Scala analysis: xen11-chalmers-tetrachordal-10-05
Inverted-Prime 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: 9/8 203.910002 major whole tone 5: 7/6 266.870906 septimal minor third 6: 6/5 315.641287 minor third 7: 98/81 329.831809 8: 56/45 378.602191 septimal narrow major third 9: 5/4 386.313714 major third 10: 32/25 427.372572 classic diminished fourth 11: 9/7 435.084095 septimal major third, BP third 12: 4/3 498.044999 perfect fourth 13: 3/2 701.955001 perfect fifth 14: 14/9 764.915905 septimal minor sixth 15: 25/16 772.627428 classic augmented fifth 16: 8/5 813.686286 minor sixth 17: 45/28 821.397809 septimale wide minor sixth 18: 81/49 870.168191 two (septimal major third, BP third) 19: 5/3 884.358713 major sixth, BP sixth 20: 12/7 933.129094 septimal major sixth 21: 16/9 996.089998 Pythagorean minor seventh 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: 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: 245/243 14.1905 minor BP diesis, Sensamagic comma 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 225/224 7.7115 septimal kleisma 10: 128/125 41.0589 minor diesis, diesis 11: 225/224 7.7115 septimal kleisma 12: 28/27 62.9609 Archytas' 1/3-tone 13: 9/8 203.9100 major whole tone 14: 28/27 62.9609 Archytas' 1/3-tone 15: 225/224 7.7115 septimal kleisma 16: 128/125 41.0589 minor diesis, diesis 17: 225/224 7.7115 septimal kleisma 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: 28/27 62.9609 Archytas' 1/3-tone 22: 135/128 92.1787 major chroma, major limma 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: 4 225/224 7.712 cents septimal kleisma 1: 4 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 2 128/125 41.059 cents minor diesis, diesis 1: 8 36/35 48.770 cents septimal diesis, 1/4-tone 1: 4 28/27 62.961 cents Archytas' 1/3-tone 1: 2 135/128 92.179 cents major chroma, major limma 1: 1 9/8 203.910 cents major whole tone 2: 4 36/35 48.770 cents septimal diesis, 1/4-tone 2: 2 405/392 56.482 cents greenwoodma 2: 8 28/27 62.961 cents Archytas' 1/3-tone 2: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 243/224 140.949 cents Archytas' 2/3-tone 2: 2 35/32 155.140 cents septimal neutral second 2: 2 7/6 266.871 cents septimal minor third 3: 2 405/392 56.482 cents greenwoodma 3: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 3: 2 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 3: 8 16/15 111.731 cents minor diatonic semitone 3: 2 784/729 125.922 cents two (Archytas' 1/3-tone) 3: 2 35/32 155.140 cents septimal neutral second 3: 4 9/8 203.910 cents major whole tone 3: 2 75/64 274.582 cents classic augmented second 3: 1 98/81 329.832 cents 4: 2 729/686 105.252 cents 4: 2 16/15 111.731 cents minor diatonic semitone 4: 4 15/14 119.443 cents major diatonic semitone 4: 1 784/729 125.922 cents two (Archytas' 1/3-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: 4 245/216 218.101 cents 4: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 4: 2 6/5 315.641 cents minor third 4: 2 175/144 337.543 cents 5: 2 15/14 119.443 cents major diatonic semitone 5: 2 192/175 160.502 cents septimal 4/5-tone 5: 2 54/49 168.213 cents Zalzal's mujannab 5: 2 448/405 174.692 cents 5: 2 10/9 182.404 cents minor whole tone 5: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 5: 8 7/6 266.871 cents septimal minor third 5: 2 135/112 323.353 cents septimal wide minor third 5: 1 625/512 345.255 cents classic neutral third 5: 2 56/45 378.602 cents septimal narrow major third 6: 2 54/49 168.213 cents Zalzal's mujannab 6: 2 10/9 182.404 cents minor whole tone 6: 3 256/225 223.463 cents Neapolitan diminished third 6: 2 7/6 266.871 cents septimal minor third 6: 2 75/64 274.582 cents classic augmented second 6: 2 1715/1458 281.061 cents 6: 6 6/5 315.641 cents minor third 6: 2 243/196 372.123 cents 6: 4 5/4 386.314 cents major third 7: 4 8/7 231.174 cents septimal whole tone 7: 4 6/5 315.641 cents minor third 7: 2 135/112 323.353 cents septimal wide minor third 7: 6 98/81 329.832 cents 7: 2 216/175 364.412 cents 7: 2 5/4 386.314 cents major third 7: 2 1125/896 394.025 cents 7: 1 32/25 427.373 cents classic diminished fourth 7: 2 9/7 435.084 cents septimal major third, BP third 8: 2 32/27 294.135 cents Pythagorean minor third 8: 2 135/112 323.353 cents septimal wide minor third 8: 2 175/144 337.543 cents 8: 2 216/175 364.412 cents 8: 8 56/45 378.602 cents septimal narrow major third 8: 1 81/64 407.820 cents Pythagorean major third 8: 4 9/7 435.084 cents septimal major third, BP third 8: 2 2025/1568 442.796 cents 8: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 9: 2 243/196 372.123 cents 9: 2 56/45 378.602 cents septimal narrow major third 9: 4 5/4 386.314 cents major third 9: 2 2744/2187 392.793 cents 9: 4 32/25 427.373 cents classic diminished fourth 9: 1 2025/1568 442.796 cents 9: 2 125/96 456.986 cents classic augmented third 9: 2 21/16 470.781 cents narrow fourth 9: 2 324/245 483.854 cents 9: 4 4/3 498.045 cents perfect fourth 10: 2 5/4 386.314 cents major third 10: 2 32/25 427.373 cents classic diminished fourth 10: 4 9/7 435.084 cents septimal major third, BP third 10: 4 1568/1215 441.563 cents 10: 2 3645/2744 491.566 cents 10: 2 4/3 498.045 cents perfect fourth 10: 2 75/56 505.757 cents marvelous fourth 10: 2 27/20 519.551 cents acute fourth 10: 1 49/36 533.742 cents Arabic lute acute fourth 10: 2 112/81 561.006 cents 10: 2 45/32 590.224 cents diatonic tritone 11: 2 9/7 435.084 cents septimal major third, BP third 11: 4 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 11: 2 1152/875 476.143 cents 11: 2 896/675 490.333 cents 11: 2 75/56 505.757 cents marvelous fourth 11: 2 49/36 533.742 cents Arabic lute acute fourth 11: 1 6561/4802 540.336 cents 11: 2 48/35 546.815 cents septimal semi-augmented fourth 11: 2 25/18 568.717 cents classic augmented fourth 11: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 11: 2 81/56 638.994 cents 11: 2 35/24 653.185 cents septimal semi-diminished fifth 12: 2 324/245 483.854 cents 12: 2 896/675 490.333 cents 12: 4 4/3 498.045 cents perfect fourth 12: 4 135/98 554.527 cents 12: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 12: 2 343/243 596.703 cents 12: 2 64/45 609.776 cents 2nd tritone 12: 1 36/25 631.283 cents classic diminished fifth 12: 2 35/24 653.185 cents septimal semi-diminished fifth 12: 2 375/256 660.896 cents double augmented fourth 12: 2 3/2 701.955 cents perfect fifth 13: 2 4/3 498.045 cents perfect fourth 13: 2 512/375 539.104 cents double diminished fifth 13: 2 48/35 546.815 cents septimal semi-augmented fourth 13: 1 25/18 568.717 cents classic augmented fourth 13: 2 45/32 590.224 cents diatonic tritone 13: 2 486/343 603.297 cents 13: 2 10/7 617.488 cents Euler's tritone 13: 4 196/135 645.473 cents 13: 4 3/2 701.955 cents perfect fifth 13: 2 675/448 709.667 cents 13: 2 245/162 716.146 cents 14: 2 48/35 546.815 cents septimal semi-augmented fourth 14: 2 112/81 561.006 cents 14: 2 10/7 617.488 cents Euler's tritone 14: 2 36/25 631.283 cents classic diminished fifth 14: 2 35/24 653.185 cents septimal semi-diminished fifth 14: 1 9604/6561 659.664 cents 14: 2 72/49 666.258 cents Arabic lute grave fifth 14: 2 112/75 694.243 cents marvelous fifth 14: 2 675/448 709.667 cents 14: 2 875/576 723.857 cents 14: 4 54/35 750.725 cents septimal semi-augmented fifth 14: 2 14/9 764.916 cents septimal minor sixth 15: 2 64/45 609.776 cents 2nd tritone 15: 2 81/56 638.994 cents 15: 1 72/49 666.258 cents Arabic lute grave fifth 15: 2 40/27 680.449 cents grave fifth 15: 2 112/75 694.243 cents marvelous fifth 15: 2 3/2 701.955 cents perfect fifth 15: 2 5488/3645 708.434 cents 15: 4 1215/784 758.437 cents 15: 4 14/9 764.916 cents septimal minor sixth 15: 2 25/16 772.627 cents classic augmented fifth 15: 2 8/5 813.686 cents minor sixth 16: 4 3/2 701.955 cents perfect fifth 16: 2 245/162 716.146 cents 16: 2 32/21 729.219 cents wide fifth 16: 2 192/125 743.014 cents classic diminished sixth 16: 1 3136/2025 757.204 cents two (septimal narrow major third) 16: 4 25/16 772.627 cents classic augmented fifth 16: 2 2187/1372 807.207 cents 16: 4 8/5 813.686 cents minor sixth 16: 2 45/28 821.398 cents septimale wide minor sixth 16: 2 392/243 827.877 cents 17: 2 54/35 750.725 cents septimal semi-augmented fifth 17: 2 3136/2025 757.204 cents two (septimal narrow major third) 17: 4 14/9 764.916 cents septimal minor sixth 17: 1 128/81 792.180 cents Pythagorean minor sixth 17: 8 45/28 821.398 cents septimale wide minor sixth 17: 2 175/108 835.588 cents 17: 2 288/175 862.457 cents 17: 2 224/135 876.647 cents narrow septimal major sixth 17: 2 27/16 905.865 cents Pythagorean major sixth 18: 2 14/9 764.916 cents septimal minor sixth 18: 1 25/16 772.627 cents classic augmented fifth 18: 2 1792/1125 805.975 cents 18: 2 8/5 813.686 cents minor sixth 18: 2 175/108 835.588 cents 18: 6 81/49 870.168 cents two (septimal major third, BP third) 18: 2 224/135 876.647 cents narrow septimal major sixth 18: 4 5/3 884.359 cents major sixth, BP sixth 18: 4 7/4 968.826 cents harmonic seventh 19: 4 8/5 813.686 cents minor sixth 19: 2 392/243 827.877 cents 19: 6 5/3 884.359 cents major sixth, BP sixth 19: 2 2916/1715 918.939 cents 19: 2 128/75 925.418 cents diminished seventh 19: 2 12/7 933.129 cents septimal major sixth 19: 3 225/128 976.537 cents augmented sixth 19: 2 9/5 1017.596 cents just minor seventh, BP seventh 19: 2 49/27 1031.787 cents 20: 2 45/28 821.398 cents septimale wide minor sixth 20: 1 1024/625 854.745 cents two (classic diminished fourth) 20: 2 224/135 876.647 cents narrow septimal major sixth 20: 8 12/7 933.129 cents septimal major sixth 20: 2 140/81 947.320 cents 20: 2 9/5 1017.596 cents just minor seventh, BP seventh 20: 2 405/224 1025.308 cents 20: 2 49/27 1031.787 cents 20: 2 175/96 1039.498 cents 20: 2 28/15 1080.557 cents grave major seventh 21: 2 288/175 862.457 cents 21: 2 5/3 884.359 cents major sixth, BP sixth 21: 2 140/81 947.320 cents 21: 4 432/245 981.899 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: 1 729/392 1074.078 cents 21: 4 28/15 1080.557 cents grave major seventh 21: 2 15/8 1088.269 cents classic major seventh 21: 2 1372/729 1094.748 cents 22: 1 81/49 870.168 cents two (septimal major third, BP third) 22: 2 128/75 925.418 cents diminished seventh 22: 4 16/9 996.090 cents Pythagorean minor seventh 22: 2 64/35 1044.860 cents septimal neutral seventh 22: 2 729/392 1074.078 cents 22: 8 15/8 1088.269 cents classic major seventh 22: 2 1225/648 1102.459 cents 22: 2 48/25 1129.328 cents classic diminished octave 22: 2 784/405 1143.518 cents 23: 2 12/7 933.129 cents septimal major sixth 23: 2 64/35 1044.860 cents septimal neutral seventh 23: 2 448/243 1059.051 cents 23: 2 15/8 1088.269 cents classic major seventh 23: 1 1225/648 1102.459 cents 23: 2 48/25 1129.328 cents classic diminished octave 23: 8 27/14 1137.039 cents septimal major seventh 23: 2 784/405 1143.518 cents 23: 4 35/18 1151.230 cents septimal semi-diminished octave 24: 1 16/9 996.090 cents Pythagorean minor seventh 24: 2 256/135 1107.821 cents octave - major chroma 24: 4 27/14 1137.039 cents septimal major seventh 24: 8 35/18 1151.230 cents septimal semi-diminished octave 24: 2 125/64 1158.941 cents classic augmented seventh, octave - minor diesis 24: 4 486/245 1185.809 cents 24: 4 448/225 1192.288 cents Highest number of different intervals for one interval class: 12 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 63.0 111.7 203.9 266.9 315.6 329.8 378.6 386.3 427.4 435.1 498.0 702.0 764.9 772.6 813.7 821.4 870.2 884.4 933.1 996.1 1088.3 1137.0 1151.2 1200.0 48.8 : 14.2 63.0 155.1 218.1 266.9 281.1 329.8 337.5 378.6 386.3 449.3 653.2 716.1 723.9 764.9 772.6 821.4 835.6 884.4 947.3 1039.5 1088.3 1102.5 1151.2 1200.0 63.0 : 48.8 140.9 203.9 252.7 266.9 315.6 323.4 364.4 372.1 435.1 639.0 702.0 709.7 750.7 758.4 807.2 821.4 870.2 933.1 1025.3 1074.1 1088.3 1137.0 1185.8 1200.0 111.7 : 92.2 155.1 203.9 218.1 266.9 274.6 315.6 323.4 386.3 590.2 653.2 660.9 702.0 709.7 758.4 772.6 821.4 884.4 976.5 1025.3 1039.5 1088.3 1137.0 1151.2 1200.0 203.9 : 63.0 111.7 125.9 174.7 182.4 223.5 231.2 294.1 498.0 561.0 568.7 609.8 617.5 666.3 680.4 729.2 792.2 884.4 933.1 947.3 996.1 1044.9 1059.1 1107.8 1200.0 266.9 : 48.8 63.0 111.7 119.4 160.5 168.2 231.2 435.1 498.0 505.8 546.8 554.5 603.3 617.5 666.3 729.2 821.4 870.2 884.4 933.1 981.9 996.1 1044.9 1137.0 1200.0 315.6 : 14.2 63.0 70.7 111.7 119.4 182.4 386.3 449.3 457.0 498.0 505.8 554.5 568.7 617.5 680.4 772.6 821.4 835.6 884.4 933.1 947.3 996.1 1088.3 1151.2 1200.0 329.8 : 48.8 56.5 97.5 105.3 168.2 372.1 435.1 442.8 483.9 491.6 540.3 554.5 603.3 666.3 758.4 807.2 821.4 870.2 918.9 933.1 981.9 1074.1 1137.0 1185.8 1200.0 378.6 : 7.7 48.8 56.5 119.4 323.4 386.3 394.0 435.1 442.8 491.6 505.8 554.5 617.5 709.7 758.4 772.6 821.4 870.2 884.4 933.1 1025.3 1088.3 1137.0 1151.2 1200.0 386.3 : 41.1 48.8 111.7 315.6 378.6 386.3 427.4 435.1 483.9 498.0 546.8 609.8 702.0 750.7 764.9 813.7 862.5 876.6 925.4 1017.6 1080.6 1129.3 1143.5 1192.3 1200.0 427.4 : 7.7 70.7 274.6 337.5 345.3 386.3 394.0 442.8 457.0 505.8 568.7 660.9 709.7 723.9 772.6 821.4 835.6 884.4 976.5 1039.5 1088.3 1102.5 1151.2 1158.9 1200.0 435.1 : 63.0 266.9 329.8 337.5 378.6 386.3 435.1 449.3 498.0 561.0 653.2 702.0 716.1 764.9 813.7 827.9 876.6 968.8 1031.8 1080.6 1094.7 1143.5 1151.2 1192.3 1200.0 498.0 : 203.9 266.9 274.6 315.6 323.4 372.1 386.3 435.1 498.0 590.2 639.0 653.2 702.0 750.7 764.9 813.7 905.9 968.8 1017.6 1031.8 1080.6 1088.3 1129.3 1137.0 1200.0 702.0 : 63.0 70.7 111.7 119.4 168.2 182.4 231.2 294.1 386.3 435.1 449.3 498.0 546.8 561.0 609.8 702.0 764.9 813.7 827.9 876.6 884.4 925.4 933.1 996.1 1200.0 764.9 : 7.7 48.8 56.5 105.3 119.4 168.2 231.2 323.4 372.1 386.3 435.1 483.9 498.0 546.8 639.0 702.0 750.7 764.9 813.7 821.4 862.5 870.2 933.1 1137.0 1200.0 772.6 : 41.1 48.8 97.5 111.7 160.5 223.5 315.6 364.4 378.6 427.4 476.1 490.3 539.1 631.3 694.2 743.0 757.2 806.0 813.7 854.7 862.5 925.4 1129.3 1192.3 1200.0 813.7 : 7.7 56.5 70.7 119.4 182.4 274.6 323.4 337.5 386.3 435.1 449.3 498.0 590.2 653.2 702.0 716.1 764.9 772.6 813.7 821.4 884.4 1088.3 1151.2 1158.9 1200.0 821.4 : 48.8 63.0 111.7 174.7 266.9 315.6 329.8 378.6 427.4 441.6 490.3 582.5 645.5 694.2 708.4 757.2 764.9 806.0 813.7 876.6 1080.6 1143.5 1151.2 1192.3 1200.0 870.2 : 14.2 63.0 125.9 218.1 266.9 281.1 329.8 378.6 392.8 441.6 533.7 596.7 645.5 659.7 708.4 716.1 757.2 764.9 827.9 1031.8 1094.7 1102.5 1143.5 1151.2 1200.0 884.4 : 48.8 111.7 203.9 252.7 266.9 315.6 364.4 378.6 427.4 519.6 582.5 631.3 645.5 694.2 702.0 743.0 750.7 813.7 1017.6 1080.6 1088.3 1129.3 1137.0 1185.8 1200.0 933.1 : 63.0 155.1 203.9 218.1 266.9 315.6 329.8 378.6 470.8 533.7 582.5 596.7 645.5 653.2 694.2 702.0 764.9 968.8 1031.8 1039.5 1080.6 1088.3 1137.0 1151.2 1200.0 996.1 : 92.2 140.9 155.1 203.9 252.7 266.9 315.6 407.8 470.8 519.6 533.7 582.5 590.2 631.3 639.0 702.0 905.9 968.8 976.5 1017.6 1025.3 1074.1 1088.3 1137.0 1200.0 1088.3: 48.8 63.0 111.7 160.5 174.7 223.5 315.6 378.6 427.4 441.6 490.3 498.0 539.1 546.8 609.8 813.7 876.6 884.4 925.4 933.1 981.9 996.1 1044.9 1107.8 1200.0 1137.0: 14.2 63.0 111.7 125.9 174.7 266.9 329.8 378.6 392.8 441.6 449.3 490.3 498.0 561.0 764.9 827.9 835.6 876.6 884.4 933.1 947.3 996.1 1059.1 1151.2 1200.0 1151.2: 48.8 97.5 111.7 160.5 252.7 315.6 364.4 378.6 427.4 435.1 476.1 483.9 546.8 750.7 813.7 821.4 862.5 870.2 918.9 933.1 981.9 1044.9 1137.0 1185.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 7.7115 .. 203.9100 cents 28/25, 196.1985 cents 225/224, 7.7115 cents 2: 48.7704 .. 266.8709 cents 245/216, 218.1005 cents 32/35,-155.1396 cents 3: 56.4819 .. 329.8318 cents 38416/32805, 273.3499 cents 1215/1372,-210.3890 cents 4: 105.2523 .. 337.5433 cents 60025/52488, 232.2910 cents 59049/67228,-224.5795 cents 5: 119.4428 .. 378.6022 cents 784/675, 259.1594 cents 216/245,-218.1005 cents 6: 168.2132 .. 386.3137 cents 245/216, 218.1005 cents 1215/1372,-210.3890 cents 7: 231.1741 .. 435.0841 cents 9/8, 203.9100 cents 32/35,-155.1396 cents 8: 294.1350 .. 449.2746 cents 35/32, 155.1396 cents 224/243,-140.9491 cents 9: 372.1232 .. 498.0450 cents 784/729, 125.9218 cents 6561/6860,-77.1514 cents 10: 386.3137 .. 590.2237 cents 9/8, 203.9100 cents 15/16,-111.7313 cents 11: 435.0841 .. 653.1846 cents 245/216, 218.1005 cents 32/35,-155.1396 cents 12: 483.8545 .. 701.9550 cents 245/216, 218.1005 cents 7776/8575,-169.3301 cents 13: 498.0450 .. 716.1455 cents 245/216, 218.1005 cents 8/9,-203.9100 cents 14: 546.8154 .. 764.9159 cents 245/216, 218.1005 cents 7776/8575,-169.3301 cents 15: 609.7763 .. 813.6863 cents 9/8, 203.9100 cents 32/35,-155.1396 cents 16: 701.9550 .. 827.8768 cents 784/729, 125.9218 cents 15/16,-111.7313 cents 17: 750.7254 .. 905.8650 cents 35/32, 155.1396 cents 6561/6860,-77.1514 cents 18: 764.9159 .. 968.8259 cents 9/8, 203.9100 cents 224/243,-140.9491 cents 19: 813.6863 .. 1031.7868 cents 245/216, 218.1005 cents 32/35,-155.1396 cents 20: 821.3978 .. 1080.5572 cents 784/675, 259.1594 cents 1215/1372,-210.3890 cents 21: 862.4567 .. 1094.7477 cents 60025/52488, 232.2910 cents 216/245,-218.1005 cents 22: 870.1682 .. 1143.5181 cents 38416/32805, 273.3499 cents 59049/67228,-224.5795 cents 23: 933.1291 .. 1151.2296 cents 245/216, 218.1005 cents 1215/1372,-210.3890 cents 24: 996.0900 .. 1192.2885 cents 28/25, 196.1985 cents 32/35,-155.1396 cents
SHOW DATA
Number of notes : 25 -- Interval properties -- Smallest interval : 225/224, 7.7115 cents, class 1 Average step (divided formal octave): 48.0000 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 6.224451 Largest / Average step : 4.248125 Largest / Smallest step : 26.442248 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 : 48.24985 cents, oct.: 1206.24621 cents Scale is not proper Step pattern alph. order: ABACDABAEFEDGDEFEABADCABA Step pattern size order : DBDFEDBDACAEGEACADBDEFDBD Scale is not a Constant Structure Scale diversity : 1.420649 Lumma stability : 0.012853 Lumma impropriety factor : 0.918716 Number of different interval sizes : 128 = 5.33333 / class Number of one step interval sizes : 7 Highest interval variety : 12 Mean interval variety : 9.75000 = 39/4 Median interval variety : 8 Lowest interval variety : 7 Smallest interval difference : 2460375/2458624, 1.2325 cents Number of recognisable fifths : 26, average 704.6365 cents Number of appreciable fifths : 22, average 702.5440 cents Scale contains a complete diamond : 1 3 5 15 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% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 12-13 -- Rational properties -- Prime limit : 7 Odd number limit : 6561 (O: 6561 U: 6561) Highest odd numerator or denominator: 81 Scale harmonicity : 0.010301 Average absolute harmonicity : 0.120717 Specific harmonicity : 0.089011 Fundamental : 1/1587600, -20.5984 octaves, 0.0002 Hz. Guide tone : 3175200, 21.5984 octaves, 830713494.944 Hz. Exponens Consonantiae : 5.040948E+12, 42.19683 octaves Euler's gradus suavitatis : 66 Sum of Mann's harmonic distance : 512.0, average 20.48000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 27.47961, average 1.09918 Sum of Tenney's harmonic distance : 54.49803, average 2.17992 Vogel's harmonic complexity : 40.52000 Wille's k value : 1240312 Wilson's harmonic complexity : 72 Rectangular lattice diameter : 16 Triangular lattice diameter : 8 Lattice compactness : 1357.94088, average 4.17828 Lattice compactness (without 2's) : 913.31906, average 2.81021 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -4 .. 5 0.52000 49 1 3: -4 .. 4 0.00000 38 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: 66 / 25 = 2.64000
FIT/MODE
25: 1 0 1 2 2 1 0 1 0 1 0 1 5 1 0 1 0 1 0 1 2 2 1 0 1 N I SD: 12.3410 c. M: 21.1291 c. 28: 1 0 2 2 1 1 1 1 0 1 0 2 4 2 0 1 0 1 1 1 1 2 2 0 1 N I SD: 11.6546 c. M: 20.1038 c. 29: 1 1 1 2 1 2 0 1 0 1 1 1 5 1 1 1 0 1 0 2 1 2 1 1 1 N I SD: 12.6973 c. M: 20.0883 c. 30: 1 1 1 2 2 1 0 1 1 1 0 1 6 1 0 1 1 1 0 1 2 2 1 1 1 N I SD: 11.9383 c. M: 18.6022 c. 31: 1 1 1 2 2 1 1 1 0 1 0 2 5 2 0 1 0 1 1 1 2 2 1 1 1 N I SD: 9.0411 c. M: 18.5553 c. 32: 1 1 1 2 2 1 1 1 0 1 1 1 6 1 1 1 0 1 1 1 2 2 1 1 1 N I SD: 11.1723 c. M:-16.4100 c. 34: 1 1 1 3 2 1 0 2 0 1 0 2 6 2 0 1 0 2 0 1 2 3 1 1 1 N I SD: 8.8908 c. M: 15.4820 c. 38: 2 0 2 2 2 2 0 2 0 2 0 2 6 2 0 2 0 2 0 2 2 2 2 0 2 N I SD: 10.5866 c. M: 14.7327 c. 39: 2 0 2 3 2 1 1 1 1 1 0 2 7 2 0 1 1 1 1 1 2 3 2 0 2 N I SD: 8.9548 c. M: 13.6863 c. 41: 2 0 2 3 2 2 0 2 0 2 0 2 7 2 0 2 0 2 0 2 2 3 2 0 2 N I SD: 5.9821 c. M: 11.6518 c. 49: 2 1 2 3 3 2 0 2 1 1 1 2 9 2 1 1 1 2 0 2 3 3 2 1 2 N I SD: 8.0722 c. M: 11.4645 c. 50: 2 1 2 3 3 2 1 2 0 2 0 3 8 3 0 2 0 2 1 2 3 3 2 1 2 N I SD: 6.0196 c. M:-11.9100 c. 53: 2 1 2 4 3 2 1 2 0 2 0 3 9 3 0 2 0 2 1 2 3 4 2 1 2 N I SD: 4.3227 c. M: 9.7908 c. 54: 2 1 2 4 3 2 1 2 0 2 1 2 10 2 1 2 0 2 1 2 3 4 2 1 2 N I SD: 5.3101 c. M: 9.3603 c. 57: 2 1 2 5 3 2 1 2 0 2 1 3 9 3 1 2 0 2 1 2 3 5 2 1 2 N I SD: 5.8061 c. M: 7.3663 c. 58: 2 1 2 5 3 2 1 2 1 2 0 3 10 3 0 2 1 2 1 2 3 5 2 1 2 N I SD: 4.9346 c. M:-8.2830 c. 69: 3 1 2 6 3 3 1 3 0 3 0 4 11 4 0 3 0 3 1 3 3 6 2 1 3 N I SD: 4.9010 c. M:-7.4100 c. 72: 3 1 3 5 4 3 1 3 0 3 0 4 12 4 0 3 0 3 1 3 4 5 3 1 3 N I SD: 3.3696 c. M: 5.9608 c. 77: 3 1 3 6 4 3 1 3 1 2 1 4 13 4 1 2 1 3 1 3 4 6 3 1 3 N I SD: 3.0519 c. M: 6.5934 c. 90: 4 1 3 7 5 4 1 3 1 3 1 4 16 4 1 3 1 3 1 4 5 7 3 1 4 N I SD: 3.8110 c. M: 5.2689 c. 91: 4 1 3 7 5 4 1 4 0 3 1 5 15 5 1 3 0 4 1 4 5 7 3 1 4 N I SD: 3.7904 c. M:-6.2368 c. 94: 4 1 4 7 5 4 1 4 0 3 1 5 16 5 1 3 0 4 1 4 5 7 4 1 4 N I SD: 2.8678 c. M: 6.0960 c. 96: 4 1 4 7 5 4 1 4 1 3 1 5 16 5 1 3 1 4 1 4 5 7 4 1 4 N I SD: 2.8227 c. M: 4.8318 c. 99: 4 1 4 8 5 4 1 4 1 3 1 5 17 5 1 3 1 4 1 4 5 8 4 1 4 N I SD: 1.9429 c. M:-3.1301 c. 118: 5 1 5 9 6 5 1 5 1 4 1 6 20 6 1 4 1 5 1 5 6 9 5 1 5 N I SD: 1.8862 c. M: 4.4081 c. 130: 5 2 5 10 7 5 2 5 1 4 1 7 22 7 1 4 1 5 2 5 7 10 5 2 5 N I SD: 1.6114 c. M: 2.7572 c. 149: 6 2 6 11 8 6 2 6 1 5 1 8 25 8 1 5 1 6 2 6 8 11 6 2 6 N I SD: 1.1231 c. M:-2.5677 c. 152: 6 2 6 12 8 6 2 6 1 5 1 8 26 8 1 5 1 6 2 6 8 12 6 2 6 N I SD: 1.0393 c. M: 1.7471 c. 171: 7 2 7 13 9 7 2 7 1 6 1 9 29 9 1 6 1 7 2 7 9 13 7 2 7 N I SD: 0.3414 c. M: 0.6976 c. 419: 17 5 17 32 22 17 5 17 3 14 3 22 71 22 3 14 3 17 5 17 22 32 17 5 17 N I SD: 0.4163 c. M: 0.6423 c. 441: 18 5 18 34 23 18 5 18 3 15 3 23 75 23 3 15 3 18 5 18 23 34 18 5 18 N I SD: 0.2657 c. M: 0.5801 c. 494: 20 6 20 38 26 20 6 20 3 17 3 26 84 26 3 17 3 20 6 20 26 38 20 6 20 N I SD: 0.2429 c. M: 0.5326 c. 590: 24 7 24 45 31 24 7 24 4 20 4 31 100 31 4 20 4 24 7 24 31 45 24 7 24 N I SD: 0.2849 c. M:-0.5202 c. 593: 24 7 24 46 31 24 7 24 4 20 4 31 101 31 4 20 4 24 7 24 31 46 24 7 24 N I SD: 0.2610 c. M:-0.4745 c. 612: 25 7 25 47 32 25 7 25 4 21 4 32 104 32 4 21 4 25 7 25 32 47 25 7 25 N I SD: 0.1814 c. M: 0.4200 c. 665: 27 8 27 51 35 27 8 27 4 23 4 35 113 35 4 23 4 27 8 27 35 51 27 8 27 N I SD: 0.2091 c. M:-0.3938 c. 742: 30 9 30 57 39 30 9 30 5 25 5 39 126 39 5 25 5 30 9 30 39 57 30 9 30 N I SD: 0.1903 c. M: 0.4184 c. 764: 31 9 31 59 40 31 9 31 5 26 5 40 130 40 5 26 5 31 9 31 40 59 31 9 31 N I SD: 0.1338 c. M:-0.2785 c. 913: 37 11 37 70 48 37 11 37 6 31 6 48 155 48 6 31 6 37 11 37 48 70 37 11 37 N I SD: 0.1224 c. M: 0.2094 c. 935: 38 11 38 72 49 38 11 38 6 32 6 49 159 49 6 32 6 38 11 38 49 72 38 11 38 N I SD: 0.0656 c. M:-0.1542 c. 1106: 45 13 45 85 58 45 13 45 7 38 7 58 188 58 7 38 7 45 13 45 58 85 45 13 45 N I SD: 0.0564 c. M: 0.1139 c. 1848: 75 22 75 142 97 75 22 75 12 63 12 97 314 97 12 63 12 75 22 75 97 142 75 22 75 N I SD: 0.0458 c. M: 0.0998 c. 2019: 82 24 82 155 106 82 24 82 13 69 13 106 343 106 13 69 13 82 24 82 106 155 82 24 82 N I SD: 0.0282 c. M:-0.0467 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: 17.4324 cents 6 .. 12 match: 6 H SD: 6.4843 cents 7 .. 14 match: 6 SD: 5.5655 cents 8 .. 16 match: 8 H SD: 7.8534 cents 9 .. 18 match: 8 S SD: 3.8216 cents 10 .. 20 match: 9 SD: 6.1642 cents 11 .. 22 match: 10 SD: 7.7802 cents 12 .. 24 match: 10 SD: 4.3673 cents 13 .. 26 match: 11 SD: 5.4737 cents 14 .. 28 match: 13 SD: 3.7111 cents 15 .. 30 match: 13 SD: 3.4560 cents 16 .. 32 match: 13 S SD: 4.0177 cents 17 .. 34 match: 14 SD: 3.7696 cents 18 .. 36 match: 15 S SD: 2.4536 cents 19 .. 38 match: 15 SD: 4.9638 cents 20 .. 40 match: 15 SD: 3.7611 cents 21 .. 42 match: 15 SD: 3.5840 cents 22 .. 44 match: 17 SD: 3.4994 cents 23 .. 46 match: 18 SD: 3.5239 cents 24 .. 48 match: 19 SD: 2.5070 cents 25 .. 50 match: 19 SD: 2.6344 cents 26 .. 52 match: 19 SD: 2.9865 cents 27 .. 54 match: 18 SD: 2.9455 cents 28 .. 56 match: 18 SD: 2.5399 cents 29 .. 58 match: 18 SD: 2.5476 cents 30 .. 60 match: 18 SD: 2.1970 cents 31 .. 62 match: 19 SD: 2.2550 cents 32 .. 64 match: 18 SD: 1.8488 cents 33 .. 66 match: 18 SD: 2.2900 cents 34 .. 68 match: 20 SD: 2.3113 cents 35 .. 70 match: 18 SD: 2.1789 cents 36 .. 72 match: 19 SD: 2.0550 cents 37 .. 74 match: 21 SD: 2.3098 cents 38 .. 76 match: 19 SD: 2.0717 cents 39 .. 78 match: 20 SD: 1.9539 cents 40 .. 80 match: 20 SD: 1.5853 cents 41 .. 82 match: 21 SD: 1.9240 cents 42 .. 84 match: 24 SD: 1.7254 cents 43 .. 86 match: 20 SD: 1.7873 cents 44 .. 88 match: 22 SD: 1.9331 cents 45 .. 90 match: 20 SD: 1.6940 cents 46 .. 92 match: 21 SD: 1.6013 cents 47 .. 94 match: 21 SD: 1.7813 cents 48 .. 96 match: 20 SD: 1.3118 cents 49 .. 98 match: 21 SD: 1.4425 cents 50 .. 100 match: 20 SD: 1.5838 cents 51 .. 102 match: 24 SD: 1.7234 cents 52 .. 104 match: 22 SD: 1.6508 cents 53 .. 106 match: 19 SD: 1.4824 cents 54 .. 108 match: 21 SD: 1.1845 cents 55 .. 110 match: 22 SD: 1.3234 cents 56 .. 112 match: 20 SD: 1.0859 cents 57 .. 114 match: 21 SD: 1.1567 cents 58 .. 116 match: 22 SD: 1.2263 cents 59 .. 118 match: 20 SD: 1.2701 cents 60 .. 120 match: 21 SD: 1.0777 cents 61 .. 122 match: 20 SD: 1.2110 cents 62 .. 124 match: 24 SD: 1.2300 cents 63 .. 126 match: 19 SD: 1.1653 cents 64 .. 128 match: 20 SD: 0.9912 cents 65 .. 130 match: 22 SD: 1.1827 cents 66 .. 132 match: 22 SD: 0.9933 cents 67 .. 134 match: 23 SD: 1.1376 cents 68 .. 136 match: 20 SD: 1.3304 cents 69 .. 138 match: 23 SD: 1.1538 cents 70 .. 140 match: 23 SD: 1.0374 cents 71 .. 142 match: 23 SD: 0.9413 cents 72 .. 144 match: 24 SD: 0.7792 cents 73 .. 146 match: 21 SD: 0.9198 cents 74 .. 148 match: 24 SD: 0.9475 cents 75 .. 150 match: 23 SD: 0.9544 cents 76 .. 152 match: 23 SD: 0.9070 cents 77 .. 154 match: 22 SD: 0.9078 cents 78 .. 156 match: 22 SD: 0.8109 cents 79 .. 158 match: 24 SD: 0.9486 cents 80 .. 160 match: 24 SD: 0.7927 cents 81 .. 162 match: 22 SD: 0.8639 cents 82 .. 164 match: 23 SD: 0.9666 cents 83 .. 166 match: 23 SD: 0.9967 cents 84 .. 168 match: 22 SD: 0.8649 cents 85 .. 170 match: 23 SD: 0.8792 cents 86 .. 172 match: 23 SD: 0.8669 cents 87 .. 174 match: 25 SD: 0.8350 cents 88 .. 176 match: 20 SD: 0.8133 cents 89 .. 178 match: 22 SD: 0.7614 cents 90 .. 180 match: 24 SD: 0.6283 cents 91 .. 182 match: 22 SD: 0.8477 cents 92 .. 184 match: 23 SD: 0.8826 cents 93 .. 186 match: 21 SD: 0.9837 cents 94 .. 188 match: 24 SD: 0.7328 cents 95 .. 190 match: 23 SD: 0.7223 cents 96 .. 192 match: 23 SD: 0.7114 cents 97 .. 194 match: 24 SD: 0.8246 cents 99 .. 198 match: 24 SD: 0.7769 cents 100 .. 200 match: 24 SD: 0.7621 cents 101 .. 202 match: 23 SD: 0.6904 cents 102 .. 204 match: 23 SD: 0.6461 cents 103 .. 206 match: 24 SD: 0.6476 cents 104 .. 208 match: 25 SD: 0.5652 cents 105 .. 210 match: 24 SD: 0.5786 cents 106 .. 212 match: 23 SD: 0.6423 cents 108 .. 216 match: 25 SD: 0.5977 cents 109 .. 218 match: 22 SD: 0.6103 cents 110 .. 220 match: 24 SD: 0.5653 cents 111 .. 222 match: 23 SD: 0.6606 cents 112 .. 224 match: 25 SD: 0.6008 cents 113 .. 226 match: 23 SD: 0.6728 cents 114 .. 228 match: 25 SD: 0.5990 cents 115 .. 230 match: 25 SD: 0.5722 cents 116 .. 232 match: 24 SD: 0.7153 cents 117 .. 234 match: 23 SD: 0.7250 cents 118 .. 236 match: 24 SD: 0.6607 cents 119 .. 238 match: 25 SD: 0.5789 cents 120 .. 240 match: 24 SD: 0.5544 cents 121 .. 242 match: 23 SD: 0.6727 cents 122 .. 244 match: 25 SD: 0.6501 cents 124 .. 248 match: 24 SD: 0.6536 cents 125 .. 250 match: 24 SD: 0.6137 cents 126 .. 252 match: 25 SD: 0.5641 cents 127 .. 254 match: 23 SD: 0.6169 cents 128 .. 256 match: 25 SD: 0.5671 cents 129 .. 258 match: 24 SD: 0.5573 cents 130 .. 260 match: 25 SD: 0.5033 cents 131 .. 262 match: 24 SD: 0.6103 cents 132 .. 264 match: 25 SD: 0.4930 cents 133 .. 266 match: 24 SD: 0.5061 cents 134 .. 268 match: 24 SD: 0.5527 cents 135 .. 270 match: 25 SD: 0.4460 cents 138 .. 276 match: 24 SD: 0.4640 cents 139 .. 278 match: 25 SD: 0.4566 cents 144 .. 288 match: 25 SD: 0.3668 cents 145 .. 290 match: 24 SD: 0.5441 cents 146 .. 292 match: 25 SD: 0.5200 cents 147 .. 294 match: 25 SD: 0.4991 cents 150 .. 300 match: 25 SD: 0.4451 cents 152 .. 304 match: 24 SD: 0.4923 cents 153 .. 306 match: 25 SD: 0.4587 cents 159 .. 318 match: 24 SD: 0.5297 cents 160 .. 320 match: 25 SD: 0.4118 cents 162 .. 324 match: 25 SD: 0.4053 cents 165 .. 330 match: 25 SD: 0.4052 cents 167 .. 334 match: 25 SD: 0.3609 cents 168 .. 336 match: 25 SD: 0.3023 cents 210 .. 420 match: 25 SD: 0.2541 cents 240 .. 480 match: 25 SD: 0.2174 cents 270 .. 540 match: 25 SD: 0.1930 cents 318 .. 636 match: 25 SD: 0.1865 cents 320 .. 640 match: 25 SD: 0.1832 cents 343 .. 686 match: 25 SD: 0.1760 cents 360 .. 720 match: 25 SD: 0.1437 cents 432 .. 864 match: 25 SD: 0.1312 cents 450 .. 900 match: 25 SD: 0.1281 cents 480 .. 960 match: 25 SD: 0.1156 cents 486 .. 972 match: 25 SD: 0.1154 cents 504 .. 1008 match: 25 SD: 0.1119 cents 528 .. 1056 match: 25 SD: 0.1040 cents 560 .. 1120 match: 25 SD: 0.0980 cents 600 .. 1200 match: 25 SD: 0.0874 cents