Scala analysis: synstargam
Maximal harmony {81/80, 126/125, 1029/1024} Fokker block
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 200/189 97.936519 4: 35/32 155.139620 septimal neutral second 5: 10/9 182.403712 minor whole tone 6: 8/7 231.174094 septimal whole tone 7: 7/6 266.870906 septimal minor third 8: 25/21 301.846520 BP second, quasi-equal minor third 9: 175/144 337.543332 10: 5/4 386.313714 major third 11: 80/63 413.577806 wide major third 12: 21/16 470.780907 narrow fourth 13: 4/3 498.044999 perfect fourth 14: 175/128 541.453334 15: 25/18 568.717426 classic augmented fourth 16: 10/7 617.487807 Euler's tritone 17: 35/24 653.184619 septimal semi-diminished fifth 18: 3/2 701.955001 perfect fifth 19: 32/21 729.219093 wide fifth 20: 25/16 772.627428 classic augmented fifth 21: 100/63 799.891520 quasi-equal minor sixth 22: 105/64 857.094621 septimal neutral sixth 23: 5/3 884.358713 major sixth, BP sixth 24: 12/7 933.129094 septimal major sixth 25: 7/4 968.825906 harmonic seventh 26: 25/14 1003.801521 middle minor seventh 27: 175/96 1039.498333 28: 15/8 1088.268715 classic major seventh 29: 40/21 1115.532807 acute major seventh 30: 35/18 1151.229619 septimal semi-diminished octave 31: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 36/35 48.7704 septimal diesis, 1/4-tone 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 3: 64/63 27.2641 septimal comma, Archytas' comma 4: 1323/1280 57.2031 5: 64/63 27.2641 septimal comma, Archytas' comma 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 36/35 48.7704 septimal diesis, 1/4-tone 11: 64/63 27.2641 septimal comma, Archytas' comma 12: 1323/1280 57.2031 13: 64/63 27.2641 septimal comma, Archytas' comma 14: 525/512 43.4083 Avicenna enharmonic diesis 15: 64/63 27.2641 septimal comma, Archytas' comma 16: 36/35 48.7704 septimal diesis, 1/4-tone 17: 49/48 35.6968 slendro diesis, septimal 1/6-tone 18: 36/35 48.7704 septimal diesis, 1/4-tone 19: 64/63 27.2641 septimal comma, Archytas' comma 20: 525/512 43.4083 Avicenna enharmonic diesis 21: 64/63 27.2641 septimal comma, Archytas' comma 22: 1323/1280 57.2031 23: 64/63 27.2641 septimal comma, Archytas' comma 24: 36/35 48.7704 septimal diesis, 1/4-tone 25: 49/48 35.6968 slendro diesis, septimal 1/6-tone 26: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 27: 49/48 35.6968 slendro diesis, septimal 1/6-tone 28: 36/35 48.7704 septimal diesis, 1/4-tone 29: 64/63 27.2641 septimal comma, Archytas' comma 30: 49/48 35.6968 slendro diesis, septimal 1/6-tone 31: 36/35 48.7704 septimal diesis, 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 9 64/63 27.264 cents septimal comma, Archytas' comma 1: 3 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 7 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 525/512 43.408 cents Avicenna enharmonic diesis 1: 7 36/35 48.770 cents septimal diesis, 1/4-tone 1: 3 1323/1280 57.203 cents 2: 1 3200/3087 62.240 cents 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 9 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 6 256/245 76.034 cents septimal minor semitone 2: 14 21/20 84.467 cents minor semitone 3: 3 200/189 97.937 cents 3: 2 1225/1152 106.369 cents 3: 11 16/15 111.731 cents minor diatonic semitone 3: 8 15/14 119.443 cents major diatonic semitone 3: 1 343/320 120.164 cents 3: 2 2205/2048 127.876 cents 3: 4 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 4: 8 160/147 146.707 cents 4: 2 49/45 147.428 cents BP minor semitone 4: 12 35/32 155.140 cents septimal neutral second 4: 6 192/175 160.502 cents septimal 4/5-tone 4: 3 441/400 168.934 cents two (minor semitone) 5: 12 10/9 182.404 cents minor whole tone 5: 1 4096/3675 187.766 cents 5: 1 384/343 195.477 cents 5: 5 28/25 196.198 cents middle second 5: 12 9/8 203.910 cents major whole tone 6: 1 640/567 209.668 cents 6: 1 245/216 218.101 cents 6: 20 8/7 231.174 cents septimal whole tone 6: 1 343/300 231.895 cents 6: 8 147/128 239.607 cents 7: 5 512/441 258.438 cents 7: 1 400/343 266.150 cents 7: 14 7/6 266.871 cents septimal minor third 7: 3 75/64 274.582 cents classic augmented second 7: 3 288/245 279.944 cents 7: 5 189/160 288.377 cents 8: 3 32/27 294.135 cents Pythagorean minor third 8: 7 25/21 301.847 cents BP second, quasi-equal minor third 8: 1 343/288 302.568 cents 8: 2 1225/1024 310.279 cents two (septimal neutral second) 8: 18 6/5 315.641 cents minor third 9: 2 1600/1323 329.111 cents 9: 4 175/144 337.543 cents 9: 8 128/105 342.905 cents septimal neutral third 9: 4 60/49 350.617 cents smaller approximation to neutral third 9: 6 49/40 351.338 cents larger approximation to neutral third 9: 4 315/256 359.050 cents 9: 2 216/175 364.412 cents 9: 1 3969/3200 372.844 cents 10: 1 100/81 364.807 cents grave major third 10: 1 1280/1029 377.881 cents 10: 4 56/45 378.602 cents septimal narrow major third 10: 17 5/4 386.314 cents major third 10: 3 1536/1225 391.676 cents 10: 5 63/50 400.108 cents quasi-equal major third 11: 9 80/63 413.578 cents wide major third 11: 5 245/192 422.011 cents 11: 6 32/25 427.373 cents classic diminished fourth 11: 8 9/7 435.084 cents septimal major third, BP third 11: 1 1029/800 435.805 cents 11: 2 1323/1024 443.517 cents 12: 1 5120/3969 440.842 cents 12: 3 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 12: 10 64/49 462.348 cents 2 septatones or septatonic major third 12: 2 98/75 463.069 cents 12: 15 21/16 470.781 cents narrow fourth 13: 21 4/3 498.045 cents perfect fourth 13: 3 75/56 505.757 cents marvelous fourth 13: 1 343/256 506.478 cents 13: 6 27/20 519.551 cents acute fourth 14: 3 256/189 525.309 cents 14: 4 200/147 533.021 cents 14: 4 49/36 533.742 cents Arabic lute acute fourth 14: 4 175/128 541.453 cents 14: 11 48/35 546.815 cents septimal semi-augmented fourth 14: 5 441/320 555.248 cents 15: 7 25/18 568.717 cents classic augmented fourth 15: 4 1024/735 574.079 cents 15: 1 480/343 581.791 cents 15: 12 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 15: 5 45/32 590.224 cents diatonic tritone 15: 1 1728/1225 595.586 cents 15: 1 567/400 604.018 cents 16: 1 800/567 595.982 cents 16: 1 1225/864 604.414 cents 16: 5 64/45 609.776 cents 2nd tritone 16: 12 10/7 617.488 cents Euler's tritone 16: 1 343/240 618.209 cents 16: 4 735/512 625.921 cents 16: 7 36/25 631.283 cents classic diminished fifth 17: 5 640/441 644.752 cents 17: 11 35/24 653.185 cents septimal semi-diminished fifth 17: 4 256/175 658.547 cents 17: 4 72/49 666.258 cents Arabic lute grave fifth 17: 4 147/100 666.979 cents 17: 3 189/128 674.691 cents 18: 6 40/27 680.449 cents grave fifth 18: 1 512/343 693.522 cents 3 septatones or septatonic fifth 18: 3 112/75 694.243 cents marvelous fifth 18: 21 3/2 701.955 cents perfect fifth 19: 15 32/21 729.219 cents wide fifth 19: 2 75/49 736.931 cents BP fifth 19: 10 49/32 737.652 cents 19: 3 54/35 750.725 cents septimal semi-augmented fifth 19: 1 3969/2560 759.158 cents 20: 2 2048/1323 756.483 cents 20: 1 1600/1029 764.195 cents 20: 8 14/9 764.916 cents septimal minor sixth 20: 6 25/16 772.627 cents classic augmented fifth 20: 5 384/245 777.989 cents 20: 9 63/40 786.422 cents narrow minor sixth 21: 5 100/63 799.892 cents quasi-equal minor sixth 21: 3 1225/768 808.324 cents 21: 17 8/5 813.686 cents minor sixth 21: 4 45/28 821.398 cents septimale wide minor sixth 21: 1 1029/640 822.119 cents 21: 1 81/50 835.193 cents acute minor sixth 22: 1 6400/3969 827.156 cents two (wide major third) 22: 2 175/108 835.588 cents 22: 4 512/315 840.950 cents 22: 6 80/49 848.662 cents smaller approximation to neutral sixth 22: 4 49/30 849.383 cents larger approximation to neutral sixth 22: 8 105/64 857.095 cents septimal neutral sixth 22: 4 288/175 862.457 cents 22: 2 1323/800 870.889 cents 23: 18 5/3 884.359 cents major sixth, BP sixth 23: 2 2048/1225 889.721 cents 23: 1 576/343 897.432 cents 23: 7 42/25 898.153 cents quasi-equal major sixth 23: 3 27/16 905.865 cents Pythagorean major sixth 24: 5 320/189 911.623 cents 24: 3 245/144 920.056 cents 24: 3 128/75 925.418 cents diminished seventh 24: 14 12/7 933.129 cents septimal major sixth 24: 1 343/200 933.850 cents 24: 5 441/256 941.562 cents two (narrow fourth) 25: 8 256/147 960.393 cents 25: 1 600/343 968.105 cents 25: 20 7/4 968.826 cents harmonic seventh 25: 1 432/245 981.899 cents 25: 1 567/320 990.332 cents 26: 12 16/9 996.090 cents Pythagorean minor seventh 26: 5 25/14 1003.802 cents middle minor seventh 26: 1 343/192 1004.523 cents 26: 1 3675/2048 1012.234 cents 26: 12 9/5 1017.596 cents just minor seventh, BP seventh 27: 3 800/441 1031.066 cents 27: 6 175/96 1039.498 cents 27: 12 64/35 1044.860 cents septimal neutral seventh 27: 2 90/49 1052.572 cents 27: 8 147/80 1053.293 cents 28: 4 50/27 1066.762 cents grave major seventh 28: 2 4096/2205 1072.124 cents 28: 1 640/343 1079.836 cents 28: 8 28/15 1080.557 cents grave major seventh 28: 11 15/8 1088.269 cents classic major seventh 28: 2 2304/1225 1093.631 cents two (septimal semi-augmented fourth) 28: 3 189/100 1102.063 cents 29: 14 40/21 1115.533 cents acute major seventh 29: 6 245/128 1123.966 cents 29: 9 48/25 1129.328 cents classic diminished octave 29: 1 27/14 1137.039 cents septimal major seventh 29: 1 3087/1600 1137.760 cents 30: 3 2560/1323 1142.797 cents 30: 7 35/18 1151.230 cents septimal semi-diminished octave 30: 2 1024/525 1156.592 cents 30: 7 96/49 1164.303 cents 30: 3 49/25 1165.024 cents BP eighth 30: 9 63/32 1172.736 cents octave - septimal comma Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 5.73333 = 86/15
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 28 29 30 31 0.0 : 35.7 70.7 97.9 155.1 182.4 231.2 266.9 301.8 337.5 386.3 413.6 470.8 498.0 541.5 568.7 617.5 653.2 702.0 729.2 772.6 799.9 857.1 884.4 933.1 968.8 1003.8 1039.5 1088.3 1115.5 1151.2 1200.0 35.7 : 35.0 62.2 119.4 146.7 195.5 231.2 266.1 301.8 350.6 377.9 435.1 462.3 505.8 533.0 581.8 617.5 666.3 693.5 736.9 764.2 821.4 848.7 897.4 933.1 968.1 1003.8 1052.6 1079.8 1115.5 1164.3 1200.0 70.7 : 27.3 84.5 111.7 160.5 196.2 231.2 266.9 315.6 342.9 400.1 427.4 470.8 498.0 546.8 582.5 631.3 658.5 702.0 729.2 786.4 813.7 862.5 898.2 933.1 968.8 1017.6 1044.9 1080.6 1129.3 1165.0 1200.0 97.9 : 57.2 84.5 133.2 168.9 203.9 239.6 288.4 315.6 372.8 400.1 443.5 470.8 519.6 555.2 604.0 631.3 674.7 702.0 759.2 786.4 835.2 870.9 905.9 941.6 990.3 1017.6 1053.3 1102.1 1137.8 1172.7 1200.0 155.1 : 27.3 76.0 111.7 146.7 182.4 231.2 258.4 315.6 342.9 386.3 413.6 462.3 498.0 546.8 574.1 617.5 644.8 702.0 729.2 778.0 813.7 848.7 884.4 933.1 960.4 996.1 1044.9 1080.6 1115.5 1142.8 1200.0 182.4 : 48.8 84.5 119.4 155.1 203.9 231.2 288.4 315.6 359.0 386.3 435.1 470.8 519.6 546.8 590.2 617.5 674.7 702.0 750.7 786.4 821.4 857.1 905.9 933.1 968.8 1017.6 1053.3 1088.3 1115.5 1172.7 1200.0 231.2 : 35.7 70.7 106.4 155.1 182.4 239.6 266.9 310.3 337.5 386.3 422.0 470.8 498.0 541.5 568.7 625.9 653.2 702.0 737.7 772.6 808.3 857.1 884.4 920.1 968.8 1004.5 1039.5 1066.8 1124.0 1151.2 1200.0 266.9 : 35.0 70.7 119.4 146.7 203.9 231.2 274.6 301.8 350.6 386.3 435.1 462.3 505.8 533.0 590.2 617.5 666.3 702.0 736.9 772.6 821.4 848.7 884.4 933.1 968.8 1003.8 1031.1 1088.3 1115.5 1164.3 1200.0 301.8 : 35.7 84.5 111.7 168.9 196.2 239.6 266.9 315.6 351.3 400.1 427.4 470.8 498.0 555.2 582.5 631.3 667.0 702.0 737.7 786.4 813.7 849.4 898.2 933.9 968.8 996.1 1053.3 1080.6 1129.3 1165.0 1200.0 337.5 : 48.8 76.0 133.2 160.5 203.9 231.2 279.9 315.6 364.4 391.7 435.1 462.3 519.6 546.8 595.6 631.3 666.3 702.0 750.7 778.0 813.7 862.5 898.2 933.1 960.4 1017.6 1044.9 1093.6 1129.3 1164.3 1200.0 386.3 : 27.3 84.5 111.7 155.1 182.4 231.2 266.9 315.6 342.9 386.3 413.6 470.8 498.0 546.8 582.5 617.5 653.2 702.0 729.2 764.9 813.7 849.4 884.4 911.6 968.8 996.1 1044.9 1080.6 1115.5 1151.2 1200.0 413.6 : 57.2 84.5 127.9 155.1 203.9 239.6 288.4 315.6 359.0 386.3 443.5 470.8 519.6 555.2 590.2 625.9 674.7 702.0 737.7 786.4 822.1 857.1 884.4 941.6 968.8 1017.6 1053.3 1088.3 1124.0 1172.7 1200.0 470.8 : 27.3 70.7 97.9 146.7 182.4 231.2 258.4 301.8 329.1 386.3 413.6 462.3 498.0 533.0 568.7 617.5 644.8 680.4 729.2 764.9 799.9 827.2 884.4 911.6 960.4 996.1 1031.1 1066.8 1115.5 1142.8 1200.0 498.0 : 43.4 70.7 119.4 155.1 203.9 231.2 274.6 301.8 359.0 386.3 435.1 470.8 505.8 541.5 590.2 617.5 653.2 702.0 737.7 772.6 799.9 857.1 884.4 933.1 968.8 1003.8 1039.5 1088.3 1115.5 1172.7 1200.0 541.5 : 27.3 76.0 111.7 160.5 187.8 231.2 258.4 315.6 342.9 391.7 427.4 462.3 498.0 546.8 574.1 609.8 658.5 694.2 729.2 756.5 813.7 841.0 889.7 925.4 960.4 996.1 1044.9 1072.1 1129.3 1156.6 1200.0 568.7 : 48.8 84.5 133.2 160.5 203.9 231.2 288.4 315.6 364.4 400.1 435.1 470.8 519.6 546.8 582.5 631.3 667.0 702.0 729.2 786.4 813.7 862.5 898.2 933.1 968.8 1017.6 1044.9 1102.1 1129.3 1172.7 1200.0 617.5 : 35.7 84.5 111.7 155.1 182.4 239.6 266.9 315.6 351.3 386.3 422.0 470.8 498.0 533.7 582.5 618.2 653.2 680.4 737.7 764.9 813.7 849.4 884.4 920.1 968.8 996.1 1053.3 1080.6 1124.0 1151.2 1200.0 653.2 : 48.8 76.0 119.4 146.7 203.9 231.2 279.9 315.6 350.6 386.3 435.1 462.3 498.0 546.8 582.5 617.5 644.8 702.0 729.2 778.0 813.7 848.7 884.4 933.1 960.4 1017.6 1044.9 1088.3 1115.5 1164.3 1200.0 702.0 : 27.3 70.7 97.9 155.1 182.4 231.2 266.9 301.8 337.5 386.3 413.6 449.3 498.0 533.7 568.7 596.0 653.2 680.4 729.2 764.9 799.9 835.6 884.4 911.6 968.8 996.1 1039.5 1066.8 1115.5 1151.2 1200.0 729.2 : 43.4 70.7 127.9 155.1 203.9 239.6 274.6 310.3 359.0 386.3 422.0 470.8 506.5 541.5 568.7 625.9 653.2 702.0 737.7 772.6 808.3 857.1 884.4 941.6 968.8 1012.2 1039.5 1088.3 1124.0 1172.7 1200.0 772.6 : 27.3 84.5 111.7 160.5 196.2 231.2 266.9 315.6 342.9 378.6 427.4 463.1 498.0 525.3 582.5 609.8 658.5 694.2 729.2 764.9 813.7 841.0 898.2 925.4 968.8 996.1 1044.9 1080.6 1129.3 1156.6 1200.0 799.9 : 57.2 84.5 133.2 168.9 203.9 239.6 288.4 315.6 351.3 400.1 435.8 470.8 498.0 555.2 582.5 631.3 667.0 702.0 737.7 786.4 813.7 870.9 898.2 941.6 968.8 1017.6 1053.3 1102.1 1129.3 1172.7 1200.0 857.1 : 27.3 76.0 111.7 146.7 182.4 231.2 258.4 294.1 342.9 378.6 413.6 440.8 498.0 525.3 574.1 609.8 644.8 680.4 729.2 756.5 813.7 841.0 884.4 911.6 960.4 996.1 1044.9 1072.1 1115.5 1142.8 1200.0 884.4 : 48.8 84.5 119.4 155.1 203.9 231.2 266.9 315.6 351.3 386.3 413.6 470.8 498.0 546.8 582.5 617.5 653.2 702.0 729.2 786.4 813.7 857.1 884.4 933.1 968.8 1017.6 1044.9 1088.3 1115.5 1172.7 1200.0 933.1 : 35.7 70.7 106.4 155.1 182.4 218.1 266.9 302.6 337.5 364.8 422.0 449.3 498.0 533.7 568.7 604.4 653.2 680.4 737.7 764.9 808.3 835.6 884.4 920.1 968.8 996.1 1039.5 1066.8 1124.0 1151.2 1200.0 968.8 : 35.0 70.7 119.4 146.7 182.4 231.2 266.9 301.8 329.1 386.3 413.6 462.3 498.0 533.0 568.7 617.5 644.8 702.0 729.2 772.6 799.9 848.7 884.4 933.1 960.4 1003.8 1031.1 1088.3 1115.5 1164.3 1200.0 1003.8: 35.7 84.5 111.7 147.4 196.2 231.9 266.9 294.1 351.3 378.6 427.4 463.1 498.0 533.7 582.5 609.8 667.0 694.2 737.7 764.9 813.7 849.4 898.2 925.4 968.8 996.1 1053.3 1080.6 1129.3 1165.0 1200.0 1039.5: 48.8 76.0 111.7 160.5 196.2 231.2 258.4 315.6 342.9 391.7 427.4 462.3 498.0 546.8 574.1 631.3 658.5 702.0 729.2 778.0 813.7 862.5 889.7 933.1 960.4 1017.6 1044.9 1093.6 1129.3 1164.3 1200.0 1088.3: 27.3 63.0 111.7 147.4 182.4 209.7 266.9 294.1 342.9 378.6 413.6 449.3 498.0 525.3 582.5 609.8 653.2 680.4 729.2 764.9 813.7 841.0 884.4 911.6 968.8 996.1 1044.9 1080.6 1115.5 1151.2 1200.0 1115.5: 35.7 84.5 120.2 155.1 182.4 239.6 266.9 315.6 351.3 386.3 422.0 470.8 498.0 555.2 582.5 625.9 653.2 702.0 737.7 786.4 813.7 857.1 884.4 941.6 968.8 1017.6 1053.3 1088.3 1124.0 1172.7 1200.0 1151.2: 48.8 84.5 119.4 146.7 203.9 231.2 279.9 315.6 350.6 386.3 435.1 462.3 519.6 546.8 590.2 617.5 666.3 702.0 750.7 778.0 821.4 848.7 905.9 933.1 981.9 1017.6 1052.6 1088.3 1137.0 1164.3 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 57.2031 cents 83349/81920, 29.9390 cents 64/63, 27.2641 cents 2: 62.2397 .. 84.4672 cents 64827/64000, 22.2275 cents 4096000/4084101, 5.0366 cents 3: 97.9365 .. 133.2376 cents 5103/5000, 35.3011 cents 4000/3969, 13.4693 cents 4: 146.7069 .. 168.9344 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 5: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 6: 209.6678 .. 239.6068 cents 83349/81920, 29.9390 cents 5120/5103, 5.7578 cents 7: 258.4382 .. 288.3772 cents 83349/81920, 29.9390 cents 65536/64827, 18.8314 cents 8: 294.1350 .. 315.6413 cents 81/80, 21.5063 cents 5120/5103, 5.7578 cents 9: 329.1106 .. 372.8444 cents 5250987/5120000, 43.7338 cents 4000/3969, 13.4693 cents 10: 364.8074 .. 400.1085 cents 5103/5000, 35.3011 cents 320000/321489,-8.0370 cents 11: 413.5778 .. 443.5168 cents 83349/81920, 29.9390 cents 4000/3969, 13.4693 cents 12: 440.8419 .. 470.7809 cents 83349/81920, 29.9390 cents 5242880/5250987,-2.6749 cents 13: 498.0450 .. 519.5513 cents 81/80, 21.5063 cents 64/63, 27.2641 cents 14: 525.3091 .. 555.2481 cents 83349/81920, 29.9390 cents 5120/5103, 5.7578 cents 15: 568.7174 .. 604.0185 cents 5103/5000, 35.3011 cents 4000/3969, 13.4693 cents 16: 595.9815 .. 631.2826 cents 5103/5000, 35.3011 cents 320000/321489,-8.0370 cents 17: 644.7519 .. 674.6909 cents 83349/81920, 29.9390 cents 4000/3969, 13.4693 cents 18: 680.4487 .. 701.9550 cents 81/80, 21.5063 cents 5120/5103, 5.7578 cents 19: 729.2191 .. 759.1581 cents 83349/81920, 29.9390 cents 64/63, 27.2641 cents 20: 756.4832 .. 786.4222 cents 83349/81920, 29.9390 cents 5242880/5250987,-2.6749 cents 21: 799.8915 .. 835.1926 cents 5103/5000, 35.3011 cents 4000/3969, 13.4693 cents 22: 827.1556 .. 870.8894 cents 5250987/5120000, 43.7338 cents 320000/321489,-8.0370 cents 23: 884.3587 .. 905.8650 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 24: 911.6228 .. 941.5618 cents 83349/81920, 29.9390 cents 5120/5103, 5.7578 cents 25: 960.3932 .. 990.3322 cents 83349/81920, 29.9390 cents 65536/64827, 18.8314 cents 26: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 5120/5103, 5.7578 cents 27: 1031.0656 .. 1053.2931 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 28: 1066.7624 .. 1102.0635 cents 5103/5000, 35.3011 cents 4000/3969, 13.4693 cents 29: 1115.5328 .. 1137.7603 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 30: 1142.7969 .. 1172.7359 cents 83349/81920, 29.9390 cents 4096000/4084101, 5.0366 cents
SHOW DATA
Number of notes : 31 -- Interval properties -- Smallest interval : 64/63, 27.2641 cents, class 1 Average step (divided formal octave): 38.7097 cents Largest one step interval : 1323/1280, 57.2031 cents Average / Smallest step : 1.419804 Largest / Average step : 1.477747 Largest / Smallest step : 2.098111 Median interval of one step : 49/48, 35.6968 cents, amount: 7 Most common interval of one step : 64/63, 27.2641 cents, amount: 9 Least squares average step : 38.55795 cents, oct.: 1195.29640 cents Scale is not proper Step pattern alph. order: ABCDCEABAECDCFCEAECFCDCEABAECAE Step pattern size order : CBAFAECBCEAFADAECEADAFAECBCEACE Scale is a Constant Structure, by a margin of 0.39576 cents Scale diversity : 1.381165 Lumma stability : 0.294143 Lumma impropriety factor : 0.024551 Number of different interval sizes : 172 = 5.73333 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 5.73333 = 86/15 Median interval variety : 4.5 Lowest interval variety : 4 Smallest interval difference : 4375/4374, 0.3958 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 21 Most common triad is 0.0 498.045 701.955 cents, amount: 12 Number of recognisable fifths : 25, average 700.6923 cents Best fifths form a closed circle Scale contains a complete diamond : 1 3 7 21 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 7 Formal octave complements present : 9 = 29.0323% Scale is differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined Scale is differentially coherent in interval classes 5 and 6 combined -- Rational properties -- Prime limit : 7 Odd number limit : 3969 (O: 3969 U: 3969) Highest odd numerator or denominator: 189 Scale harmonicity : 0.015078 Average absolute harmonicity : 0.098159 Specific harmonicity : 0.091367 Fundamental : 1/24192, -14.5622 octaves, 0.0108 Hz. Guide tone : 117600, 16.8435 octaves, 30767166.479 Hz. Exponens Consonantiae : 2.844979E+09, 31.40577 octaves Euler's gradus suavitatis : 47 Sum of Mann's harmonic distance : 1275.5, average 41.14516 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 40.61221, average 1.31007 Sum of Tenney's harmonic distance : 79.86038, average 2.57614 Vogel's harmonic complexity : 25.54839 Wille's k value : 16537 Wilson's harmonic complexity : 43 Rectangular lattice diameter : 9 Triangular lattice diameter : 6 Lattice compactness : 2170.96129, average 4.37694 Lattice compactness (without 2's) : 1057.81830, average 2.13270 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -7 .. 5 -0.96774 84 1 3: -3 .. 1 -0.64516 30 2 5: 0 .. 2 1.00000 31 7 7: -1 .. 2 0.06452 22 21 Average exponent except 2's : 13 / 31 = 0.41935 Average absolute exponent except 2's: 83 / 31 = 2.67742 Scale is weakly epimorphic with val: <31 49 70 87| Scale is JI-epimorphic with val: <31 49 72 87| = patent
FIT/MODE
31: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 7.2368 c. M:-18.1925 c. 32: 1 1 1 1 1 1 1 1 1 1 1 2 0 1 1 1 1 2 0 2 0 2 1 1 1 1 1 1 1 1 1 N D3 SD: 10.2043 c. M: 17.4878 c. 33: 1 1 1 1 1 1 1 1 1 2 0 2 1 1 1 1 1 1 1 1 1 2 0 2 1 1 1 1 1 1 1 N D3 S SD: 9.9927 c. M:-15.6327 c. 35: 1 1 1 2 0 2 1 1 1 1 1 2 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 2 1 1 1 N D3 SD: 9.9044 c. M:-18.0450 c. 36: 1 1 1 2 0 2 1 1 1 2 0 2 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 2 0 2 1 N D3 SD: 8.7889 c. M:-15.8455 c. 41: 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 2 1 1 1 2 1 1 2 N D3 S SD: 8.2084 c. M: 15.5921 c. 44: 1 2 1 2 1 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 1 2 1 2 2 1 1 2 1 1 2 N D3 SD: 7.7681 c. M:-12.9923 c. 45: 1 2 1 2 1 2 1 1 2 1 2 2 1 1 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 N D3 SD: 7.5793 c. M: 13.1846 c. 46: 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 2 1 1 2 P M ME S SD: 6.0072 c. M:-13.5898 c. 47: 1 2 1 2 1 2 1 2 1 2 1 2 2 1 1 2 2 1 2 1 1 3 1 2 1 1 2 2 1 1 2 N D3 SD: 7.8568 c. M:-12.5933 c. 48: 1 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 1 2 1 2 1 2 1 2 2 1 2 2 1 1 2 N D3 SD: 7.1018 c. M:-12.4567 c. 50: 1 2 1 2 2 2 1 2 1 2 1 3 1 2 1 2 1 2 1 2 1 3 1 2 1 2 1 2 1 2 2 N SD: 7.1112 c. M: 11.6968 c. 51: 2 1 1 3 1 2 1 2 1 2 2 2 1 2 1 2 2 2 1 2 1 2 2 2 1 2 1 2 1 2 2 N D3 SD: 6.3386 c. M:-11.3620 c. 53: 2 1 1 3 1 2 2 1 2 2 1 3 1 2 1 2 2 2 1 2 1 3 1 2 2 1 2 2 1 2 2 N SD: 4.5827 c. M:-9.5862 c. 54: 2 1 1 3 1 2 2 2 1 2 2 2 1 2 2 2 1 3 1 2 1 3 1 2 2 1 2 2 1 2 2 N SD: 6.4059 c. M:-9.5720 c. 56: 2 1 2 2 2 2 2 1 2 2 1 3 1 2 2 2 2 2 1 2 1 3 1 3 1 2 2 2 1 2 2 N SD: 6.3388 c. M:-11.7005 c. 57: 2 1 2 2 2 2 2 1 2 2 2 2 2 2 1 2 2 2 2 2 1 3 1 2 2 2 1 3 1 2 2 P D3 SD: 5.9330 c. M: 7.9194 c. 61: 2 2 1 3 1 3 2 1 2 3 1 3 1 3 1 2 2 3 1 2 2 3 1 2 2 2 2 2 2 2 2 N SD: 5.6141 c. M:-9.4261 c. 62: 2 2 1 3 1 3 2 2 1 3 1 3 2 2 1 3 2 2 2 2 1 3 2 2 2 2 2 2 2 1 3 P T3 SD: 5.2737 c. M: 9.2941 c. 63: 2 2 1 3 2 2 2 2 2 2 2 3 1 2 2 2 2 3 1 3 1 3 1 3 2 2 2 2 2 1 3 N SD: 5.2275 c. M: 8.3725 c. 64: 2 2 1 3 2 2 2 2 2 3 1 3 2 2 1 3 2 2 2 2 2 3 1 3 2 2 1 3 1 2 3 N SD: 5.2202 c. M: 9.2828 c. 66: 2 2 1 4 1 3 2 2 2 2 2 3 1 3 1 3 2 3 1 2 2 3 2 2 2 2 2 3 1 2 3 N SD: 5.0656 c. M: 8.9911 c. 67: 2 2 1 4 1 3 2 2 2 3 1 3 2 2 2 2 2 3 2 2 2 3 1 3 2 2 2 3 1 2 3 N SD: 4.5038 c. M: 8.5326 c. 68: 2 2 2 3 1 3 2 2 2 3 1 4 1 3 1 3 2 3 1 3 1 4 1 3 2 2 2 3 1 2 3 N SD: 4.1163 c. M:-7.9458 c. 72: 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 3 2 2 2 3 2 2 3 P D3 S SD: 3.5521 c. M: 8.1200 c. 75: 2 2 2 4 1 3 3 2 2 3 2 3 2 3 2 3 2 3 2 2 2 4 1 3 3 2 2 3 2 2 3 N SD: 4.5336 c. M:-7.2826 c. 78: 2 3 1 4 2 3 2 3 2 3 2 4 1 3 2 3 2 4 1 3 2 4 1 4 2 2 3 3 2 2 3 N SD: 4.5071 c. M:-7.5441 c. 81: 2 3 2 3 2 4 2 2 3 3 2 4 2 3 1 4 2 3 2 3 2 4 2 3 2 3 2 3 2 3 3 P SD: 4.3483 c. M: 6.9915 c. 82: 2 3 2 4 1 4 2 3 2 3 2 4 2 3 2 3 3 3 2 3 2 4 1 4 2 3 2 3 2 3 3 N SD: 4.1554 c. M: 6.7940 c. 84: 3 2 2 4 2 3 3 2 3 3 2 4 2 3 2 3 3 3 2 3 2 4 2 3 3 2 3 3 2 3 3 P SD: 2.9755 c. M:-7.1603 c. 85: 3 2 2 4 2 3 3 2 3 3 2 4 2 3 2 4 2 4 2 3 2 4 2 3 3 2 3 3 2 3 3 N SD: 3.9352 c. M:-6.6561 c. 87: 3 2 2 4 2 4 2 3 2 4 2 4 2 3 2 4 2 4 2 3 2 4 2 4 2 3 2 4 2 2 4 N SD: 3.2442 c. M: 6.5088 c. 90: 3 2 2 5 2 3 3 3 2 4 2 4 2 4 2 3 3 4 2 3 2 4 2 4 3 2 3 4 2 2 4 N SD: 3.7598 c. M:-5.2133 c. 95: 3 3 2 4 2 4 3 3 3 4 2 4 2 4 2 4 3 4 2 3 2 5 2 4 3 2 3 4 2 3 4 N SD: 3.4415 c. M: 5.9068 c. 97: 3 3 2 5 2 4 3 2 3 4 2 5 2 4 2 4 3 4 2 3 3 4 2 4 3 3 3 4 2 3 4 N SD: 3.4098 c. M: 6.0082 c. 98: 3 3 2 5 2 4 3 3 3 4 2 4 3 3 2 4 3 4 3 3 2 5 2 4 3 3 3 4 2 3 4 P SD: 3.2767 c. M:-5.5230 c. 99: 3 3 2 5 2 4 3 3 3 4 2 5 2 4 2 4 3 4 2 4 2 5 2 4 3 3 3 4 2 3 4 N SD: 1.7534 c. M:-4.0012 c. 130: 4 4 3 6 3 5 4 4 4 5 3 6 3 5 3 5 4 5 3 5 3 6 3 5 4 4 4 5 3 4 5 P SD: 2.1478 c. M:-3.9951 c. 140: 4 4 3 7 3 6 4 4 4 6 3 7 3 5 3 6 4 6 3 5 3 7 3 6 4 4 4 6 3 4 6 N SD: 1.7157 c. M: 3.6508 c. 147: 4 5 3 7 3 6 5 4 4 6 4 7 3 5 4 6 4 6 3 6 3 7 3 6 5 4 4 6 4 4 6 N SD: 2.1961 c. M: 3.0438 c. 152: 5 4 3 8 3 6 5 4 5 6 3 8 3 6 3 6 5 6 3 6 3 8 3 6 5 4 5 6 3 5 6 N SD: 2.1001 c. M:-3.7769 c. 156: 5 4 4 7 4 6 5 4 5 6 4 7 4 5 4 6 5 6 4 5 4 7 4 6 5 4 5 6 4 5 6 P SD: 2.0228 c. M: 3.8015 c. 166: 5 5 4 7 4 7 5 5 5 6 4 8 4 6 4 6 5 7 4 6 4 8 3 7 5 5 5 7 3 5 7 N SD: 1.9585 c. M: 3.3324 c. 171: 5 5 4 8 4 7 5 5 5 7 4 8 4 6 4 7 5 7 4 6 4 8 4 7 5 5 5 7 4 5 7 N SD: 0.5008 c. M: 1.1025 c. 270: 8 8 6 13 6 11 8 8 8 11 6 13 6 10 6 11 8 11 6 10 6 13 6 11 8 8 8 11 6 8 11 N SD: 0.3615 c. M:-0.7689 c. 441: 13 13 10 21 10 18 13 13 13 18 10 21 10 16 10 18 13 18 10 16 10 21 10 18 13 13 13 18 10 13 18 N SD: 0.1358 c. M: 0.3227 c. 1106: 33 32 25 53 25 45 33 32 33 45 25 53 25 40 25 45 33 45 25 40 25 53 25 45 33 32 33 45 25 33 45 N SD: 0.1245 c. M: 0.2873 c. 1137: 34 33 26 54 26 46 34 33 34 46 26 54 26 41 26 46 34 46 26 41 26 54 26 46 34 33 34 46 26 34 46 N SD: 0.1156 c. M:-0.2216 c. 1277: 38 37 29 61 29 52 38 37 38 52 29 61 29 46 29 52 38 52 29 46 29 61 29 52 38 37 38 52 29 38 52 N SD: 0.1257 c. M: 0.2075 c. 1308: 39 38 30 62 30 53 39 38 39 53 30 62 30 47 30 53 39 53 30 47 30 62 30 53 39 38 39 53 30 39 53 N SD: 0.1185 c. M:-0.2286 c. 1376: 41 40 31 66 31 56 41 40 41 56 31 66 31 50 31 56 41 56 31 50 31 66 31 56 41 40 41 56 31 41 56 N SD: 0.1067 c. M: 0.2621 c. 1407: 42 41 32 67 32 57 42 41 42 57 32 67 32 51 32 57 42 57 32 51 32 67 32 57 42 41 42 57 32 42 57 N SD: 0.0936 c. M:-0.1965 c. 1547: 46 45 35 74 35 63 46 45 46 63 35 74 35 56 35 63 46 63 35 56 35 74 35 63 46 45 46 63 35 46 63 N SD: 0.0793 c. M: 0.1990 c. 1578: 47 46 36 75 36 64 47 46 47 64 36 75 36 57 36 64 47 64 36 57 36 75 36 64 47 46 47 64 36 47 64 N SD: 0.0659 c. M:-0.1623 c. 1848: 55 54 42 88 42 75 55 54 55 75 42 88 42 67 42 75 55 75 42 67 42 88 42 75 55 54 55 75 42 55 75 N SD: 0.0698 c. M:-0.1190 c. 1988: 59 58 45 95 45 81 59 58 59 81 45 95 45 72 45 81 59 81 45 72 45 95 45 81 59 58 59 81 45 59 81 N SD: 0.0681 c. M: 0.1498 c. 2019: 60 59 46 96 46 82 60 59 60 82 46 96 46 73 46 82 60 82 46 73 46 96 46 82 60 59 60 82 46 60 82 N SD: 0.0531 c. M:-0.1318 c. 2460: 73 72 56 117 56 100 73 72 73 100 56 117 56 89 56 100 73 100 56 89 56 117 56 100 73 72 73 100 56 73 100 N SD: 0.0566 c. M:-0.1123 c. 2513: 75 73 57 120 57 102 75 73 75 102 57 120 57 91 57 102 75 102 57 91 57 120 57 102 75 73 75 102 57 75 102 N SD: 0.0492 c. M:-0.1170 c. 2684: 80 78 61 128 61 109 80 78 80 109 61 128 61 97 61 109 80 109 61 97 61 128 61 109 80 78 80 109 61 80 109 N SD: 0.0337 c. M: 0.0757 c.
FIT/HARMONIC
1 .. 2 match: 1 H SD: 0.0000 cents 2 .. 4 match: 2 H SD: 0.0000 cents 3 .. 6 match: 3 H SD: 0.0000 cents 4 .. 8 match: 4 H SD: 0.0000 cents 5 .. 10 match: 5 H SD: 5.5179 cents 6 .. 12 match: 6 H SD: 1.6441 cents 7 .. 14 match: 7 H SD: 4.1263 cents 8 .. 16 match: 8 H SD: 3.6105 cents 9 .. 18 match: 9 H SD: 2.8414 cents 10 .. 20 match: 10 H SD: 3.6900 cents 11 .. 22 match: 11 H SD: 2.6084 cents 12 .. 24 match: 12 H SD: 2.2311 cents 13 .. 26 match: 13 H SD: 4.9051 cents 14 .. 28 match: 14 H SD: 2.9178 cents 15 .. 30 match: 15 H SD: 2.8489 cents 16 .. 32 match: 16 H SD: 2.5140 cents 17 .. 34 match: 17 H SD: 3.0638 cents 18 .. 36 match: 18 H SD: 2.2324 cents 19 .. 38 match: 19 H SD: 2.3626 cents 20 .. 40 match: 19 S SD: 2.6502 cents 21 .. 42 match: 21 H SD: 2.4420 cents 22 .. 44 match: 22 H SD: 2.2645 cents 23 .. 46 match: 23 H SD: 2.4712 cents 24 .. 48 match: 23 S SD: 2.0750 cents 25 .. 50 match: 24 S SD: 2.3943 cents 26 .. 52 match: 23 SD: 2.7034 cents 27 .. 54 match: 24 SD: 2.4303 cents 28 .. 56 match: 25 SD: 1.9995 cents 29 .. 58 match: 25 S SD: 2.1338 cents 30 .. 60 match: 27 SD: 1.9691 cents 31 .. 62 match: 26 SD: 2.0727 cents 32 .. 64 match: 27 SD: 1.7768 cents 33 .. 66 match: 27 SD: 1.5951 cents 34 .. 68 match: 27 SD: 1.8596 cents 35 .. 70 match: 28 SD: 1.8005 cents 36 .. 72 match: 30 SD: 1.4679 cents 37 .. 74 match: 27 SD: 1.7103 cents 38 .. 76 match: 28 SD: 1.6539 cents 39 .. 78 match: 27 SD: 1.7025 cents 40 .. 80 match: 27 SD: 1.7278 cents 41 .. 82 match: 29 SD: 1.3629 cents 42 .. 84 match: 29 SD: 1.2040 cents 46 .. 92 match: 30 SD: 1.3218 cents 48 .. 96 match: 30 SD: 1.0145 cents 49 .. 98 match: 30 SD: 1.3031 cents 50 .. 100 match: 30 SD: 1.3722 cents 51 .. 102 match: 31 SD: 1.1074 cents 52 .. 104 match: 31 SD: 0.9815 cents 60 .. 120 match: 30 SD: 1.1423 cents 61 .. 122 match: 31 SD: 1.1249 cents 63 .. 126 match: 31 SD: 1.0091 cents 64 .. 128 match: 31 SD: 0.9473 cents 70 .. 140 match: 31 SD: 0.8849 cents 73 .. 146 match: 31 SD: 0.8468 cents 78 .. 156 match: 31 SD: 0.8389 cents 80 .. 160 match: 31 SD: 0.8116 cents 83 .. 166 match: 31 SD: 0.7952 cents 84 .. 168 match: 31 SD: 0.6267 cents 96 .. 192 match: 31 SD: 0.5469 cents 116 .. 232 match: 31 SD: 0.5131 cents 120 .. 240 match: 31 SD: 0.5043 cents 125 .. 250 match: 31 SD: 0.4964 cents 126 .. 252 match: 31 SD: 0.3975 cents 144 .. 288 match: 31 SD: 0.3791 cents 168 .. 336 match: 31 SD: 0.3348 cents 188 .. 376 match: 31 SD: 0.3251 cents 189 .. 378 match: 31 SD: 0.3071 cents 192 .. 384 match: 31 SD: 0.2734 cents 224 .. 448 match: 31 SD: 0.2574 cents 236 .. 472 match: 31 SD: 0.2443 cents 237 .. 474 match: 31 SD: 0.2309 cents 240 .. 480 match: 31 SD: 0.2202 cents 287 .. 574 match: 31 SD: 0.2195 cents 288 .. 576 match: 31 SD: 0.1327 cents 378 .. 756 match: 31 SD: 0.1250 cents 432 .. 864 match: 31 SD: 0.1183 cents 468 .. 936 match: 31 SD: 0.1175 cents 480 .. 960 match: 31 SD: 0.1135 cents 504 .. 1008 match: 31 SD: 0.1012 cents 567 .. 1134 match: 31 SD: 0.0955 cents 576 .. 1152 match: 31 SD: 0.0853 cents