.223716 diatonic tritone 13: 64/45 609.776284 2nd tritone 14: 81/56 638.994097 15: 3/2 701.955001 perfect fifth 16: 14/9 764.915905 septimal minor sixth 17: 8/5 813.686286 minor sixth 18: 225/128 976.537429 augmented sixth 19: 16/9 996.089998 Pythagorean minor seventh 20: 405/224 1025.307811 21: 729/392 1074.078192 22: 15/8 1088.268715 classic major seventh 23: 27/14 1137.039096 septimal major seventh 24: 35/18 1151.229619 septimal semi-diminished octave 25: 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: 245/243 14.1905 minor BP diesis, Sensamagic comma 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 3645/3584 29.2178 7: 2048/2025 19.5526 diaschisma 8: 1125/1024 162.8511 double augmented prime 9: 36/35 48.7704 septimal diesis, 1/4-tone 10: 28/27 62.9609 Archytas' 1/3-tone 11: 28/27 62.9609 Archytas' 1/3-tone 12: 3645/3584 29.2178 13: 2048/2025 19.5526 diaschisma 14: 3645/3584 29.2178 15: 28/27 62.9609 Archytas' 1/3-tone 16: 28/27 62.9609 Archytas' 1/3-tone 17: 36/35 48.7704 septimal diesis, 1/4-tone 18: 1125/1024 162.8511 double augmented prime 19: 2048/2025 19.5526 diaschisma 20: 3645/3584 29.2178 21: 36/35 48.7704 septimal diesis, 1/4-tone 22: 245/243 14.1905 minor BP diesis, Sensamagic comma 23: 36/35 48.7704 septimal diesis, 1/4-tone 24: 245/243 14.1905 minor BP diesis, Sensamagic comma 25: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 4 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 3 2048/2025 19.553 cents diaschisma 1: 4 3645/3584 29.218 cents 1: 8 36/35 48.770 cents septimal diesis, 1/4-tone 1: 4 28/27 62.961 cents Archytas' 1/3-tone 1: 2 1125/1024 162.851 cents double augmented prime 2: 4 36/35 48.770 cents septimal diesis, 1/4-tone 2: 8 28/27 62.961 cents Archytas' 1/3-tone 2: 2 6561/6272 77.988 cents 2: 2 135/128 92.179 cents major chroma, major limma 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 784/729 125.922 cents two (Archytas' 1/3-tone) 2: 2 10/9 182.404 cents minor whole tone 2: 2 2025/1792 211.622 cents 3: 2 6860/6561 77.151 cents 3: 1 6561/6272 77.988 cents 3: 2 135/128 92.179 cents major chroma, major limma 3: 2 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 3: 8 16/15 111.731 cents minor diatonic semitone 3: 2 35/32 155.140 cents septimal neutral second 3: 2 448/405 174.692 cents 3: 2 2025/1792 211.622 cents 3: 2 8/7 231.174 cents septimal whole tone 3: 2 75/64 274.582 cents classic augmented second 4: 2 16/15 111.731 cents minor diatonic semitone 4: 5 784/729 125.922 cents two (Archytas' 1/3-tone) 4: 4 243/224 140.949 cents Archytas' 2/3-tone 4: 2 192/175 160.502 cents septimal 4/5-tone 4: 2 448/405 174.692 cents 4: 2 9/8 203.910 cents major whole tone 4: 4 3645/3136 260.392 cents 4: 2 32/27 294.135 cents Pythagorean minor third 4: 2 175/144 337.543 cents 5: 2 35/32 155.140 cents septimal neutral second 5: 2 192/175 160.502 cents septimal 4/5-tone 5: 6 448/405 174.692 cents 5: 3 9/8 203.910 cents major whole tone 5: 2 256/225 223.463 cents Neapolitan diminished third 5: 2 75/64 274.582 cents classic augmented second 5: 2 6561/5488 309.162 cents 5: 2 135/112 323.353 cents septimal wide minor third 5: 2 896/729 357.096 cents 5: 2 10125/8192 366.761 cents double augmented second 6: 2 448/405 174.692 cents 6: 2 21952/19683 188.883 cents 6: 2 9/8 203.910 cents major whole tone 6: 3 256/225 223.463 cents Neapolitan diminished third 6: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 6: 2 7/6 266.871 cents septimal minor third 6: 4 135/112 323.353 cents septimal wide minor third 6: 2 243/196 372.123 cents 6: 6 5/4 386.314 cents major third 7: 2 256/225 223.463 cents Neapolitan diminished third 7: 4 12544/10935 237.653 cents 7: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 7: 2 6/5 315.641 cents minor third 7: 1 98/81 329.832 cents 7: 2 175/144 337.543 cents 7: 2 243/196 372.123 cents 7: 2 5/4 386.314 cents major third 7: 2 512/405 405.866 cents narrow diminished fourth 7: 4 18225/14336 415.532 cents 7: 2 9/7 435.084 cents septimal major third, BP third 8: 1 614656/531441 251.844 cents 8: 2 7/6 266.871 cents septimal minor third 8: 2 1024/875 272.233 cents 8: 2 7168/6075 286.423 cents 8: 2 56/45 378.602 cents septimal narrow major third 8: 4 5/4 386.314 cents major third 8: 6 9/7 435.084 cents septimal major third, BP third 8: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 8: 2 32805/25088 464.302 cents 8: 2 675/512 478.492 cents wide augmented third 9: 2 7168/6075 286.423 cents 9: 2 351232/295245 300.614 cents 9: 2 6/5 315.641 cents minor third 9: 1 32/25 427.373 cents classic diminished fourth 9: 4 9/7 435.084 cents septimal major third, BP third 9: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 9: 2 32805/25088 464.302 cents 9: 2 675/512 478.492 cents wide augmented third 9: 2 324/245 483.854 cents 9: 4 4/3 498.045 cents perfect fourth 9: 2 175/128 541.453 cents 10: 2 98/81 329.832 cents 10: 2 4096/3375 335.194 cents double diminished fourth 10: 1 200704/164025 349.384 cents 10: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 10: 2 324/245 483.854 cents 10: 4 4/3 498.045 cents perfect fourth 10: 2 980/729 512.236 cents 10: 2 59049/43904 513.072 cents 10: 4 1215/896 527.263 cents 10: 2 112/81 561.006 cents 10: 2 45/32 590.224 cents diatonic tritone 11: 2 200704/164025 349.384 cents 11: 2 56/45 378.602 cents septimal narrow major third 11: 4 4/3 498.045 cents perfect fourth 11: 2 1215/896 527.263 cents 11: 2 175/128 541.453 cents 11: 4 48/35 546.815 cents septimal semi-augmented fourth 11: 2 112/81 561.006 cents 11: 2 2187/1568 576.033 cents 11: 2 45/32 590.224 cents diatonic tritone 11: 2 64/45 609.776 cents 2nd tritone 11: 1 50625/32768 753.075 cents 12: 2 114688/91125 398.155 cents 12: 1 81/64 407.820 cents Pythagorean major third 12: 2 980/729 512.236 cents 12: 2 48/35 546.815 cents septimal semi-augmented fourth 12: 4 112/81 561.006 cents 12: 2 2187/1568 576.033 cents 12: 4 45/32 590.224 cents diatonic tritone 12: 2 64/45 609.776 cents 2nd tritone 12: 4 81/56 638.994 cents 12: 2 25/16 772.627 cents classic augmented fifth 13: 2 32/25 427.373 cents classic diminished fourth 13: 4 112/81 561.006 cents 13: 2 45/32 590.224 cents diatonic tritone 13: 4 64/45 609.776 cents 2nd tritone 13: 2 3136/2187 623.967 cents 13: 4 81/56 638.994 cents 13: 2 35/24 653.185 cents septimal semi-diminished fifth 13: 2 729/490 687.764 cents 13: 1 128/81 792.180 cents Pythagorean minor sixth 13: 2 91125/57344 801.845 cents 14: 1 65536/50625 446.925 cents two (Neapolitan diminished third) 14: 2 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: 4 35/24 653.185 cents septimal semi-diminished fifth 14: 2 256/175 658.547 cents 14: 2 1792/1215 672.737 cents 14: 4 3/2 701.955 cents perfect fifth 14: 2 45/28 821.398 cents septimale wide minor sixth 14: 2 164025/100352 850.616 cents 15: 2 64/45 609.776 cents 2nd tritone 15: 2 81/56 638.994 cents 15: 4 1792/1215 672.737 cents 15: 2 87808/59049 686.928 cents 15: 2 729/490 687.764 cents 15: 4 3/2 701.955 cents perfect fifth 15: 2 245/162 716.146 cents 15: 2 54/35 750.725 cents septimal semi-augmented fifth 15: 1 164025/100352 850.616 cents 15: 2 3375/2048 864.806 cents double augmented fifth 15: 2 81/49 870.168 cents two (septimal major third, BP third) 16: 2 256/175 658.547 cents 16: 4 3/2 701.955 cents perfect fifth 16: 2 245/162 716.146 cents 16: 2 1024/675 721.508 cents narrow diminished sixth 16: 2 50176/32805 735.698 cents 16: 2 54/35 750.725 cents septimal semi-augmented fifth 16: 4 14/9 764.916 cents septimal minor sixth 16: 1 25/16 772.627 cents classic augmented fifth 16: 2 5/3 884.359 cents major sixth, BP sixth 16: 2 295245/175616 899.386 cents 16: 2 6075/3584 913.577 cents 17: 2 1024/675 721.508 cents narrow diminished sixth 17: 2 50176/32805 735.698 cents 17: 2 54/35 750.725 cents septimal semi-augmented fifth 17: 6 14/9 764.916 cents septimal minor sixth 17: 4 8/5 813.686 cents minor sixth 17: 2 45/28 821.398 cents septimale wide minor sixth 17: 2 6075/3584 913.577 cents 17: 2 875/512 927.767 cents 17: 2 12/7 933.129 cents septimal major sixth 17: 1 531441/307328 948.156 cents 18: 2 14/9 764.916 cents septimal minor sixth 18: 4 28672/18225 784.468 cents 18: 2 405/256 794.134 cents wide augmented fifth 18: 2 8/5 813.686 cents minor sixth 18: 2 392/243 827.877 cents 18: 2 288/175 862.457 cents 18: 1 81/49 870.168 cents two (septimal major third, BP third) 18: 2 5/3 884.359 cents major sixth, BP sixth 18: 2 140/81 947.320 cents 18: 4 10935/6272 962.347 cents 18: 2 225/128 976.537 cents augmented sixth 19: 6 8/5 813.686 cents minor sixth 19: 2 392/243 827.877 cents 19: 4 224/135 876.647 cents narrow septimal major sixth 19: 2 12/7 933.129 cents septimal major sixth 19: 2 140/81 947.320 cents 19: 3 225/128 976.537 cents augmented sixth 19: 2 16/9 996.090 cents Pythagorean minor seventh 19: 2 19683/10976 1011.117 cents 19: 2 405/224 1025.308 cents 20: 2 16384/10125 833.239 cents double diminished seventh 20: 2 729/448 842.904 cents 20: 2 224/135 876.647 cents narrow septimal major sixth 20: 2 10976/6561 890.838 cents 20: 2 128/75 925.418 cents diminished seventh 20: 2 225/128 976.537 cents augmented sixth 20: 3 16/9 996.090 cents Pythagorean minor seventh 20: 6 405/224 1025.308 cents 20: 2 175/96 1039.498 cents 20: 2 64/35 1044.860 cents septimal neutral seventh 21: 2 288/175 862.457 cents 21: 2 27/16 905.865 cents Pythagorean major sixth 21: 4 6272/3645 939.608 cents 21: 2 16/9 996.090 cents Pythagorean minor seventh 21: 2 405/224 1025.308 cents 21: 2 175/96 1039.498 cents 21: 4 448/243 1059.051 cents 21: 5 729/392 1074.078 cents 21: 2 15/8 1088.269 cents classic major seventh 22: 2 128/75 925.418 cents diminished seventh 22: 2 7/4 968.826 cents harmonic seventh 22: 2 3584/2025 988.378 cents 22: 2 405/224 1025.308 cents 22: 2 64/35 1044.860 cents septimal neutral seventh 22: 8 15/8 1088.269 cents classic major seventh 22: 2 1225/648 1102.459 cents 22: 2 256/135 1107.821 cents octave - major chroma 22: 1 12544/6561 1122.012 cents 22: 2 6561/3430 1122.849 cents 23: 2 3584/2025 988.378 cents 23: 2 9/5 1017.596 cents just minor seventh, BP seventh 23: 2 729/392 1074.078 cents 23: 2 15/8 1088.269 cents classic major seventh 23: 1 1225/648 1102.459 cents 23: 2 256/135 1107.821 cents octave - major chroma 23: 2 12544/6561 1122.012 cents 23: 8 27/14 1137.039 cents septimal major seventh 23: 4 35/18 1151.230 cents septimal semi-diminished octave 24: 2 2048/1125 1037.149 cents double diminished octave 24: 4 27/14 1137.039 cents septimal major seventh 24: 8 35/18 1151.230 cents septimal semi-diminished octave 24: 4 7168/3645 1170.782 cents 24: 3 2025/1024 1180.447 cents 2 tritones 24: 4 486/245 1185.809 cents Highest number of different intervals for one interval class: 11 Average number of different intervals per interval class: 9.75000 = 39/4
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 0.0 : 48.8 63.0 111.7 125.9 174.7 203.9 223.5 386.3 435.1 498.0 561.0 590.2 609.8 639.0 702.0 764.9 813.7 976.5 996.1 1025.3 1074.1 1088.3 1137.0 1151.2 1200.0 48.8 : 14.2 63.0 77.2 125.9 155.1 174.7 337.5 386.3 449.3 512.2 541.5 561.0 590.2 653.2 716.1 764.9 927.8 947.3 976.5 1025.3 1039.5 1088.3 1102.5 1151.2 1200.0 63.0 : 48.8 63.0 111.7 140.9 160.5 323.4 372.1 435.1 498.0 527.3 546.8 576.0 639.0 702.0 750.7 913.6 933.1 962.3 1011.1 1025.3 1074.1 1088.3 1137.0 1185.8 1200.0 111.7 : 14.2 63.0 92.2 111.7 274.6 323.4 386.3 449.3 478.5 498.0 527.3 590.2 653.2 702.0 864.8 884.4 913.6 962.3 976.5 1025.3 1039.5 1088.3 1137.0 1151.2 1200.0 125.9 : 48.8 78.0 97.5 260.4 309.2 372.1 435.1 464.3 483.9 513.1 576.0 639.0 687.8 850.6 870.2 899.4 948.2 962.3 1011.1 1025.3 1074.1 1122.8 1137.0 1185.8 1200.0 174.7 : 29.2 48.8 211.6 260.4 323.4 386.3 415.5 435.1 464.3 527.3 590.2 639.0 801.8 821.4 850.6 899.4 913.6 962.3 976.5 1025.3 1074.1 1088.3 1137.0 1151.2 1200.0 203.9 : 19.6 182.4 231.2 294.1 357.1 386.3 405.9 435.1 498.0 561.0 609.8 772.6 792.2 821.4 870.2 884.4 933.1 947.3 996.1 1044.9 1059.1 1107.8 1122.0 1170.8 1200.0 223.5 : 162.9 211.6 274.6 337.5 366.8 386.3 415.5 478.5 541.5 590.2 753.1 772.6 801.8 850.6 864.8 913.6 927.8 976.5 1025.3 1039.5 1088.3 1102.5 1151.2 1180.4 1200.0 386.3 : 48.8 111.7 174.7 203.9 223.5 252.7 315.6 378.6 427.4 590.2 609.8 639.0 687.8 702.0 750.7 764.9 813.7 862.5 876.6 925.4 939.6 988.4 1017.6 1037.1 1200.0 435.1 : 63.0 125.9 155.1 174.7 203.9 266.9 329.8 378.6 541.5 561.0 590.2 639.0 653.2 702.0 716.1 764.9 813.7 827.9 876.6 890.8 939.6 968.8 988.4 1151.2 1200.0 498.0 : 63.0 92.2 111.7 140.9 203.9 266.9 315.6 478.5 498.0 527.3 576.0 590.2 639.0 653.2 702.0 750.7 764.9 813.7 827.9 876.6 905.9 925.4 1088.3 1137.0 1200.0 561.0 : 29.2 48.8 78.0 140.9 203.9 252.7 415.5 435.1 464.3 513.1 527.3 576.0 590.2 639.0 687.8 702.0 750.7 764.9 813.7 842.9 862.5 1025.3 1074.1 1137.0 1200.0 590.2 : 19.6 48.8 111.7 174.7 223.5 386.3 405.9 435.1 483.9 498.0 546.8 561.0 609.8 658.5 672.7 721.5 735.7 784.5 813.7 833.2 996.1 1044.9 1107.8 1170.8 1200.0 609.8 : 29.2 92.2 155.1 203.9 366.8 386.3 415.5 464.3 478.5 527.3 541.5 590.2 639.0 653.2 702.0 716.1 764.9 794.1 813.7 976.5 1025.3 1088.3 1151.2 1180.4 1200.0 639.0 : 63.0 125.9 174.7 337.5 357.1 386.3 435.1 449.3 498.0 512.2 561.0 609.8 624.0 672.7 686.9 735.7 764.9 784.5 947.3 996.1 1059.1 1122.0 1151.2 1170.8 1200.0 702.0 : 63.0 111.7 274.6 294.1 323.4 372.1 386.3 435.1 449.3 498.0 546.8 561.0 609.8 624.0 672.7 702.0 721.5 884.4 933.1 996.1 1059.1 1088.3 1107.8 1137.0 1200.0 764.9 : 48.8 211.6 231.2 260.4 309.2 323.4 372.1 386.3 435.1 483.9 498.0 546.8 561.0 609.8 639.0 658.5 821.4 870.2 933.1 996.1 1025.3 1044.9 1074.1 1137.0 1200.0 813.7 : 162.9 182.4 211.6 260.4 274.6 323.4 337.5 386.3 435.1 449.3 498.0 512.2 561.0 590.2 609.8 772.6 821.4 884.4 947.3 976.5 996.1 1025.3 1088.3 1151.2 1200.0 976.5 : 19.6 48.8 97.5 111.7 160.5 174.7 223.5 272.2 286.4 335.2 349.4 398.2 427.4 446.9 609.8 658.5 721.5 784.5 813.7 833.2 862.5 925.4 988.4 1037.1 1200.0 996.1 : 29.2 78.0 92.2 140.9 155.1 203.9 252.7 266.9 315.6 329.8 378.6 407.8 427.4 590.2 639.0 702.0 764.9 794.1 813.7 842.9 905.9 968.8 1017.6 1180.4 1200.0 1025.3: 48.8 63.0 111.7 125.9 174.7 223.5 237.7 286.4 300.6 349.4 378.6 398.2 561.0 609.8 672.7 735.7 764.9 784.5 813.7 876.6 939.6 988.4 1151.2 1170.8 1200.0 1074.1: 14.2 63.0 77.2 125.9 174.7 188.9 237.7 251.8 300.6 329.8 349.4 512.2 561.0 624.0 686.9 716.1 735.7 764.9 827.9 890.8 939.6 1102.5 1122.0 1151.2 1200.0 1088.3: 48.8 63.0 111.7 160.5 174.7 223.5 237.7 286.4 315.6 335.2 498.0 546.8 609.8 672.7 702.0 721.5 750.7 813.7 876.6 925.4 1088.3 1107.8 1137.0 1185.8 1200.0 1137.0: 14.2 63.0 111.7 125.9 174.7 188.9 237.7 266.9 286.4 449.3 498.0 561.0 624.0 653.2 672.7 702.0 764.9 827.9 876.6 1039.5 1059.1 1088.3 1137.0 1151.2 1200.0 1151.2: 48.8 97.5 111.7 160.5 174.7 223.5 252.7 272.2 435.1 483.9 546.8 609.8 639.0 658.5 687.8 750.7 813.7 862.5 1025.3 1044.9 1074.1 1122.8 1137.0 1185.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 14.1905 .. 162.8511 cents 54675/50176, 148.6606 cents 245/243, 14.1905 cents 2: 48.7704 .. 211.6215 cents 1125/1024, 162.8511 cents 4096/4375,-114.0808 cents 3: 77.1514 .. 274.5824 cents 98415/87808, 197.4310 cents 2458624/2657205,-134.4701 cents 4: 111.7313 .. 337.5433 cents 875/768, 225.8120 cents 1024/1125,-162.8511 cents 5: 155.1396 .. 366.7611 cents 2025/1792, 211.6215 cents 9/10,-182.4037 cents 6: 174.6922 .. 386.3137 cents 2025/1792, 211.6215 cents 3670016/4100625,-192.0690 cents 7: 223.4626 .. 435.0841 cents 2025/1792, 211.6215 cents 1024/1125,-162.8511 cents 8: 251.8436 .. 478.4924 cents 358722675/314703872, 226.6488 cent 4302592/4782969,-183.2405 cents 9: 286.4235 .. 541.4533 cents 151875/131072, 255.0299 cents 3670016/4100625,-192.0690 cents 10: 329.8318 .. 590.2237 cents 3645/3136, 260.3919 cents 1792/2025,-211.6215 cents 11: 349.3844 .. 753.0749 cents 403.69048 cents 6422528/7381125,-240.8393 cents 12: 398.1548 .. 772.6274 cents 2278125/1835008, 374.4727 cents -354.92010 cents 13: 427.3726 .. 801.8452 cents 2278125/1835008, 374.4727 cents 512/625,-345.2549 cents 14: 446.9251 .. 850.6156 cents 403.69048 cents -354.92010 cents 15: 609.7763 .. 870.1682 cents 3645/3136, 260.3919 cents 6422528/7381125,-240.8393 cents 16: 658.5467 .. 913.5765 cents 151875/131072, 255.0299 cents 1792/2025,-211.6215 cents 17: 721.5076 .. 948.1564 cents 358722675/314703872, 226.6488 cent 3670016/4100625,-192.0690 cents 18: 764.9159 .. 976.5374 cents 2025/1792, 211.6215 cents 4302592/4782969,-183.2405 cents 19: 813.6863 .. 1025.3078 cents 2025/1792, 211.6215 cents 1024/1125,-162.8511 cents 20: 833.2389 .. 1044.8604 cents 2025/1792, 211.6215 cents 3670016/4100625,-192.0690 cents 21: 862.4567 .. 1088.2687 cents 875/768, 225.8120 cents 9/10,-182.4037 cents 22: 925.4176 .. 1122.8486 cents 98415/87808, 197.4310 cents 1024/1125,-162.8511 cents 23: 988.3785 .. 1151.2296 cents 1125/1024, 162.8511 cents 2458624/2657205,-134.4701 cents 24: 1037.1489 .. 1185.8095 cents 54675/50176, 148.6606 cents 4096/4375,-114.0808 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 245/243, 14.1905 cents, class 1 Average step (divided formal octave): 48.0000 cents Largest one step interval : 1125/1024, 162.8511 cents Average / Smallest step : 3.382539 Largest / Average step : 3.392732 Largest / Smallest step : 11.476050 Median interval of one step : 36/35, 48.7704 cents, amount: 8 Most common interval of one step : 36/35, 48.7704 cents, amount: 8 Least squares average step : 48.99138 cents, oct.: 1224.78442 cents Scale is not proper Step pattern alph. order: ABABACDEAFFCDCFFAEDCABABA Step pattern size order : DADADCBFDEECBCEEDFBCDADAD Scale is not a Constant Structure Scale diversity : 1.441894 Lumma stability : 0.023651 Lumma impropriety factor : 0.918716 Number of different interval sizes : 128 = 5.33333 / class Number of one step interval sizes : 6 Highest interval variety : 11 Mean interval variety : 9.75000 = 39/4 Median interval variety : 7.5 Lowest interval variety : 6 Smallest interval difference : 43046721/43025920, 0.8368 cents Number of recognisable fifths : 22, average 700.5889 cents Number of appreciable fifths : 12, average 701.9550 cents Scale contains a complete diamond : 7 9 27 81 405 Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 25 = 100.0000% Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 12-13 -- Rational properties -- Prime limit : 7 Odd number limit : 531441 (O: 531441 U: 531441) Highest odd numerator or denominator: 729 Scale harmonicity : 0.008792 Average absolute harmonicity : 0.111850 Specific harmonicity : 0.074549 Fundamental : 1/114307200, -26.7683 octaves, 0.0000 Hz. Guide tone : 228614400, 27.7683 octaves, 59811371635.949 Hz. Exponens Consonantiae : 2.613227E+16, 54.53668 octaves Euler's gradus suavitatis : 80 Sum of Mann's harmonic distance : 2929.0, average 117.16000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 37.24032, average 1.48961 Sum of Tenney's harmonic distance : 73.67342, average 2.94694 Vogel's harmonic complexity : 49.52000 Wille's k value : 100465312 Wilson's harmonic complexity : 84 Rectangular lattice diameter : 20 Triangular lattice diameter : 12 Lattice compactness : 1971.61003, average 6.06649 Lattice compactness (without 2's) : 1207.61044, average 3.71572 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -7 .. 8 0.52000 81 1 3: -6 .. 6 0.00000 58 4 5: -2 .. 2 0.00000 14 8 7: -2 .. 2 0.00000 14 12 Average exponent except 2's : 0 / 25 = 0.00000 Average absolute exponent except 2's: 86 / 25 = 3.44000
FIT/MODE
25: 1 0 1 1 1 0 1 3 1 1 2 0 1 0 2 1 1 3 1 0 1 1 1 0 1 N I SD: 13.5092 c. M:-18.0782 c. 27: 1 0 2 0 1 1 0 4 1 1 2 0 1 0 2 1 1 4 0 1 1 0 2 0 1 N I SD: 12.7264 c. M:-21.6020 c. 28: 1 0 2 0 1 1 0 4 1 2 1 1 0 1 1 2 1 4 0 1 1 0 2 0 1 N I SD: 10.3896 c. M: 20.1038 c. 30: 1 1 1 0 1 1 1 4 1 1 2 1 0 1 2 1 1 4 1 1 1 0 1 1 1 N I SD: 11.3455 c. M:-18.0450 c. 31: 1 1 1 0 2 0 1 4 1 2 1 1 1 1 1 2 1 4 1 0 2 0 1 1 1 N I SD: 11.0806 c. M:-19.0704 c. 32: 1 1 1 0 2 0 1 4 2 1 2 1 0 1 2 1 2 4 1 0 2 0 1 1 1 N I SD: 10.7624 c. M:-16.4100 c. 34: 1 1 1 1 1 1 0 5 1 2 2 1 0 1 2 2 1 5 0 1 1 1 1 1 1 N I SD: 8.8104 c. M: 15.2547 c. 36: 1 1 1 1 1 1 1 5 1 2 2 1 0 1 2 2 1 5 1 1 1 1 1 1 1 N I SD: 8.6881 c. M:-15.4370 c. 38: 2 0 2 0 2 0 1 5 2 2 2 1 0 1 2 2 2 5 1 0 2 0 2 0 2 N I SD: 9.6284 c. M:-14.7815 c. 39: 2 0 2 0 2 1 0 6 1 2 2 1 1 1 2 2 1 6 0 1 2 0 2 0 2 N I SD: 8.5735 c. M: 13.6863 c. 41: 2 0 2 0 2 1 1 5 2 2 2 1 1 1 2 2 2 5 1 1 2 0 2 0 2 N I SD: 5.8998 c. M:-10.6838 c. 53: 2 1 2 1 2 1 1 7 2 3 3 1 1 1 3 3 2 7 1 1 2 1 2 1 2 N I SD: 4.3945 c. M: 9.9272 c. 54: 2 1 2 1 2 1 1 7 3 2 3 2 0 2 3 2 3 7 1 1 2 1 2 1 2 N I SD: 6.2206 c. M: 9.7763 c. 55: 2 1 2 1 2 1 1 8 2 3 3 1 1 1 3 3 2 8 1 1 2 1 2 1 2 N I SD: 4.4438 c. M:-7.5464 c. 69: 3 1 2 1 3 2 1 9 3 4 3 2 1 2 3 4 3 9 1 2 3 1 2 1 3 N I SD: 4.3121 c. M:-7.3835 c. 74: 3 1 3 1 3 2 1 10 3 4 4 1 2 1 4 4 3 10 1 2 3 1 3 1 3 N I SD: 4.1695 c. M:-6.9008 c. 75: 3 1 3 1 3 2 1 10 3 4 4 2 1 2 4 4 3 10 1 2 3 1 3 1 3 N I SD: 1.9597 c. M:-4.0900 c. 96: 4 1 4 1 4 2 2 13 4 5 5 2 2 2 5 5 4 13 2 2 4 1 4 1 4 N I SD: 1.8249 c. M:-3.9100 c. 118: 5 1 5 1 5 3 2 16 5 6 6 3 2 3 6 6 5 16 2 3 5 1 5 1 5 N I SD: 1.6680 c. M:-3.8879 c. 130: 5 2 5 2 5 3 2 18 5 7 7 3 2 3 7 7 5 18 2 3 5 2 5 2 5 N I SD: 1.6620 c. M:-3.3090 c. 149: 6 2 6 2 6 3 3 20 6 8 8 3 3 3 8 8 6 20 3 3 6 2 6 2 6 N I SD: 1.8680 c. M: 2.9373 c. 152: 6 2 6 2 6 4 2 21 6 8 8 4 2 4 8 8 6 21 2 4 6 2 6 2 6 N I SD: 1.1845 c. M: 2.4099 c. 171: 7 2 7 2 7 4 3 23 7 9 9 4 3 4 9 9 7 23 3 4 7 2 7 2 7 N I SD: 0.5237 c. M:-1.0988 c. 246: 10 3 10 3 10 6 4 33 10 13 13 6 4 6 13 13 10 33 4 6 10 3 10 3 10 N I SD: 0.6869 c. M:-0.9680 c. 248: 10 3 10 3 10 6 4 34 10 13 13 6 4 6 13 13 10 34 4 6 10 3 10 3 10 N I SD: 0.4761 c. M: 0.8819 c. 323: 13 4 13 4 13 8 5 44 13 17 17 8 5 8 17 17 13 44 5 8 13 4 13 4 13 N I SD: 0.3395 c. M:-0.5524 c. 419: 17 5 17 5 17 10 7 57 17 22 22 10 7 10 22 22 17 57 7 10 17 5 17 5 17 N I SD: 0.2464 c. M:-0.5687 c. 494: 20 6 20 6 20 12 8 67 20 26 26 12 8 12 26 26 20 67 8 12 20 6 20 6 20 N I SD: 0.1774 c. M:-0.3940 c. 742: 30 9 30 9 30 18 12 101 30 39 39 18 12 18 39 39 30 101 12 18 30 9 30 9 30 N I SD: 0.1633 c. M:-0.2820 c. 913: 37 11 37 11 37 22 15 124 37 48 48 22 15 22 48 48 37 124 15 22 37 11 37 11 37 N I SD: 0.1345 c. M: 0.2556 c. 935: 38 11 38 11 38 23 15 127 38 49 49 23 15 23 49 49 38 127 15 23 38 11 38 11 38 N I SD: 0.1097 c. M:-0.1542 c. 1106: 45 13 45 13 45 27 18 150 45 58 58 27 18 27 58 58 45 150 18 27 45 13 45 13 45 N I SD: 0.0439 c. M:-0.0683 c. 1848: 75 22 75 22 75 45 30 251 75 97 97 45 30 45 97 97 75 251 30 45 75 22 75 22 75 N I SD: 0.0431 c. M: 0.0859 c. 2019: 82 24 82 24 82 49 33 274 82 106 106 49 33 49 106 106 82 274 33 49 82 24 82 24 82 N I SD: 0.0402 c. M: 0.0812 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: 23.5575 cents 4 .. 8 match: 4 H SD: 1.9279 cents 5 .. 10 match: 5 H SD: 14.3018 cents 6 .. 12 match: 6 H SD: 14.3928 cents 7 .. 14 match: 7 H SD: 6.8776 cents 8 .. 16 match: 8 H SD: 3.6950 cents 9 .. 18 match: 8 S SD: 5.2172 cents 10 .. 20 match: 8 SD: 4.1544 cents 11 .. 22 match: 11 H SD: 8.5508 cents 12 .. 24 match: 11 SD: 5.1200 cents 13 .. 26 match: 12 SD: 4.8594 cents 14 .. 28 match: 11 SD: 3.4901 cents 15 .. 30 match: 13 SD: 3.8764 cents 16 .. 32 match: 14 S SD: 3.1086 cents 17 .. 34 match: 14 SD: 4.3384 cents 18 .. 36 match: 14 SD: 2.7233 cents 19 .. 38 match: 15 SD: 4.8202 cents 20 .. 40 match: 17 SD: 2.9960 cents 21 .. 42 match: 16 SD: 3.1552 cents 22 .. 44 match: 17 SD: 3.1730 cents 23 .. 46 match: 18 SD: 3.4472 cents 24 .. 48 match: 18 SD: 2.2920 cents 25 .. 50 match: 18 SD: 2.5074 cents 26 .. 52 match: 19 SD: 2.9367 cents 27 .. 54 match: 21 SD: 2.2635 cents 28 .. 56 match: 20 SD: 2.2057 cents 29 .. 58 match: 18 SD: 2.1886 cents 30 .. 60 match: 18 SD: 2.5255 cents 31 .. 62 match: 19 SD: 2.1445 cents 32 .. 64 match: 19 SD: 1.7518 cents 33 .. 66 match: 20 SD: 2.2869 cents 34 .. 68 match: 20 SD: 2.3412 cents 35 .. 70 match: 21 SD: 2.2015 cents 36 .. 72 match: 22 SD: 1.6181 cents 37 .. 74 match: 22 SD: 2.0457 cents 38 .. 76 match: 20 SD: 1.7105 cents 39 .. 78 match: 19 SD: 1.7209 cents 40 .. 80 match: 23 SD: 1.5462 cents 41 .. 82 match: 23 SD: 1.8347 cents 42 .. 84 match: 24 SD: 1.6196 cents 43 .. 86 match: 22 SD: 1.8541 cents 44 .. 88 match: 23 SD: 1.7297 cents 45 .. 90 match: 22 SD: 1.3925 cents 46 .. 92 match: 20 SD: 1.8043 cents 47 .. 94 match: 23 SD: 1.5497 cents 48 .. 96 match: 23 SD: 1.4950 cents 49 .. 98 match: 24 SD: 1.3942 cents 52 .. 104 match: 24 SD: 1.3906 cents 53 .. 106 match: 20 SD: 1.4265 cents 54 .. 108 match: 22 SD: 1.1735 cents 55 .. 110 match: 23 SD: 1.2642 cents 56 .. 112 match: 23 SD: 1.0306 cents 57 .. 114 match: 23 SD: 0.9608 cents 58 .. 116 match: 22 SD: 1.0925 cents 59 .. 118 match: 23 SD: 1.1659 cents 60 .. 120 match: 23 SD: 1.2318 cents 61 .. 122 match: 23 SD: 1.4124 cents 62 .. 124 match: 24 SD: 1.2526 cents 63 .. 126 match: 23 SD: 1.0271 cents 64 .. 128 match: 24 SD: 1.0519 cents 65 .. 130 match: 24 SD: 1.0542 cents 66 .. 132 match: 24 SD: 0.9853 cents 67 .. 134 match: 24 SD: 1.0265 cents 68 .. 136 match: 23 SD: 1.0995 cents 69 .. 138 match: 24 SD: 1.1390 cents 70 .. 140 match: 24 SD: 1.1043 cents 71 .. 142 match: 24 SD: 0.9995 cents 72 .. 144 match: 24 SD: 0.8254 cents 76 .. 152 match: 24 SD: 0.8429 cents 78 .. 156 match: 25 SD: 0.7722 cents 83 .. 166 match: 24 SD: 0.8785 cents 84 .. 168 match: 24 SD: 0.9213 cents 85 .. 170 match: 24 SD: 0.9051 cents 86 .. 172 match: 24 SD: 0.8561 cents 87 .. 174 match: 25 SD: 0.7984 cents 88 .. 176 match: 24 SD: 0.6803 cents 89 .. 178 match: 24 SD: 0.8816 cents 90 .. 180 match: 24 SD: 0.8189 cents 91 .. 182 match: 24 SD: 0.8868 cents 92 .. 184 match: 24 SD: 0.7685 cents 93 .. 186 match: 24 SD: 0.8040 cents 94 .. 188 match: 24 SD: 0.6346 cents 98 .. 196 match: 24 SD: 0.8633 cents 99 .. 198 match: 24 SD: 0.7708 cents 101 .. 202 match: 25 SD: 0.7320 cents 102 .. 204 match: 25 SD: 0.6418 cents 103 .. 206 match: 25 SD: 0.6245 cents 104 .. 208 match: 25 SD: 0.5139 cents 130 .. 260 match: 25 SD: 0.4724 cents 135 .. 270 match: 25 SD: 0.4530 cents 136 .. 272 match: 25 SD: 0.4449 cents 144 .. 288 match: 25 SD: 0.4037 cents 160 .. 320 match: 25 SD: 0.3947 cents 162 .. 324 match: 25 SD: 0.3940 cents 168 .. 336 match: 25 SD: 0.3080 cents 209 .. 418 match: 25 SD: 0.2939 cents 210 .. 420 match: 25 SD: 0.2920 cents 216 .. 432 match: 25 SD: 0.2824 cents 224 .. 448 match: 25 SD: 0.2719 cents 238 .. 476 match: 25 SD: 0.2667 cents 239 .. 478 match: 25 SD: 0.2591 cents 240 .. 480 match: 25 SD: 0.2415 cents 248 .. 496 match: 25 SD: 0.2402 cents 256 .. 512 match: 25 SD: 0.2312 cents 280 .. 560 match: 25 SD: 0.2173 cents 303 .. 606 match: 25 SD: 0.2126 cents 312 .. 624 match: 25 SD: 0.2052 cents 318 .. 636 match: 25 SD: 0.1810 cents 320 .. 640 match: 25 SD: 0.1744 cents 360 .. 720 match: 25 SD: 0.1467 cents 384 .. 768 match: 25 SD: 0.1438 cents 408 .. 816 match: 25 SD: 0.1428 cents 423 .. 846 match: 25 SD: 0.1384 cents 450 .. 900 match: 25 SD: 0.1200 cents 480 .. 960 match: 25 SD: 0.1044 cents 567 .. 1134 match: 25 SD: 0.1037 cents 585 .. 1170 match: 25 SD: 0.1011 cents 600 .. 1200 match: 25 SD: 0.0987 cents