Scala analysis: partch-29-av
29-tone JI scale from Partch's Adapted Viola 1928-30
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 33/32 53.272943 undecimal comma, al-Farabi's 1/4-tone 2: 21/20 84.467193 minor semitone 3: 15/14 119.442808 major diatonic semitone 4: 12/11 150.637059 undecimal neutral second, 3/4-tone 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: 6/5 315.641287 minor third 9: 11/9 347.407941 undecimal neutral third 10: 5/4 386.313714 major third 11: 9/7 435.084095 septimal major third, BP third 12: 4/3 498.044999 perfect fourth 13: 11/8 551.317942 undecimal semi-augmented fourth 14: 7/5 582.512193 septimal or Huygens' tritone, BP fourth 15: 10/7 617.487807 Euler's tritone 16: 16/11 648.682058 undecimal semi-diminished fifth 17: 3/2 701.955001 perfect fifth 18: 14/9 764.915905 septimal minor sixth 19: 8/5 813.686286 minor sixth 20: 18/11 852.592059 undecimal neutral sixth 21: 5/3 884.358713 major sixth, BP sixth 22: 12/7 933.129094 septimal major sixth 23: 7/4 968.825906 harmonic seventh 24: 9/5 1017.596288 just minor seventh, BP seventh 25: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 26: 28/15 1080.557192 grave major seventh 27: 40/21 1115.532807 acute major seventh 28: 64/33 1146.727057 33rd subharmonic 29: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 1: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 2: 56/55 31.1943 undecimal diesis, konbini comma 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 56/55 31.1943 undecimal diesis, konbini comma 5: 55/54 31.7667 telepathma 6: 36/35 48.7704 septimal diesis, 1/4-tone 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 55/54 31.7667 telepathma 10: 45/44 38.9058 1/5-tone 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 28/27 62.9609 Archytas' 1/3-tone 13: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 14: 56/55 31.1943 undecimal diesis, konbini comma 15: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 16: 56/55 31.1943 undecimal diesis, konbini comma 17: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 18: 28/27 62.9609 Archytas' 1/3-tone 19: 36/35 48.7704 septimal diesis, 1/4-tone 20: 45/44 38.9058 1/5-tone 21: 55/54 31.7667 telepathma 22: 36/35 48.7704 septimal diesis, 1/4-tone 23: 49/48 35.6968 slendro diesis, septimal 1/6-tone 24: 36/35 48.7704 septimal diesis, 1/4-tone 25: 55/54 31.7667 telepathma 26: 56/55 31.1943 undecimal diesis, konbini comma 27: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 28: 56/55 31.1943 undecimal diesis, konbini comma 29: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 6 56/55 31.194 cents undecimal diesis, konbini comma 1: 4 55/54 31.767 cents telepathma 1: 3 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 2 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 2 45/44 38.906 cents 1/5-tone 1: 6 36/35 48.770 cents septimal diesis, 1/4-tone 1: 4 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 2 28/27 62.961 cents Archytas' 1/3-tone 2: 6 80/77 66.170 cents 2: 2 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 4 22/21 80.537 cents undecimal minor semitone 2: 8 21/20 84.467 cents minor semitone 2: 2 81/77 87.676 cents 2: 1 1089/1024 106.546 cents two (undecimal comma, al-Farabi's 1/4-tone) 2: 2 16/15 111.731 cents minor diatonic semitone 2: 2 77/72 116.234 cents undecimal secor 3: 3 128/121 97.364 cents undecimal semitone 3: 2 200/189 97.937 cents 3: 2 16/15 111.731 cents minor diatonic semitone 3: 4 77/72 116.234 cents undecimal secor 3: 8 15/14 119.443 cents major diatonic semitone 3: 2 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 3: 2 693/640 137.740 cents 3: 2 49/45 147.428 cents BP minor semitone 3: 2 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 4: 2 320/297 129.131 cents 4: 2 160/147 146.707 cents 4: 2 49/45 147.428 cents BP minor semitone 4: 4 12/11 150.637 cents undecimal neutral second, 3/4-tone 4: 2 35/32 155.140 cents septimal neutral second 4: 4 11/10 165.004 cents Ptolemy's second, 4/5-tone 4: 2 54/49 168.213 cents Zalzal's mujannab 4: 1 441/400 168.934 cents two (minor semitone) 4: 2 495/448 172.716 cents 4: 4 10/9 182.404 cents minor whole tone 4: 2 28/25 196.198 cents middle second 4: 2 9/8 203.910 cents major whole tone 5: 2 256/231 177.901 cents 5: 4 10/9 182.404 cents minor whole tone 5: 2 28/25 196.198 cents middle second 5: 2 121/108 196.771 cents 5: 9 9/8 203.910 cents major whole tone 5: 2 112/99 213.598 cents 5: 4 8/7 231.174 cents septimal whole tone 5: 2 63/55 235.104 cents 5: 2 55/48 235.677 cents undecimal semi-augmented whole tone 6: 2 112/99 213.598 cents 6: 2 154/135 227.965 cents 6: 4 8/7 231.174 cents septimal whole tone 6: 2 63/55 235.104 cents 6: 4 55/48 235.677 cents undecimal semi-augmented whole tone 6: 1 225/196 238.886 cents two (major diatonic semitone) 6: 2 81/70 252.680 cents Al-Hwarizmi's lute middle finger 6: 2 64/55 262.368 cents 6: 6 7/6 266.871 cents septimal minor third 6: 2 90/77 270.080 cents 6: 2 33/28 284.447 cents undecimal minor third 7: 2 64/55 262.368 cents 7: 2 220/189 262.941 cents 7: 6 7/6 266.871 cents septimal minor third 7: 2 90/77 270.080 cents 7: 4 33/28 284.447 cents undecimal minor third 7: 2 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 7: 2 25/21 301.847 cents BP second, quasi-equal minor third 7: 6 6/5 315.641 cents minor third 7: 2 77/64 320.144 cents Keemun minor third 7: 1 98/81 329.832 cents 8: 2 32/27 294.135 cents Pythagorean minor third 8: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 8: 4 25/21 301.847 cents BP second, quasi-equal minor third 8: 6 6/5 315.641 cents minor third 8: 2 77/64 320.144 cents Keemun minor third 8: 2 40/33 333.041 cents 8: 2 11/9 347.408 cents undecimal neutral third 8: 2 60/49 350.617 cents smaller approximation to neutral third 8: 2 49/40 351.338 cents larger approximation to neutral third 8: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 8: 2 99/80 368.914 cents 8: 2 56/45 378.602 cents septimal narrow major third 9: 4 40/33 333.041 cents 9: 2 11/9 347.408 cents undecimal neutral third 9: 4 60/49 350.617 cents smaller approximation to neutral third 9: 2 49/40 351.338 cents larger approximation to neutral third 9: 2 99/80 368.914 cents 9: 2 56/45 378.602 cents septimal narrow major third 9: 2 96/77 381.811 cents 9: 4 5/4 386.314 cents major third 9: 2 63/50 400.108 cents quasi-equal major third 9: 2 121/96 400.681 cents 9: 2 14/11 417.508 cents undecimal diminished fourth or major third 9: 1 32/25 427.373 cents classic diminished fourth 10: 1 100/81 364.807 cents grave major third 10: 4 96/77 381.811 cents 10: 4 5/4 386.314 cents major third 10: 2 63/50 400.108 cents quasi-equal major third 10: 2 121/96 400.681 cents 10: 2 80/63 413.578 cents wide major third 10: 2 14/11 417.508 cents undecimal diminished fourth or major third 10: 4 77/60 431.875 cents 10: 4 9/7 435.084 cents septimal major third, BP third 10: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 10: 2 72/55 466.278 cents undecimal semi-diminished fourth 11: 2 80/63 413.578 cents wide major third 11: 2 14/11 417.508 cents undecimal diminished fourth or major third 11: 2 77/60 431.875 cents 11: 4 9/7 435.084 cents septimal major third, BP third 11: 2 165/128 439.587 cents 11: 2 128/99 444.772 cents 11: 2 98/75 463.069 cents 11: 2 72/55 466.278 cents undecimal semi-diminished fourth 11: 4 55/42 466.851 cents 11: 2 21/16 470.781 cents narrow fourth 11: 4 4/3 498.045 cents perfect fourth 11: 1 162/121 505.184 cents 12: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 12: 1 64/49 462.348 cents 2 septatones or septatonic major third 12: 2 72/55 466.278 cents undecimal semi-diminished fourth 12: 2 55/42 466.851 cents 12: 2 21/16 470.781 cents narrow fourth 12: 2 297/224 488.357 cents 12: 10 4/3 498.045 cents perfect fourth 12: 2 27/20 519.551 cents acute fourth 12: 2 49/36 533.742 cents Arabic lute acute fourth 12: 2 15/11 536.951 cents undecimal augmented fourth 12: 2 48/35 546.815 cents septimal semi-augmented fourth 13: 6 4/3 498.045 cents perfect fourth 13: 2 75/56 505.757 cents marvelous fourth 13: 2 27/20 519.551 cents acute fourth 13: 4 224/165 529.239 cents 13: 2 200/147 533.021 cents 13: 6 11/8 551.318 cents undecimal semi-augmented fourth 13: 1 25/18 568.717 cents classic augmented fourth 13: 4 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 13: 2 108/77 585.721 cents 14: 2 110/81 529.812 cents 14: 1 49/36 533.742 cents Arabic lute acute fourth 14: 2 15/11 536.951 cents undecimal augmented fourth 14: 2 48/35 546.815 cents septimal semi-augmented fourth 14: 2 135/98 554.527 cents 14: 4 320/231 564.215 cents 14: 6 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 14: 2 363/256 604.591 cents 14: 2 77/54 614.279 cents 14: 2 10/7 617.488 cents Euler's tritone 14: 2 63/44 621.418 cents 14: 2 36/25 631.283 cents classic diminished fifth 15: 2 25/18 568.717 cents classic augmented fourth 15: 2 88/63 578.582 cents 15: 2 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 15: 2 108/77 585.721 cents 15: 2 512/363 595.409 cents 15: 6 10/7 617.488 cents Euler's tritone 15: 4 231/160 635.785 cents 15: 2 196/135 645.473 cents 15: 2 35/24 653.185 cents septimal semi-diminished fifth 15: 2 22/15 663.049 cents undecimal diminished fifth 15: 1 72/49 666.258 cents Arabic lute grave fifth 15: 2 81/55 670.188 cents 16: 2 77/54 614.279 cents 16: 4 10/7 617.488 cents Euler's tritone 16: 1 36/25 631.283 cents classic diminished fifth 16: 6 16/11 648.682 cents undecimal semi-diminished fifth 16: 2 147/100 666.979 cents 16: 4 165/112 670.761 cents 16: 2 40/27 680.449 cents grave fifth 16: 2 112/75 694.243 cents marvelous fifth 16: 6 3/2 701.955 cents perfect fifth 17: 2 35/24 653.185 cents septimal semi-diminished fifth 17: 2 22/15 663.049 cents undecimal diminished fifth 17: 2 72/49 666.258 cents Arabic lute grave fifth 17: 2 40/27 680.449 cents grave fifth 17: 10 3/2 701.955 cents perfect fifth 17: 2 448/297 711.643 cents 17: 2 32/21 729.219 cents wide fifth 17: 2 84/55 733.149 cents 17: 2 55/36 733.722 cents undecimal semi-augmented fifth 17: 1 49/32 737.652 cents 17: 2 54/35 750.725 cents septimal semi-augmented fifth 18: 1 121/81 694.816 cents two (undecimal neutral third) 18: 4 3/2 701.955 cents perfect fifth 18: 2 32/21 729.219 cents wide fifth 18: 4 84/55 733.149 cents 18: 2 55/36 733.722 cents undecimal semi-augmented fifth 18: 2 75/49 736.931 cents BP fifth 18: 2 99/64 755.228 cents 18: 2 256/165 760.413 cents 18: 4 14/9 764.916 cents septimal minor sixth 18: 2 120/77 768.125 cents 18: 2 11/7 782.492 cents undecimal augmented fifth 18: 2 63/40 786.422 cents narrow minor sixth 19: 2 55/36 733.722 cents undecimal semi-augmented fifth 19: 2 54/35 750.725 cents septimal semi-augmented fifth 19: 4 14/9 764.916 cents septimal minor sixth 19: 4 120/77 768.125 cents 19: 2 11/7 782.492 cents undecimal augmented fifth 19: 2 63/40 786.422 cents narrow minor sixth 19: 2 192/121 799.319 cents 19: 2 100/63 799.892 cents quasi-equal minor sixth 19: 4 8/5 813.686 cents minor sixth 19: 4 77/48 818.189 cents 19: 1 81/50 835.193 cents acute minor sixth 20: 1 25/16 772.627 cents classic augmented fifth 20: 2 11/7 782.492 cents undecimal augmented fifth 20: 2 192/121 799.319 cents 20: 2 100/63 799.892 cents quasi-equal minor sixth 20: 4 8/5 813.686 cents minor sixth 20: 2 77/48 818.189 cents 20: 2 45/28 821.398 cents septimale wide minor sixth 20: 2 160/99 831.086 cents 20: 2 80/49 848.662 cents smaller approximation to neutral sixth 20: 4 49/30 849.383 cents larger approximation to neutral sixth 20: 2 18/11 852.592 cents undecimal neutral sixth 20: 4 33/20 866.959 cents 21: 2 45/28 821.398 cents septimale wide minor sixth 21: 2 160/99 831.086 cents 21: 2 44/27 845.453 cents neutral sixth 21: 2 80/49 848.662 cents smaller approximation to neutral sixth 21: 2 49/30 849.383 cents larger approximation to neutral sixth 21: 2 18/11 852.592 cents undecimal neutral sixth 21: 2 33/20 866.959 cents 21: 2 128/77 879.856 cents 21: 6 5/3 884.359 cents major sixth, BP sixth 21: 4 42/25 898.153 cents quasi-equal major sixth 21: 1 121/72 898.726 cents 21: 2 27/16 905.865 cents Pythagorean major sixth 22: 1 81/49 870.168 cents two (septimal major third, BP third) 22: 2 128/77 879.856 cents 22: 6 5/3 884.359 cents major sixth, BP sixth 22: 2 42/25 898.153 cents quasi-equal major sixth 22: 2 121/72 898.726 cents 22: 4 56/33 915.553 cents 22: 2 77/45 929.920 cents 22: 6 12/7 933.129 cents septimal major sixth 22: 2 189/110 937.059 cents 22: 2 55/32 937.632 cents 23: 2 56/33 915.553 cents 23: 2 77/45 929.920 cents 23: 6 12/7 933.129 cents septimal major sixth 23: 2 55/32 937.632 cents 23: 2 140/81 947.320 cents 23: 1 392/225 961.114 cents 23: 4 96/55 964.323 cents 23: 2 110/63 964.896 cents 23: 4 7/4 968.826 cents harmonic seventh 23: 2 135/77 972.035 cents 23: 2 99/56 986.402 cents 24: 2 96/55 964.323 cents 24: 2 110/63 964.896 cents 24: 4 7/4 968.826 cents harmonic seventh 24: 2 99/56 986.402 cents 24: 9 16/9 996.090 cents Pythagorean minor seventh 24: 2 216/121 1003.229 cents 24: 2 25/14 1003.802 cents middle minor seventh 24: 4 9/5 1017.596 cents just minor seventh, BP seventh 24: 2 231/128 1022.099 cents 25: 2 16/9 996.090 cents Pythagorean minor seventh 25: 2 25/14 1003.802 cents middle minor seventh 25: 4 9/5 1017.596 cents just minor seventh, BP seventh 25: 2 896/495 1027.284 cents 25: 1 800/441 1031.066 cents 25: 2 49/27 1031.787 cents 25: 4 20/11 1034.996 cents large minor seventh 25: 2 64/35 1044.860 cents septimal neutral seventh 25: 4 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 25: 2 90/49 1052.572 cents 25: 2 147/80 1053.293 cents 25: 2 297/160 1070.869 cents 26: 2 20/11 1034.996 cents large minor seventh 26: 2 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 26: 2 90/49 1052.572 cents 26: 2 1280/693 1062.260 cents 26: 2 50/27 1066.762 cents grave major seventh 26: 8 28/15 1080.557 cents grave major seventh 26: 4 144/77 1083.766 cents 26: 2 15/8 1088.269 cents classic major seventh 26: 2 189/100 1102.063 cents 26: 3 121/64 1102.636 cents two (undecimal semi-augmented fourth) 27: 2 144/77 1083.766 cents 27: 2 15/8 1088.269 cents classic major seventh 27: 1 2048/1089 1093.454 cents 27: 2 154/81 1112.324 cents 27: 8 40/21 1115.533 cents acute major seventh 27: 4 21/11 1119.463 cents undecimal major seventh 27: 2 48/25 1129.328 cents classic diminished octave 27: 6 77/40 1133.830 cents 27: 2 27/14 1137.039 cents septimal major seventh 28: 2 27/14 1137.039 cents septimal major seventh 28: 4 64/33 1146.727 cents 33rd subharmonic 28: 6 35/18 1151.230 cents septimal semi-diminished octave 28: 2 88/45 1161.094 cents 28: 2 96/49 1164.303 cents 28: 3 49/25 1165.024 cents BP eighth 28: 4 108/55 1168.233 cents 28: 6 55/28 1168.806 cents Highest number of different intervals for one interval class: 12 Average number of different intervals per interval class: 10.57143 = 74/7
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 0.0 : 53.3 84.5 119.4 150.6 182.4 231.2 266.9 315.6 347.4 386.3 435.1 498.0 551.3 582.5 617.5 648.7 702.0 764.9 813.7 852.6 884.4 933.1 968.8 1017.6 1049.4 1080.6 1115.5 1146.7 1200.0 53.3 : 31.2 66.2 97.4 129.1 177.9 213.6 262.4 294.1 333.0 381.8 444.8 498.0 529.2 564.2 595.4 648.7 711.6 760.4 799.3 831.1 879.9 915.6 964.3 996.1 1027.3 1062.3 1093.5 1146.7 1200.0 84.5 : 35.0 66.2 97.9 146.7 182.4 231.2 262.9 301.8 350.6 413.6 466.9 498.0 533.0 564.2 617.5 680.4 729.2 768.1 799.9 848.7 884.4 933.1 964.9 996.1 1031.1 1062.3 1115.5 1168.8 1200.0 119.4 : 31.2 63.0 111.7 147.4 196.2 228.0 266.9 315.6 378.6 431.9 463.1 498.0 529.2 582.5 645.5 694.2 733.1 764.9 813.7 849.4 898.2 929.9 961.1 996.1 1027.3 1080.6 1133.8 1165.0 1200.0 150.6 : 31.8 80.5 116.2 165.0 196.8 235.7 284.4 347.4 400.7 431.9 466.9 498.0 551.3 614.3 663.0 702.0 733.7 782.5 818.2 867.0 898.7 929.9 964.9 996.1 1049.4 1102.6 1133.8 1168.8 1200.0 182.4 : 48.8 84.5 133.2 165.0 203.9 252.7 315.6 368.9 400.1 435.1 466.3 519.6 582.5 631.3 670.2 702.0 750.7 786.4 835.2 867.0 898.2 933.1 964.3 1017.6 1070.9 1102.1 1137.0 1168.2 1200.0 231.2 : 35.7 84.5 116.2 155.1 203.9 266.9 320.1 351.3 386.3 417.5 470.8 533.7 582.5 621.4 653.2 702.0 737.7 786.4 818.2 849.4 884.4 915.6 968.8 1022.1 1053.3 1088.3 1119.5 1151.2 1200.0 266.9 : 48.8 80.5 119.4 168.2 231.2 284.4 315.6 350.6 381.8 435.1 498.0 546.8 585.7 617.5 666.3 702.0 750.7 782.5 813.7 848.7 879.9 933.1 986.4 1017.6 1052.6 1083.8 1115.5 1164.3 1200.0 315.6 : 31.8 70.7 119.4 182.4 235.7 266.9 301.8 333.0 386.3 449.3 498.0 537.0 568.7 617.5 653.2 702.0 733.7 764.9 799.9 831.1 884.4 937.6 968.8 1003.8 1035.0 1066.8 1115.5 1151.2 1200.0 347.4 : 38.9 87.7 150.6 203.9 235.1 270.1 301.3 354.5 417.5 466.3 505.2 537.0 585.7 621.4 670.2 702.0 733.1 768.1 799.3 852.6 905.9 937.1 972.0 1003.2 1035.0 1083.8 1119.5 1168.2 1200.0 386.3 : 48.8 111.7 165.0 196.2 231.2 262.4 315.6 378.6 427.4 466.3 498.0 546.8 582.5 631.3 663.0 694.2 729.2 760.4 813.7 867.0 898.2 933.1 964.3 996.1 1044.9 1080.6 1129.3 1161.1 1200.0 435.1 : 63.0 116.2 147.4 182.4 213.6 266.9 329.8 378.6 417.5 449.3 498.0 533.7 582.5 614.3 645.5 680.4 711.6 764.9 818.2 849.4 884.4 915.6 947.3 996.1 1031.8 1080.6 1112.3 1151.2 1200.0 498.0 : 53.3 84.5 119.4 150.6 203.9 266.9 315.6 354.5 386.3 435.1 470.8 519.6 551.3 582.5 617.5 648.7 702.0 755.2 786.4 821.4 852.6 884.4 933.1 968.8 1017.6 1049.4 1088.3 1137.0 1200.0 551.3 : 31.2 66.2 97.4 150.6 213.6 262.4 301.3 333.0 381.8 417.5 466.3 498.0 529.2 564.2 595.4 648.7 702.0 733.1 768.1 799.3 831.1 879.9 915.6 964.3 996.1 1035.0 1083.8 1146.7 1200.0 582.5 : 35.0 66.2 119.4 182.4 231.2 270.1 301.8 350.6 386.3 435.1 466.9 498.0 533.0 564.2 617.5 670.8 702.0 736.9 768.1 799.9 848.7 884.4 933.1 964.9 1003.8 1052.6 1115.5 1168.8 1200.0 617.5 : 31.2 84.5 147.4 196.2 235.1 266.9 315.6 351.3 400.1 431.9 463.1 498.0 529.2 582.5 635.8 667.0 702.0 733.1 764.9 813.7 849.4 898.2 929.9 968.8 1017.6 1080.6 1133.8 1165.0 1200.0 648.7 : 53.3 116.2 165.0 203.9 235.7 284.4 320.1 368.9 400.7 431.9 466.9 498.0 551.3 604.6 635.8 670.8 702.0 733.7 782.5 818.2 867.0 898.7 937.6 986.4 1049.4 1102.6 1133.8 1168.8 1200.0 702.0 : 63.0 111.7 150.6 182.4 231.2 266.9 315.6 347.4 378.6 413.6 444.8 498.0 551.3 582.5 617.5 648.7 680.4 729.2 764.9 813.7 845.5 884.4 933.1 996.1 1049.4 1080.6 1115.5 1146.7 1200.0 764.9 : 48.8 87.7 119.4 168.2 203.9 252.7 284.4 315.6 350.6 381.8 435.1 488.4 519.6 554.5 585.7 617.5 666.3 702.0 750.7 782.5 821.4 870.2 933.1 986.4 1017.6 1052.6 1083.8 1137.0 1200.0 813.7 : 38.9 70.7 119.4 155.1 203.9 235.7 266.9 301.8 333.0 386.3 439.6 470.8 505.8 537.0 568.7 617.5 653.2 702.0 733.7 772.6 821.4 884.4 937.6 968.8 1003.8 1035.0 1088.3 1151.2 1200.0 852.6 : 31.8 80.5 116.2 165.0 196.8 228.0 262.9 294.1 347.4 400.7 431.9 466.9 498.0 529.8 578.6 614.3 663.0 694.8 733.7 782.5 845.5 898.7 929.9 964.9 996.1 1049.4 1112.3 1161.1 1200.0 884.4 : 48.8 84.5 133.2 165.0 196.2 231.2 262.4 315.6 368.9 400.1 435.1 466.3 498.0 546.8 582.5 631.3 663.0 702.0 750.7 813.7 867.0 898.2 933.1 964.3 1017.6 1080.6 1129.3 1168.2 1200.0 933.1 : 35.7 84.5 116.2 147.4 182.4 213.6 266.9 320.1 351.3 386.3 417.5 449.3 498.0 533.7 582.5 614.3 653.2 702.0 764.9 818.2 849.4 884.4 915.6 968.8 1031.8 1080.6 1119.5 1151.2 1200.0 968.8 : 48.8 80.5 111.7 146.7 177.9 231.2 284.4 315.6 350.6 381.8 413.6 462.3 498.0 546.8 578.6 617.5 666.3 729.2 782.5 813.7 848.7 879.9 933.1 996.1 1044.9 1083.8 1115.5 1164.3 1200.0 1017.6: 31.8 63.0 97.9 129.1 182.4 235.7 266.9 301.8 333.0 364.8 413.6 449.3 498.0 529.8 568.7 617.5 680.4 733.7 764.9 799.9 831.1 884.4 947.3 996.1 1035.0 1066.8 1115.5 1151.2 1200.0 1049.4: 31.2 66.2 97.4 150.6 203.9 235.1 270.1 301.3 333.0 381.8 417.5 466.3 498.0 537.0 585.7 648.7 702.0 733.1 768.1 799.3 852.6 915.6 964.3 1003.2 1035.0 1083.8 1119.5 1168.2 1200.0 1080.6: 35.0 66.2 119.4 172.7 203.9 238.9 270.1 301.8 350.6 386.3 435.1 466.9 505.8 554.5 617.5 670.8 702.0 736.9 768.1 821.4 884.4 933.1 972.0 1003.8 1052.6 1088.3 1137.0 1168.8 1200.0 1115.5: 31.2 84.5 137.7 168.9 203.9 235.1 266.9 315.6 351.3 400.1 431.9 470.8 519.6 582.5 635.8 667.0 702.0 733.1 786.4 849.4 898.2 937.1 968.8 1017.6 1053.3 1102.1 1133.8 1165.0 1200.0 1146.7: 53.3 106.5 137.7 172.7 203.9 235.7 284.4 320.1 368.9 400.7 439.6 488.4 551.3 604.6 635.8 670.8 702.0 755.2 818.2 867.0 905.9 937.6 986.4 1022.1 1070.9 1102.6 1133.8 1168.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 31.1943 .. 62.9609 cents 55/54, 31.7667 cents 56/55, 31.1943 cents 2: 62.9609 .. 116.2338 cents 33/32, 53.2729 cents 1/1, 0.0000 cents 3: 97.3641 .. 165.0042 cents 1331/1280, 67.6401 cents 9216/9317,-18.8697 cents 4: 129.1308 .. 203.9100 cents 2673/2560, 74.7792 cents 3200/3267,-35.8735 cents 5: 177.9012 .. 235.6767 cents 4235/4096, 57.7755 cents 2048/2079,-26.0089 cents 6: 213.5980 .. 284.4470 cents 3267/3136, 70.8491 cents 1792/1815,-22.0787 cents 7: 262.3683 .. 329.8318 cents 2695/2592, 67.4635 cents 1792/1815,-22.0787 cents 8: 294.1350 .. 378.6022 cents 21/20, 84.4672 cents 48/49,-35.6968 cents 9: 333.0408 .. 427.3726 cents 132/125, 94.3318 cents 75/77,-45.5614 cents 10: 364.8074 .. 466.2783 cents 1458/1375, 101.4709 cents 625/648,-62.5651 cents 11: 413.5778 .. 505.1841 cents 5103/4840, 91.6063 cents 550/567,-52.7005 cents 12: 449.2746 .. 546.8154 cents 1296/1225, 97.5408 cents 4235/4374,-55.9095 cents 13: 498.0450 .. 585.7212 cents 81/77, 87.6762 cents 35/36,-48.7704 cents 14: 529.8117 .. 631.2826 cents 1458/1375, 101.4709 cents 4235/4374,-55.9095 cents 15: 568.7174 .. 670.1883 cents 1458/1375, 101.4709 cents 625/648,-62.5651 cents 16: 614.2788 .. 701.9550 cents 81/77, 87.6762 cents 4235/4374,-55.9095 cents 17: 653.1846 .. 750.7254 cents 1296/1225, 97.5408 cents 35/36,-48.7704 cents 18: 694.8159 .. 786.4222 cents 5103/4840, 91.6063 cents 4235/4374,-55.9095 cents 19: 733.7217 .. 835.1926 cents 1458/1375, 101.4709 cents 550/567,-52.7005 cents 20: 772.6274 .. 866.9592 cents 132/125, 94.3318 cents 625/648,-62.5651 cents 21: 821.3978 .. 905.8650 cents 21/20, 84.4672 cents 75/77,-45.5614 cents 22: 870.1682 .. 937.6317 cents 2695/2592, 67.4635 cents 48/49,-35.6968 cents 23: 915.5530 .. 986.4020 cents 3267/3136, 70.8491 cents 1792/1815,-22.0787 cents 24: 964.3233 .. 1022.0988 cents 4235/4096, 57.7755 cents 1792/1815,-22.0787 cents 25: 996.0900 .. 1070.8692 cents 2673/2560, 74.7792 cents 2048/2079,-26.0089 cents 26: 1034.9958 .. 1102.6359 cents 1331/1280, 67.6401 cents 3200/3267,-35.8735 cents 27: 1083.7662 .. 1137.0391 cents 33/32, 53.2729 cents 9216/9317,-18.8697 cents 28: 1137.0391 .. 1168.8057 cents 55/54, 31.7667 cents 1/1, 0.0000 cents
SHOW DATA
Number of notes : 29 -- Interval properties -- Smallest interval : 56/55, 31.1943 cents, class 1 Average step (divided formal octave): 41.3793 cents Largest one step interval : 28/27, 62.9609 cents Average / Smallest step : 1.326504 Largest / Average step : 1.521555 Largest / Smallest step : 2.018350 Median interval of one step : 49/48, 35.6968 cents, amount: 2 Least squares average step : 41.60921 cents, oct.: 1206.66701 cents Scale is not proper Step pattern alph. order: ABCBDEFEDGEHABCBAHEGDEFEDBCBA Step pattern size order : GACABFDFBEFHGACAGHFEBFDFBACAG Scale is not a Constant Structure Scale diversity : 1.419187 Lumma stability : 0.051990 Lumma impropriety factor : 0.712609 Number of different interval sizes : 194 = 6.92857 / class Number of one step interval sizes : 8 Highest interval variety : 12 Mean interval variety : 10.57143 = 74/7 Median interval variety : 8.5 Lowest interval variety : 8 Smallest interval difference : 3025/3024, 0.5724 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 20 Most common triad is 0.0 498.045 701.955 cents, amount: 11 Number of recognisable fifths : 25, average 701.8276 cents Scale contains a complete diamond : 3 5 7 9 15 21 All steps are superparticular (epimoric) Length of longest harmonic part : 2 at degree 24 Length of longest subharmonic part : 2 at degree 3 Formal octave complements present : 29 = 100.0000% Scale is differentially coherent in interval class 1 Inversional symmetry on degrees : 0 Inversional symmetry on intervals : 14-15 -- Rational properties -- Prime limit : 11 Odd number limit : 1089 (O: 1089 U: 1089) Highest odd numerator or denominator: 33 Scale harmonicity : 0.010941 Average absolute harmonicity : 0.108632 Specific harmonicity : 0.080594 Fundamental : 1/110880, -16.7586 octaves, 0.0024 Hz. Guide tone : 221760, 17.7586 octaves, 58018085.361 Hz. Exponens Consonantiae : 2.458875E+10, 34.51728 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 343.0, average 11.82759 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 26.91969, average 0.92827 Sum of Tenney's harmonic distance : 54.61764, average 1.88337 Vogel's harmonic complexity : 34.51724 Wille's k value : 57172 Wilson's harmonic complexity : 58 Rectangular lattice diameter : 10 Triangular lattice diameter : 4 Lattice compactness : 1519.94577, average 3.49413 Lattice compactness (without 2's) : 894.92574, average 2.05730 Number of different primes : 5 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.51724 51 1 3: -2 .. 2 0.00000 26 2 5: -1 .. 1 0.00000 12 6 7: -1 .. 1 0.00000 12 12 11: -1 .. 1 0.00000 8 8 Average exponent except 2's : 0 / 29 = 0.00000 Average absolute exponent except 2's: 58 / 29 = 2.00000 Scale is weakly epimorphic with val: <29 43 67 80 98| Scale is weakly epimorphic with val: <29 46 68 79 101| Scale is weakly epimorphic with val: <29 47 68 80 103|
FIT/MODE
29: 1 1 1 0 1 1 1 1 1 1 1 2 1 1 1 0 2 1 1 1 1 1 1 1 1 1 1 0 2 N T3 SD: 17.8256 c. M: 29.4857 c. 30: 1 1 1 1 1 1 1 1 1 1 1 1 2 1 0 1 2 1 1 1 1 1 1 1 1 1 1 1 1 N D3 I SD: 11.5665 c. M:-18.0450 c. 31: 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 1 N D3 I SD: 6.8185 c. M: 14.5633 c. 38: 2 1 1 1 1 1 1 2 1 1 2 2 1 1 2 1 1 2 2 1 1 2 1 1 1 1 1 1 2 N I SD: 9.1805 c. M: 14.4758 c. 39: 2 1 1 1 1 1 2 1 1 2 1 2 2 1 1 1 2 2 1 2 1 1 1 2 1 1 1 1 2 N SD: 7.8300 c. M: 15.7895 c. 41: 2 1 1 1 1 2 1 2 1 1 2 2 2 1 1 1 2 2 2 1 1 2 1 2 1 1 1 1 2 N I SD: 4.2741 c. M: 6.7940 c. 68: 3 2 2 2 1 3 2 3 2 2 3 3 3 2 2 2 3 3 3 2 2 3 2 3 1 2 2 2 3 N I SD: 4.1528 c. M:-8.1865 c. 72: 3 2 2 2 2 3 2 3 2 2 3 4 3 2 2 2 3 4 3 2 2 3 2 3 2 2 2 2 3 N I SD: 1.8870 c. M: 3.2729 c. 118: 5 3 4 3 3 5 3 5 3 4 5 6 5 3 4 3 5 6 5 4 3 5 3 5 3 3 4 3 5 N I SD: 2.0416 c. M:-3.1113 c. 130: 6 3 4 3 4 5 4 5 4 4 5 7 6 3 4 3 6 7 5 4 4 5 4 5 4 3 4 3 6 N I SD: 1.7922 c. M: 3.3613 c. 152: 7 4 4 4 4 6 5 6 4 5 6 8 7 4 4 4 7 8 6 5 4 6 5 6 4 4 4 4 7 N I SD: 1.3190 c. M:-2.3749 c. 183: 8 5 5 5 5 7 6 7 5 6 7 10 8 5 5 5 8 10 7 6 5 7 6 7 5 5 5 5 8 N I SD: 1.1565 c. M: 2.2972 c. 198: 9 5 6 5 5 8 6 8 5 7 8 10 9 5 6 5 9 10 8 7 5 8 6 8 5 5 6 5 9 N I SD: 1.0709 c. M: 1.9534 c. 224: 10 6 6 6 6 9 7 9 6 7 9 12 10 6 6 6 10 12 9 7 6 9 7 9 6 6 6 6 10 N I SD: 0.8732 c. M: 1.5857 c. 229: 10 6 7 6 6 9 7 9 6 8 9 12 10 6 7 6 10 12 9 8 6 9 7 9 6 6 7 6 10 N I SD: 0.9711 c. M: 1.5564 c. 270: 12 7 8 7 7 11 8 11 7 9 11 14 12 7 8 7 12 14 11 9 7 11 8 11 7 7 8 7 12 N I SD: 0.3444 c. M: 0.7413 c. 342: 15 9 10 9 9 14 10 14 9 11 14 18 15 9 10 9 15 18 14 11 9 14 10 14 9 9 10 9 15 N I SD: 0.2813 c. M: 0.6414 c. 494: 22 13 14 13 13 20 15 20 13 16 20 26 22 13 14 13 22 26 20 16 13 20 15 20 13 13 14 13 22 N I SD: 0.2853 c. M:-0.5530 c. 612: 27 16 18 16 16 25 18 25 16 20 25 32 27 16 18 16 27 32 25 20 16 25 18 25 16 16 18 16 27 N I SD: 0.2152 c. M: 0.3491 c. 764: 34 20 22 20 20 31 23 31 20 25 31 40 34 20 22 20 34 40 31 25 20 31 23 31 20 20 22 20 34 N I SD: 0.1792 c. M:-0.3496 c. 836: 37 22 24 22 22 34 25 34 22 27 34 44 37 22 24 22 37 44 34 27 22 34 25 34 22 22 24 22 37 N I SD: 0.1606 c. M: 0.3041 c. 1053: 47 27 31 27 28 43 31 43 28 34 43 55 47 27 31 27 47 55 43 34 28 43 31 43 28 27 31 27 47 N I SD: 0.1761 c. M: 0.2883 c. 1084: 48 28 32 28 29 44 32 44 29 35 44 57 48 28 32 28 48 57 44 35 29 44 32 44 29 28 32 28 48 N I SD: 0.1620 c. M:-0.3344 c. 1106: 49 29 32 29 29 45 33 45 29 36 45 58 49 29 32 29 49 58 45 36 29 45 33 45 29 29 32 29 49 N I SD: 0.1157 c. M: 0.2108 c. 1236: 55 32 36 32 33 50 37 50 33 40 50 65 55 32 36 32 55 65 50 40 33 50 37 50 33 32 36 32 55 N I SD: 0.1063 c. M: 0.1649 c. 1506: 67 39 44 39 40 61 45 61 40 49 61 79 67 39 44 39 67 79 61 49 40 61 45 61 40 39 44 39 67 N I SD: 0.0736 c. M: 0.1405 c. 1578: 70 41 46 41 42 64 47 64 42 51 64 83 70 41 46 41 70 83 64 51 42 64 47 64 42 41 46 41 70 N I SD: 0.0624 c. M: 0.1206 c. 1848: 82 48 54 48 49 75 55 75 49 60 75 97 82 48 54 48 82 97 75 60 49 75 55 75 49 48 54 48 82 N I SD: 0.0349 c. M: 0.0638 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: 0.0000 cents 6 .. 12 match: 6 H SD: 0.0000 cents 7 .. 14 match: 7 H SD: 2.8116 cents 8 .. 16 match: 8 H SD: 3.2296 cents 9 .. 18 match: 9 H SD: 3.1778 cents 10 .. 20 match: 10 H SD: 2.8302 cents 11 .. 22 match: 11 H SD: 3.5607 cents 12 .. 24 match: 12 H SD: 2.3576 cents 13 .. 26 match: 13 H SD: 4.5057 cents 14 .. 28 match: 14 H SD: 2.6321 cents 15 .. 30 match: 15 H SD: 2.9257 cents 16 .. 32 match: 16 H SD: 3.2681 cents 17 .. 34 match: 17 H SD: 3.6881 cents 18 .. 36 match: 18 H SD: 2.1041 cents 19 .. 38 match: 19 H SD: 3.4446 cents 20 .. 40 match: 20 H SD: 2.2273 cents 21 .. 42 match: 21 H SD: 2.6349 cents 22 .. 44 match: 22 H SD: 2.6061 cents 23 .. 46 match: 22 SD: 2.9442 cents 24 .. 48 match: 24 H SD: 2.0879 cents 25 .. 50 match: 23 S SD: 2.4078 cents 26 .. 52 match: 22 SD: 2.8693 cents 27 .. 54 match: 24 SD: 2.1967 cents 28 .. 56 match: 25 SD: 1.8583 cents 29 .. 58 match: 25 SD: 2.1017 cents 30 .. 60 match: 27 SD: 1.9120 cents 31 .. 62 match: 26 SD: 1.9429 cents 32 .. 64 match: 27 SD: 1.9088 cents 33 .. 66 match: 27 SD: 2.1332 cents 34 .. 68 match: 27 SD: 2.1088 cents 35 .. 70 match: 28 SD: 1.3970 cents 36 .. 72 match: 27 SD: 1.4010 cents 37 .. 74 match: 28 SD: 1.8330 cents 38 .. 76 match: 27 SD: 1.8167 cents 39 .. 78 match: 28 SD: 1.8049 cents 40 .. 80 match: 28 SD: 1.4349 cents 42 .. 84 match: 29 SD: 1.3797 cents 48 .. 96 match: 28 SD: 1.4104 cents 49 .. 98 match: 27 SD: 1.4648 cents 52 .. 104 match: 29 SD: 1.3604 cents 53 .. 106 match: 29 SD: 1.2151 cents 54 .. 108 match: 29 SD: 1.1511 cents 55 .. 110 match: 29 SD: 1.0265 cents 60 .. 120 match: 29 SD: 0.9476 cents 66 .. 132 match: 29 SD: 0.9309 cents 72 .. 144 match: 29 SD: 0.8169 cents 80 .. 160 match: 29 SD: 0.7661 cents 84 .. 168 match: 29 SD: 0.6785 cents 90 .. 180 match: 29 SD: 0.6766 cents 95 .. 190 match: 29 SD: 0.6629 cents 96 .. 192 match: 29 SD: 0.5728 cents 99 .. 198 match: 29 SD: 0.5659 cents 112 .. 224 match: 29 SD: 0.5553 cents 119 .. 238 match: 29 SD: 0.5354 cents 120 .. 240 match: 29 SD: 0.4547 cents 126 .. 252 match: 29 SD: 0.4270 cents 140 .. 280 match: 29 SD: 0.4096 cents 144 .. 288 match: 29 SD: 0.4005 cents 154 .. 308 match: 29 SD: 0.3948 cents 155 .. 310 match: 29 SD: 0.3848 cents 156 .. 312 match: 29 SD: 0.3774 cents 165 .. 330 match: 29 SD: 0.3598 cents 168 .. 336 match: 29 SD: 0.3166 cents 180 .. 360 match: 29 SD: 0.2852 cents 196 .. 392 match: 29 SD: 0.2825 cents 198 .. 396 match: 29 SD: 0.2744 cents 200 .. 400 match: 29 SD: 0.2704 cents 216 .. 432 match: 29 SD: 0.2608 cents 220 .. 440 match: 29 SD: 0.2554 cents 224 .. 448 match: 29 SD: 0.2457 cents 240 .. 480 match: 29 SD: 0.2265 cents 252 .. 504 match: 29 SD: 0.1993 cents 264 .. 528 match: 29 SD: 0.1985 cents 280 .. 560 match: 29 SD: 0.1764 cents 324 .. 648 match: 29 SD: 0.1753 cents 336 .. 672 match: 29 SD: 0.1716 cents 350 .. 700 match: 29 SD: 0.1689 cents 360 .. 720 match: 29 SD: 0.1160 cents 420 .. 840 match: 29 SD: 0.0976 cents 504 .. 1008 match: 29 SD: 0.0754 cents