Scala analysis: dalarna-herding-mode
Dalarna Herding Mode (Andreya's Interpretation)
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 9/8 203.910002 major whole tone 2: 13/11 289.209719 tridecimal minor third 3: 6/5 315.641287 minor third 4: 11/9 347.407941 undecimal neutral third 5: 5/4 386.313714 major third 6: 14/11 417.507964 undecimal diminished fourth or major third 7: 4/3 498.044999 perfect fourth 8: 11/8 551.317942 undecimal semi-augmented fourth 9: 45/32 590.223716 diatonic tritone 10: 3/2 701.955001 perfect fifth 11: 52/33 787.254719 tridecimal minor sixth 12: 8/5 813.686286 minor sixth 13: 18/11 852.592059 undecimal neutral sixth 14: 5/3 884.358713 major sixth, BP sixth 15: 56/33 915.552963 16: 39/22 991.164720 17: 9/5 1017.596288 just minor seventh, BP seventh 18: 11/6 1049.362941 undecimal neutral seventh, 21/4-tone 19: 15/8 1088.268715 classic major seventh 20: 21/11 1119.462965 undecimal major seventh 21: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 22/21 80.5370 undecimal minor semitone 1: 9/8 203.9100 major whole tone 2: 104/99 85.2997 3: 66/65 26.4316 Winmeanma 4: 55/54 31.7667 telepathma 5: 45/44 38.9058 1/5-tone 6: 56/55 31.1943 undecimal diesis, konbini comma 7: 22/21 80.5370 undecimal minor semitone 8: 33/32 53.2729 undecimal comma, al-Farabi's 1/4-tone 9: 45/44 38.9058 1/5-tone 10: 16/15 111.7313 minor diatonic semitone 11: 104/99 85.2997 12: 66/65 26.4316 Winmeanma 13: 45/44 38.9058 1/5-tone 14: 55/54 31.7667 telepathma 15: 56/55 31.1943 undecimal diesis, konbini comma 16: 117/112 75.6118 17: 66/65 26.4316 Winmeanma 18: 55/54 31.7667 telepathma 19: 45/44 38.9058 1/5-tone 20: 56/55 31.1943 undecimal diesis, konbini comma 21: 22/21 80.5370 undecimal minor semitone
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 66/65 26.432 cents Winmeanma 1: 3 56/55 31.194 cents undecimal diesis, konbini comma 1: 3 55/54 31.767 cents telepathma 1: 4 45/44 38.906 cents 1/5-tone 1: 1 33/32 53.273 cents undecimal comma, al-Farabi's 1/4-tone 1: 1 117/112 75.612 cents 1: 2 22/21 80.537 cents undecimal minor semitone 1: 2 104/99 85.300 cents 1: 1 16/15 111.731 cents minor diatonic semitone 1: 1 9/8 203.910 cents major whole tone 2: 2 121/117 58.198 cents 2: 1 28/27 62.961 cents Archytas' 1/3-tone 2: 1 27/26 65.337 cents tridecimal comma 2: 2 126/121 70.100 cents 2: 3 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 135/128 92.179 cents major chroma, major limma 2: 1 297/280 102.043 cents 2: 1 117/110 106.806 cents 2: 4 16/15 111.731 cents minor diatonic semitone 2: 1 121/112 133.810 cents 2: 1 12/11 150.637 cents undecimal neutral second, 3/4-tone 2: 1 1664/1485 197.031 cents 2: 1 33/28 284.447 cents undecimal minor third 2: 1 13/11 289.210 cents tridecimal minor third 3: 3 55/52 97.104 cents 3: 3 35/33 101.867 cents 3: 1 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 3: 1 121/112 133.810 cents 3: 1 13/12 138.573 cents tridecimal 2/3-tone 3: 1 88/81 143.498 cents 2nd undecimal neutral second 3: 3 12/11 150.637 cents undecimal neutral second, 3/4-tone 3: 1 11/10 165.004 cents Ptolemy's second, 4/5-tone 3: 1 495/448 172.716 cents 3: 1 9/8 203.910 cents major whole tone 3: 1 256/225 223.463 cents Neapolitan diminished third 3: 1 416/363 235.937 cents 3: 2 6/5 315.641 cents minor third 3: 1 26/21 369.747 cents 4: 3 14/13 128.298 cents 2/3-tone 4: 2 11/10 165.004 cents Ptolemy's second, 4/5-tone 4: 1 495/448 172.716 cents 4: 1 195/176 177.478 cents 4: 4 10/9 182.404 cents minor whole tone 4: 2 9/8 203.910 cents major whole tone 4: 2 64/55 262.368 cents 4: 1 33/28 284.447 cents undecimal minor third 4: 1 13/11 289.210 cents tridecimal minor third 4: 1 11/9 347.408 cents undecimal neutral third 4: 1 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 4: 1 44/35 396.178 cents 4: 1 208/165 400.941 cents 5: 1 121/108 196.771 cents 5: 4 9/8 203.910 cents major whole tone 5: 2 44/39 208.835 cents 5: 2 112/99 213.598 cents 5: 1 55/48 235.677 cents undecimal semi-augmented whole tone 5: 1 405/352 242.816 cents 5: 1 32/27 294.135 cents Pythagorean minor third 5: 1 144/121 301.274 cents two (undecimal neutral second, 3/4-tone) 5: 2 6/5 315.641 cents minor third 5: 1 26/21 369.747 cents 5: 2 5/4 386.314 cents major third 5: 1 32/25 427.373 cents classic diminished fourth 5: 1 242/189 427.945 cents 5: 1 156/121 439.847 cents 6: 1 297/260 230.342 cents 6: 1 63/55 235.104 cents 6: 2 55/48 235.677 cents undecimal semi-augmented whole tone 6: 1 121/104 262.108 cents 6: 1 75/64 274.582 cents classic augmented second 6: 1 33/28 284.447 cents undecimal minor third 6: 1 13/11 289.210 cents tridecimal minor third 6: 1 32/27 294.135 cents Pythagorean minor third 6: 1 1792/1485 325.329 cents 6: 1 40/33 333.041 cents 6: 2 27/22 354.547 cents neutral third, Zalzal wosta of al-Farabi 6: 1 44/35 396.178 cents 6: 1 208/165 400.941 cents 6: 1 33/26 412.745 cents tridecimal major third 6: 1 14/11 417.508 cents undecimal diminished fourth or major third 6: 1 176/135 459.139 cents 6: 1 72/55 466.278 cents undecimal semi-diminished fourth 6: 1 55/42 466.851 cents 6: 1 130/99 471.613 cents 7: 1 121/104 262.108 cents 7: 1 7/6 266.871 cents septimal minor third 7: 1 75/64 274.582 cents classic augmented second 7: 1 495/416 301.014 cents 7: 2 6/5 315.641 cents minor third 7: 1 11/9 347.408 cents undecimal neutral third 7: 1 448/363 364.235 cents 7: 2 5/4 386.314 cents major third 7: 1 208/165 400.941 cents 7: 1 32/25 427.373 cents classic diminished fourth 7: 1 9/7 435.084 cents septimal major third, BP third 7: 1 156/121 439.847 cents 7: 1 297/224 488.357 cents 7: 6 4/3 498.045 cents perfect fourth 8: 1 495/416 301.014 cents 8: 1 105/88 305.777 cents 8: 2 11/9 347.408 cents undecimal neutral third 8: 1 5/4 386.314 cents major third 8: 1 33/26 412.745 cents tridecimal major third 8: 1 14/11 417.508 cents undecimal diminished fourth or major third 8: 1 32/25 427.373 cents classic diminished fourth 8: 1 156/121 439.847 cents 8: 2 72/55 466.278 cents undecimal semi-diminished fourth 8: 1 55/42 466.851 cents 8: 1 130/99 471.613 cents 8: 1 27/20 519.551 cents acute fourth 8: 1 88/65 524.477 cents 8: 1 224/165 529.239 cents 8: 1 110/81 529.812 cents 8: 1 15/11 536.951 cents undecimal augmented fourth 8: 1 11/8 551.318 cents undecimal semi-augmented fourth 8: 1 39/28 573.657 cents 8: 1 88/63 578.582 cents 9: 1 63/52 332.208 cents 9: 2 5/4 386.314 cents major third 9: 1 176/135 459.139 cents 9: 1 72/55 466.278 cents undecimal semi-diminished fourth 9: 1 117/88 493.120 cents tridecimal gentle fourth 9: 5 4/3 498.045 cents perfect fourth 9: 1 162/121 505.184 cents 9: 1 11/8 551.318 cents undecimal semi-augmented fourth 9: 1 484/351 556.243 cents 9: 1 168/121 568.145 cents 9: 1 25/18 568.717 cents classic augmented fourth 9: 1 45/32 590.224 cents diatonic tritone 9: 1 99/70 600.088 cents 2nd quasi-equal tritone 9: 1 78/55 604.851 cents 9: 1 64/45 609.776 cents 2nd tritone 9: 1 121/84 631.855 cents 10: 1 33/26 412.745 cents tridecimal major third 10: 1 14/11 417.508 cents undecimal diminished fourth or major third 10: 2 4/3 498.045 cents perfect fourth 10: 1 27/20 519.551 cents acute fourth 10: 1 88/65 524.477 cents 10: 1 224/165 529.239 cents 10: 2 15/11 536.951 cents undecimal augmented fourth 10: 1 39/28 573.657 cents 10: 1 416/297 583.345 cents 10: 1 45/32 590.224 cents diatonic tritone 10: 1 55/39 595.149 cents 10: 1 140/99 599.912 cents quasi-equal tritone 10: 1 36/25 631.283 cents classic diminished fifth 10: 1 121/84 631.855 cents 10: 1 13/9 636.618 cents tridecimal diminished fifth 10: 1 16/11 648.682 cents undecimal semi-diminished fifth 10: 1 22/15 663.049 cents undecimal diminished fifth 10: 1 165/112 670.761 cents 10: 1 3/2 701.955 cents perfect fifth 11: 1 4/3 498.045 cents perfect fourth 11: 1 224/165 529.239 cents 11: 1 15/11 536.951 cents undecimal augmented fourth 11: 1 11/8 551.318 cents undecimal semi-augmented fourth 11: 1 18/13 563.382 cents tridecimal augmented fourth 11: 1 168/121 568.145 cents 11: 1 25/18 568.717 cents classic augmented fourth 11: 1 99/70 600.088 cents 2nd quasi-equal tritone 11: 1 78/55 604.851 cents 11: 1 64/45 609.776 cents 2nd tritone 11: 1 297/208 616.655 cents 11: 1 56/39 626.343 cents 11: 2 22/15 663.049 cents undecimal diminished fifth 11: 1 165/112 670.761 cents 11: 1 65/44 675.523 cents 11: 1 40/27 680.449 cents grave fifth 11: 2 3/2 701.955 cents perfect fifth 11: 1 11/7 782.492 cents undecimal augmented fifth 11: 1 52/33 787.255 cents tridecimal minor sixth 12: 1 168/121 568.145 cents 12: 1 45/32 590.224 cents diatonic tritone 12: 1 55/39 595.149 cents 12: 1 140/99 599.912 cents quasi-equal tritone 12: 1 64/45 609.776 cents 2nd tritone 12: 1 36/25 631.283 cents classic diminished fifth 12: 1 121/84 631.855 cents 12: 1 351/242 643.757 cents 12: 1 16/11 648.682 cents undecimal semi-diminished fifth 12: 1 121/81 694.816 cents two (undecimal neutral third) 12: 5 3/2 701.955 cents perfect fifth 12: 1 176/117 706.880 cents 12: 1 55/36 733.722 cents undecimal semi-augmented fifth 12: 1 135/88 740.861 cents 12: 2 8/5 813.686 cents minor sixth 12: 1 104/63 867.792 cents 13: 1 63/44 621.418 cents 13: 1 56/39 626.343 cents 13: 1 16/11 648.682 cents undecimal semi-diminished fifth 13: 1 22/15 663.049 cents undecimal diminished fifth 13: 1 81/55 670.188 cents 13: 1 165/112 670.761 cents 13: 1 65/44 675.523 cents 13: 1 40/27 680.449 cents grave fifth 13: 1 99/65 728.387 cents 13: 1 84/55 733.149 cents 13: 2 55/36 733.722 cents undecimal semi-augmented fifth 13: 1 121/78 760.153 cents 13: 1 25/16 772.627 cents classic augmented fifth 13: 1 11/7 782.492 cents undecimal augmented fifth 13: 1 52/33 787.255 cents tridecimal minor sixth 13: 1 8/5 813.686 cents minor sixth 13: 2 18/11 852.592 cents undecimal neutral sixth 13: 1 176/105 894.223 cents 13: 1 832/495 898.986 cents 14: 6 3/2 701.955 cents perfect fifth 14: 1 448/297 711.643 cents 14: 1 121/78 760.153 cents 14: 1 14/9 764.916 cents septimal minor sixth 14: 1 25/16 772.627 cents classic augmented fifth 14: 1 165/104 799.059 cents 14: 2 8/5 813.686 cents minor sixth 14: 1 363/224 835.765 cents 14: 1 18/11 852.592 cents undecimal neutral sixth 14: 2 5/3 884.359 cents major sixth, BP sixth 14: 1 832/495 898.986 cents 14: 1 128/75 925.418 cents diminished seventh 14: 1 12/7 933.129 cents septimal major sixth 14: 1 208/121 937.892 cents 15: 1 99/65 728.387 cents 15: 1 84/55 733.149 cents 15: 1 55/36 733.722 cents undecimal semi-augmented fifth 15: 1 135/88 740.861 cents 15: 1 11/7 782.492 cents undecimal augmented fifth 15: 1 52/33 787.255 cents tridecimal minor sixth 15: 1 165/104 799.059 cents 15: 1 35/22 803.822 cents 15: 2 44/27 845.453 cents neutral sixth 15: 1 33/20 866.959 cents 15: 1 1485/896 874.671 cents 15: 1 27/16 905.865 cents Pythagorean major sixth 15: 1 22/13 910.790 cents tridecimal major sixth 15: 1 56/33 915.553 cents 15: 1 128/75 925.418 cents diminished seventh 15: 1 208/121 937.892 cents 15: 2 96/55 964.323 cents 15: 1 110/63 964.896 cents 15: 1 520/297 969.658 cents 16: 1 121/78 760.153 cents 16: 1 189/121 772.055 cents 16: 1 25/16 772.627 cents classic augmented fifth 16: 2 8/5 813.686 cents minor sixth 16: 1 21/13 830.253 cents 16: 2 5/3 884.359 cents major sixth, BP sixth 16: 1 121/72 898.726 cents 16: 1 27/16 905.865 cents Pythagorean major sixth 16: 1 704/405 957.184 cents 16: 1 96/55 964.323 cents 16: 2 99/56 986.402 cents 16: 2 39/22 991.165 cents 16: 4 16/9 996.090 cents Pythagorean minor seventh 16: 1 216/121 1003.229 cents 17: 1 165/104 799.059 cents 17: 1 35/22 803.822 cents 17: 1 44/27 845.453 cents neutral sixth 17: 1 18/11 852.592 cents undecimal neutral sixth 17: 1 22/13 910.790 cents tridecimal major sixth 17: 1 56/33 915.553 cents 17: 2 55/32 937.632 cents 17: 2 16/9 996.090 cents Pythagorean minor seventh 17: 4 9/5 1017.596 cents just minor seventh, BP seventh 17: 1 352/195 1022.522 cents 17: 1 896/495 1027.284 cents 17: 2 20/11 1034.996 cents large minor seventh 17: 3 13/7 1071.702 cents 16/3-tone 18: 1 21/13 830.253 cents 18: 2 5/3 884.359 cents major sixth, BP sixth 18: 1 363/208 964.063 cents 18: 1 225/128 976.537 cents augmented sixth 18: 1 16/9 996.090 cents Pythagorean minor seventh 18: 1 896/495 1027.284 cents 18: 1 20/11 1034.996 cents large minor seventh 18: 3 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 18: 1 81/44 1056.502 cents 2nd undecimal neutral seventh 18: 1 24/13 1061.427 cents tridecimal neutral seventh 18: 1 224/121 1066.190 cents 18: 1 50/27 1066.762 cents grave major seventh 18: 3 66/35 1098.133 cents 18: 3 104/55 1102.896 cents 19: 1 22/13 910.790 cents tridecimal major sixth 19: 1 56/33 915.553 cents 19: 1 1485/832 1002.969 cents 19: 1 11/6 1049.363 cents undecimal neutral seventh, 21/4-tone 19: 1 224/121 1066.190 cents 19: 4 15/8 1088.269 cents classic major seventh 19: 1 220/117 1093.194 cents 19: 1 560/297 1097.957 cents 19: 1 256/135 1107.821 cents octave - major chroma 19: 3 48/25 1129.328 cents classic diminished octave 19: 2 121/63 1129.900 cents 19: 1 52/27 1134.663 cents 19: 1 27/14 1137.039 cents septimal major seventh 19: 2 234/121 1141.802 cents 20: 1 16/9 996.090 cents Pythagorean minor seventh 20: 1 15/8 1088.269 cents classic major seventh 20: 2 99/52 1114.700 cents 20: 2 21/11 1119.463 cents undecimal major seventh 20: 1 224/117 1124.388 cents 20: 1 64/33 1146.727 cents 33rd subharmonic 20: 4 88/45 1161.094 cents 20: 3 108/55 1168.233 cents 20: 3 55/28 1168.806 cents 20: 3 65/33 1173.568 cents Highest number of different intervals for one interval class: 19 Average number of different intervals per interval class: 15.20000 = 76/5
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 0.0 : 203.9 289.2 315.6 347.4 386.3 417.5 498.0 551.3 590.2 702.0 787.3 813.7 852.6 884.4 915.6 991.2 1017.6 1049.4 1088.3 1119.5 1200.0 203.9 : 85.3 111.7 143.5 182.4 213.6 294.1 347.4 386.3 498.0 583.3 609.8 648.7 680.4 711.6 787.3 813.7 845.5 884.4 915.6 996.1 1200.0 289.2 : 26.4 58.2 97.1 128.3 208.8 262.1 301.0 412.7 498.0 524.5 563.4 595.1 626.3 702.0 728.4 760.2 799.1 830.3 910.8 1114.7 1200.0 315.6 : 31.8 70.7 101.9 182.4 235.7 274.6 386.3 471.6 498.0 537.0 568.7 599.9 675.5 702.0 733.7 772.6 803.8 884.4 1088.3 1173.6 1200.0 347.4 : 38.9 70.1 150.6 203.9 242.8 354.5 439.8 466.3 505.2 537.0 568.1 643.8 670.2 702.0 740.9 772.1 852.6 1056.5 1141.8 1168.2 1200.0 386.3 : 31.2 111.7 165.0 203.9 315.6 400.9 427.4 466.3 498.0 529.2 604.9 631.3 663.0 702.0 733.1 813.7 1017.6 1102.9 1129.3 1161.1 1200.0 417.5 : 80.5 133.8 172.7 284.4 369.7 396.2 435.1 466.9 498.0 573.7 600.1 631.9 670.8 702.0 782.5 986.4 1071.7 1098.1 1129.9 1168.8 1200.0 498.0 : 53.3 92.2 203.9 289.2 315.6 354.5 386.3 417.5 493.1 519.6 551.3 590.2 621.4 702.0 905.9 991.2 1017.6 1049.4 1088.3 1119.5 1200.0 551.3 : 38.9 150.6 235.9 262.4 301.3 333.0 364.2 439.8 466.3 498.0 537.0 568.1 648.7 852.6 937.9 964.3 996.1 1035.0 1066.2 1146.7 1200.0 590.2 : 111.7 197.0 223.5 262.4 294.1 325.3 400.9 427.4 459.1 498.0 529.2 609.8 813.7 899.0 925.4 957.2 996.1 1027.3 1107.8 1161.1 1200.0 702.0 : 85.3 111.7 150.6 182.4 213.6 289.2 315.6 347.4 386.3 417.5 498.0 702.0 787.3 813.7 845.5 884.4 915.6 996.1 1049.4 1088.3 1200.0 787.3 : 26.4 65.3 97.1 128.3 203.9 230.3 262.1 301.0 332.2 412.7 616.7 702.0 728.4 760.2 799.1 830.3 910.8 964.1 1003.0 1114.7 1200.0 813.7 : 38.9 70.7 101.9 177.5 203.9 235.7 274.6 305.8 386.3 590.2 675.5 702.0 733.7 772.6 803.8 884.4 937.6 976.5 1088.3 1173.6 1200.0 852.6 : 31.8 63.0 138.6 165.0 196.8 235.7 266.9 347.4 551.3 636.6 663.0 694.8 733.7 764.9 845.5 898.7 937.6 1049.4 1134.7 1161.1 1200.0 884.4 : 31.2 106.8 133.2 165.0 203.9 235.1 315.6 519.6 604.9 631.3 663.0 702.0 733.1 813.7 867.0 905.9 1017.6 1102.9 1129.3 1168.2 1200.0 915.6 : 75.6 102.0 133.8 172.7 203.9 284.4 488.4 573.7 600.1 631.9 670.8 702.0 782.5 835.8 874.7 986.4 1071.7 1098.1 1137.0 1168.8 1200.0 991.2 : 26.4 58.2 97.1 128.3 208.8 412.7 498.0 524.5 556.2 595.1 626.3 706.9 760.2 799.1 910.8 996.1 1022.5 1061.4 1093.2 1124.4 1200.0 1017.6: 31.8 70.7 101.9 182.4 386.3 471.6 498.0 529.8 568.7 599.9 680.4 733.7 772.6 884.4 969.7 996.1 1035.0 1066.8 1098.0 1173.6 1200.0 1049.4: 38.9 70.1 150.6 354.5 439.8 466.3 498.0 537.0 568.1 648.7 702.0 740.9 852.6 937.9 964.3 1003.2 1035.0 1066.2 1141.8 1168.2 1200.0 1088.3: 31.2 111.7 315.6 400.9 427.4 459.1 498.0 529.2 609.8 663.0 702.0 813.7 899.0 925.4 964.3 996.1 1027.3 1102.9 1129.3 1161.1 1200.0 1119.5: 80.5 284.4 369.7 396.2 427.9 466.9 498.0 578.6 631.9 670.8 782.5 867.8 894.2 933.1 964.9 996.1 1071.7 1098.1 1129.9 1168.8 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 26.4316 .. 203.9100 cents 195/176, 177.4784 cents 66/65, 26.4316 cents 2: 58.1982 .. 289.2097 cents 1521/1331, 231.0115 cents 968/1053,-145.7118 cents 3: 97.1040 .. 369.7468 cents 1352/1155, 272.6428 cents 605/676,-192.1057 cents 4: 128.2982 .. 400.9410 cents 1352/1155, 272.6428 cents 147/169,-241.4485 cents 5: 196.7709 .. 439.8468 cents 16848/14641, 243.0759 cents 6655/7488,-204.1701 cents 6: 230.3416 .. 471.6134 cents 33800/29403, 241.2719 cents 11979/13520,-209.5052 cents 7: 262.1082 .. 498.0450 cents 416/363, 235.9368 cents 11979/13520,-209.5052 cents 8: 301.0140 .. 578.5820 cents 3328/2835, 277.5680 cents 1485/1664,-197.0310 cents 9: 332.2082 .. 631.8550 cents 1573/1323, 299.6467 cents 3969/4576,-246.3738 cents 10: 412.7453 .. 701.9550 cents 13/11, 289.2097 cents 126/143,-219.1097 cents 11: 498.0450 .. 787.2547 cents 13/11, 289.2097 cents 8/9,-203.9100 cents 12: 568.1450 .. 867.7918 cents 1573/1323, 299.6467 cents 126/143,-219.1097 cents 13: 621.4180 .. 898.9860 cents 3328/2835, 277.5680 cents 3969/4576,-246.3738 cents 14: 701.9550 .. 937.8918 cents 416/363, 235.9368 cents 1485/1664,-197.0310 cents 15: 728.3866 .. 969.6584 cents 33800/29403, 241.2719 cents 11979/13520,-209.5052 cents 16: 760.1532 .. 1003.2291 cents 16848/14641, 243.0759 cents 11979/13520,-209.5052 cents 17: 799.0590 .. 1071.7018 cents 1352/1155, 272.6428 cents 6655/7488,-204.1701 cents 18: 830.2532 .. 1102.8960 cents 1352/1155, 272.6428 cents 147/169,-241.4485 cents 19: 910.7903 .. 1141.8018 cents 1521/1331, 231.0115 cents 605/676,-192.1057 cents 20: 996.0900 .. 1173.5684 cents 195/176, 177.4784 cents 968/1053,-145.7118 cents
SHOW DATA
Number of notes : 21 -- Interval properties -- Smallest interval : 66/65, 26.4316 cents, class 1 Average step (divided formal octave): 57.1429 cents Largest one step interval : 9/8, 203.9100 cents Average / Smallest step : 2.161917 Largest / Average step : 3.568425 Largest / Smallest step : 7.714639 Median interval of one step : 45/44, 38.9058 cents, amount: 4 Most common interval of one step : 45/44, 38.9058 cents, amount: 4 Least squares average step : 61.52783 cents, oct.: 1292.08442 cents Scale is not proper Step pattern alph. order: ABCDEFGHEIBCEDFJCDEFG Step pattern size order : JHACDBGEDIHADCBFACDBG Scale is not a Constant Structure Scale diversity : 1.566809 Lumma stability : 0.044053 Lumma impropriety factor : 0.903003 Number of different interval sizes : 182 = 9.10000 / class Number of one step interval sizes : 10 Highest interval variety : 19 Mean interval variety : 15.20000 = 76/5 Median interval variety : 11.5 Lowest interval variety : 10 Smallest interval difference : 9801/9800, 0.1766 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 14 Most common triad is 0.0 498.045 701.955 cents, amount: 8 Number of recognisable fifths : 17, average 702.3947 cents Scale contains a complete diamond : 1 3 5 Length of longest harmonic part : 2 at degree 13 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 9 = 42.8571% Scale is n-1 differentially coherent in interval classes 1 and 2 combined -- Rational properties -- Prime limit : 13 Odd number limit : 1485 (O: 1485 U: 1485) Highest odd numerator or denominator: 45 Scale harmonicity : 0.009973 Average absolute harmonicity : 0.124348 Specific harmonicity : 0.069429 Fundamental : 1/15840, -13.9513 octaves, 0.0165 Hz. Guide tone : 360360, 18.4591 octaves, 94279388.712 Hz. Exponens Consonantiae : 5.708102E+09, 32.41036 octaves Euler's gradus suavitatis : 63 Sum of Mann's harmonic distance : 294.0, average 14.00000 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 20.75913, average 0.98853 Sum of Tenney's harmonic distance : 40.66026, average 1.93620 Vogel's harmonic complexity : 28.61905 Wille's k value : 11137 Wilson's harmonic complexity : 64 Rectangular lattice diameter : 10 Triangular lattice diameter : 5 Lattice compactness : 764.58018, average 3.30987 Lattice compactness (without 2's) : 471.93663, average 2.04302 Number of different primes : 6 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -0.23810 33 1 3: -2 .. 2 0.28571 20 3 5: -1 .. 1 0.04762 7 7 7: 0 .. 1 0.14286 3 11: -1 .. 1 -0.19048 10 7 13: 0 .. 1 0.14286 3 3 Average exponent except 2's : 9 / 21 = 0.42857 Average absolute exponent except 2's: 43 / 21 = 2.04762
FIT/MODE
21: 3 2 0 1 0 1 1 1 1 2 1 1 0 1 1 1 0 1 1 0 2 N SD: 28.9543 c. M: 52.5921 c. 22: 4 1 1 0 1 1 1 1 1 2 1 1 1 0 1 1 1 0 1 1 1 N SD: 14.0929 c. M:-25.9916 c. 24: 4 2 0 1 1 0 2 1 1 2 2 0 1 1 0 2 0 1 1 0 2 N SD: 11.4006 c. M: 19.4630 c. 30: 5 2 1 1 1 0 2 2 1 3 2 0 1 1 1 2 0 1 1 1 2 N SD: 11.3070 c. M:-18.0450 c. 31: 5 2 1 1 1 1 2 1 1 3 2 1 1 1 1 2 0 1 1 1 2 N SD: 8.6565 c. M: 18.2420 c. 32: 5 3 0 1 1 1 2 2 1 3 2 1 1 1 0 2 1 1 1 1 2 N SD: 10.5927 c. M: 16.4100 c. 34: 6 2 1 1 1 1 2 2 1 3 2 1 1 1 1 2 1 1 1 1 2 N SD: 6.5989 c. M:-13.3879 c. 41: 7 3 1 1 1 1 3 2 1 4 3 1 1 1 1 3 1 1 1 1 3 N SD: 5.0472 c. M: 8.2359 c. 46: 8 3 1 1 2 1 3 2 2 4 3 1 2 1 1 3 1 1 2 1 3 N SD: 4.7300 c. M:-9.7763 c. 63: 11 4 2 1 2 2 4 3 2 6 4 2 2 1 2 4 1 2 2 2 4 N SD: 4.5294 c. M: 8.1682 c. 65: 11 5 1 2 2 2 4 3 2 6 5 1 2 2 2 4 1 2 2 2 4 N SD: 3.9139 c. M:-7.5240 c. 72: 12 5 2 2 2 2 5 3 2 7 5 2 2 2 2 4 2 2 2 2 5 N SD: 3.4647 c. M: 7.8314 c. 75: 13 5 2 2 2 2 5 3 3 7 5 2 2 2 2 5 2 2 2 2 5 N SD: 3.6888 c. M: 7.3179 c. 84: 14 6 2 2 3 2 6 3 3 8 6 2 2 3 2 5 2 2 3 2 6 N SD: 4.2405 c. M: 9.7349 c. 85: 14 6 2 3 2 3 5 4 3 8 6 2 2 3 2 5 2 2 3 2 6 N SD: 4.3217 c. M: 6.8568 c. 86: 15 6 2 2 3 2 6 4 2 8 6 2 3 2 3 5 2 2 3 2 6 N SD: 3.9441 c. M:-6.8216 c. 87: 15 6 2 2 3 2 6 4 3 8 6 2 3 2 2 6 2 2 3 2 6 N SD: 2.2242 c. M: 5.2081 c. 94: 16 7 2 2 3 3 6 4 3 9 7 2 3 2 3 6 2 2 3 3 6 N SD: 3.1440 c. M:-4.5800 c. 96: 16 7 2 3 3 2 7 4 3 9 7 2 3 3 2 6 2 3 3 2 7 N SD: 3.0421 c. M: 6.9630 c. 104: 18 7 2 3 3 3 7 5 3 10 7 2 4 3 2 7 2 3 3 3 7 N SD: 2.9487 c. M: 5.9940 c. 106: 18 8 2 3 3 3 7 5 3 10 8 2 3 3 3 7 2 3 3 3 7 N SD: 2.6444 c. M:-5.1981 c. 111: 19 8 2 3 4 3 7 5 4 10 8 2 4 3 3 7 2 3 4 3 7 N SD: 2.6045 c. M:-4.8614 c. 118: 20 8 3 3 4 3 8 5 4 11 8 3 4 3 3 7 3 3 4 3 8 N SD: 1.9030 c. M: 4.7240 c. 120: 20 9 3 3 4 3 8 5 4 11 9 2 4 3 4 7 3 3 4 3 8 N SD: 2.6575 c. M:-4.4470 c. 121: 21 8 3 3 4 3 8 6 4 11 8 3 4 3 3 8 3 3 4 3 8 N SD: 2.4860 c. M:-4.8176 c. 128: 22 9 3 3 4 4 8 6 4 12 9 3 4 3 4 8 3 3 4 3 9 N SD: 2.3004 c. M:-4.3670 c. 130: 22 9 3 4 4 3 9 6 4 12 9 3 4 4 3 8 3 4 4 3 9 N SD: 2.1525 c. M: 3.4724 c. 137: 23 10 3 4 4 4 9 6 4 13 10 3 4 4 4 8 3 4 4 4 9 N SD: 1.9722 c. M:-4.1551 c. 146: 25 10 3 4 5 4 10 6 5 13 11 3 5 4 3 10 3 4 4 4 10 N SD: 2.3163 c. M:-3.3558 c. 149: 25 11 3 4 5 4 10 6 5 14 11 3 5 4 4 9 3 4 5 4 10 N SD: 1.7435 c. M: 3.6669 c. 152: 26 11 3 4 5 4 10 7 5 14 11 3 5 4 4 10 3 4 5 4 10 N SD: 1.3911 c. M:-3.5721 c. 159: 27 11 4 4 5 4 11 7 5 15 11 4 5 4 4 10 4 4 5 4 11 N SD: 1.5297 c. M: 2.4855 c. 183: 31 13 4 5 6 5 12 8 6 17 13 4 6 5 5 11 4 5 6 5 12 N SD: 0.9884 c. M:-2.4798 c. 212: 36 15 5 5 7 6 14 9 7 20 15 5 7 5 6 13 5 5 7 6 14 N SD: 1.3651 c. M: 2.2613 c. 224: 38 16 5 6 7 6 15 10 7 21 16 5 7 6 6 14 5 6 7 6 15 N SD: 0.4987 c. M: 0.9380 c. 270: 46 19 6 7 9 7 18 12 9 25 19 6 9 7 7 17 6 7 9 7 18 N SD: 0.4406 c. M:-0.8874 c. 460: 78 33 10 12 15 12 31 20 15 43 33 10 15 12 12 29 10 12 15 12 31 N SD: 0.3960 c. M: 0.8832 c. 494: 84 35 11 13 16 13 33 22 16 46 35 11 16 13 13 31 11 13 16 13 33 N SD: 0.1557 c. M:-0.3751 c. 718: 122 51 16 19 23 19 48 32 23 67 51 16 23 19 19 45 16 19 23 19 48 N SD: 0.2096 c. M:-0.3245 c. 954: 162 68 21 25 31 25 64 42 31 89 68 21 31 25 25 60 21 25 31 25 64 N SD: 0.1750 c. M: 0.3745 c. 1012: 172 72 22 27 33 26 68 45 33 94 72 22 33 27 26 64 22 27 33 26 68 N SD: 0.1571 c. M:-0.2901 c. 1236: 210 88 27 33 40 32 83 55 40 115 88 27 40 33 32 78 27 33 40 32 83 N SD: 0.0987 c. M: 0.1649 c. 1506: 256 107 33 40 49 39 101 67 49 140 107 33 49 40 39 95 33 40 49 39 101 N SD: 0.0896 c. M:-0.2145 c. 1730: 294 123 38 46 56 45 116 77 56 161 123 38 56 46 45 109 38 46 56 45 116 N SD: 0.0635 c. M:-0.1271 c. 2190: 372 156 48 58 71 57 147 97 71 204 156 48 71 58 57 138 48 58 71 57 147 N SD: 0.0595 c. M:-0.1425 c. 2224: 378 158 49 59 72 58 149 99 72 207 158 49 72 59 58 140 49 59 72 58 149 N SD: 0.0653 c. M:-0.1414 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: 5.5847 cents 5 .. 10 match: 5 H SD: 1.5423 cents 6 .. 12 match: 6 H SD: 3.7231 cents 7 .. 14 match: 7 H SD: 7.0009 cents 8 .. 16 match: 8 H SD: 3.1736 cents 9 .. 18 match: 9 H SD: 6.3842 cents 10 .. 20 match: 10 H SD: 5.4757 cents 11 .. 22 match: 10 SD: 7.2938 cents 12 .. 24 match: 11 S SD: 3.2490 cents 13 .. 26 match: 11 SD: 6.7264 cents 14 .. 28 match: 13 S SD: 4.5875 cents 15 .. 30 match: 12 SD: 3.9752 cents 16 .. 32 match: 15 S SD: 4.2216 cents 17 .. 34 match: 14 SD: 4.3703 cents 18 .. 36 match: 15 SD: 3.5247 cents 19 .. 38 match: 15 SD: 4.7011 cents 20 .. 40 match: 14 SD: 3.9114 cents 21 .. 42 match: 17 S SD: 3.8056 cents 22 .. 44 match: 16 SD: 2.5151 cents 23 .. 46 match: 16 SD: 3.0749 cents 24 .. 48 match: 18 SD: 2.4339 cents 25 .. 50 match: 18 SD: 2.7331 cents 26 .. 52 match: 18 SD: 2.6553 cents 27 .. 54 match: 18 SD: 2.6191 cents 28 .. 56 match: 17 SD: 3.1199 cents 29 .. 58 match: 19 SD: 2.7435 cents 30 .. 60 match: 20 SD: 1.8903 cents 31 .. 62 match: 19 SD: 2.3595 cents 32 .. 64 match: 20 SD: 1.8307 cents 33 .. 66 match: 19 SD: 2.0296 cents 34 .. 68 match: 19 SD: 2.1848 cents 35 .. 70 match: 21 SD: 2.1077 cents 36 .. 72 match: 20 SD: 1.9481 cents 37 .. 74 match: 20 SD: 2.0856 cents 38 .. 76 match: 19 SD: 2.1389 cents 39 .. 78 match: 21 SD: 1.8442 cents 40 .. 80 match: 21 SD: 1.2311 cents 42 .. 84 match: 19 SD: 1.6899 cents 44 .. 88 match: 21 SD: 1.6331 cents 45 .. 90 match: 21 SD: 1.4314 cents 47 .. 94 match: 20 SD: 1.6097 cents 48 .. 96 match: 21 SD: 1.4097 cents 49 .. 98 match: 21 SD: 1.3642 cents 50 .. 100 match: 21 SD: 1.3561 cents 54 .. 108 match: 21 SD: 1.1401 cents 56 .. 112 match: 21 SD: 1.1128 cents 64 .. 128 match: 21 SD: 1.0464 cents 66 .. 132 match: 21 SD: 0.8412 cents 72 .. 144 match: 21 SD: 0.8110 cents 80 .. 160 match: 21 SD: 0.7414 cents 88 .. 176 match: 21 SD: 0.6998 cents 96 .. 192 match: 21 SD: 0.5519 cents 120 .. 240 match: 21 SD: 0.3762 cents 144 .. 288 match: 21 SD: 0.3724 cents 165 .. 330 match: 21 SD: 0.3667 cents 168 .. 336 match: 21 SD: 0.3528 cents 175 .. 350 match: 21 SD: 0.3420 cents 176 .. 352 match: 21 SD: 0.3162 cents 198 .. 396 match: 21 SD: 0.3039 cents 210 .. 420 match: 21 SD: 0.2984 cents 216 .. 432 match: 21 SD: 0.2514 cents 224 .. 448 match: 21 SD: 0.2471 cents 256 .. 512 match: 21 SD: 0.2439 cents 264 .. 528 match: 21 SD: 0.1426 cents 360 .. 720 match: 21 SD: 0.1183 cents 440 .. 880 match: 21 SD: 0.0998 cents 528 .. 1056 match: 21 SD: 0.0958 cents 576 .. 1152 match: 21 SD: 0.0907 cents 594 .. 1188 match: 21 SD: 0.0891 cents 600 .. 1200 match: 21 SD: 0.0868 cents