Scala analysis: xen03-wilson-positive-29
Positive, linear-mapped intonational system, 29 notes
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 28/27 62.960904 Archytas' 1/3-tone 2: 256/243 90.224996 limma, Pythagorean minor second 3: 16/15 111.731285 minor diatonic semitone 4: 10/9 182.403712 minor whole tone 5: 9/8 203.910002 major whole tone 6: 7/6 266.870906 septimal minor third 7: 32/27 294.134997 Pythagorean minor third 8: 6/5 315.641287 minor third 9: 5/4 386.313714 major third 10: 81/64 407.820003 Pythagorean major third 11: 21/16 470.780907 narrow fourth 12: 4/3 498.044999 perfect fourth 13: 112/81 561.005903 14: 1024/729 588.269995 Pythagorean diminished fifth 15: 64/45 609.776284 2nd tritone 16: 40/27 680.448711 grave fifth 17: 3/2 701.955001 perfect fifth 18: 14/9 764.915905 septimal minor sixth 19: 128/81 792.179997 Pythagorean minor sixth 20: 8/5 813.686286 minor sixth 21: 5/3 884.358713 major sixth, BP sixth 22: 27/16 905.865003 Pythagorean major sixth 23: 7/4 968.825906 harmonic seventh 24: 16/9 996.089998 Pythagorean minor seventh 25: 9/5 1017.596288 just minor seventh, BP seventh 26: 15/8 1088.268715 classic major seventh 27: 243/128 1109.775004 Pythagorean major seventh 28: 63/32 1172.735908 octave - septimal comma 29: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 64/63 27.2641 septimal comma, Archytas' comma 1: 28/27 62.9609 Archytas' 1/3-tone 2: 64/63 27.2641 septimal comma, Archytas' comma 3: 81/80 21.5063 syntonic comma, Didymus comma 4: 25/24 70.6724 classic chromatic semitone, minor chroma 5: 81/80 21.5063 syntonic comma, Didymus comma 6: 28/27 62.9609 Archytas' 1/3-tone 7: 64/63 27.2641 septimal comma, Archytas' comma 8: 81/80 21.5063 syntonic comma, Didymus comma 9: 25/24 70.6724 classic chromatic semitone, minor chroma 10: 81/80 21.5063 syntonic comma, Didymus comma 11: 28/27 62.9609 Archytas' 1/3-tone 12: 64/63 27.2641 septimal comma, Archytas' comma 13: 28/27 62.9609 Archytas' 1/3-tone 14: 64/63 27.2641 septimal comma, Archytas' comma 15: 81/80 21.5063 syntonic comma, Didymus comma 16: 25/24 70.6724 classic chromatic semitone, minor chroma 17: 81/80 21.5063 syntonic comma, Didymus comma 18: 28/27 62.9609 Archytas' 1/3-tone 19: 64/63 27.2641 septimal comma, Archytas' comma 20: 81/80 21.5063 syntonic comma, Didymus comma 21: 25/24 70.6724 classic chromatic semitone, minor chroma 22: 81/80 21.5063 syntonic comma, Didymus comma 23: 28/27 62.9609 Archytas' 1/3-tone 24: 64/63 27.2641 septimal comma, Archytas' comma 25: 81/80 21.5063 syntonic comma, Didymus comma 26: 25/24 70.6724 classic chromatic semitone, minor chroma 27: 81/80 21.5063 syntonic comma, Didymus comma 28: 28/27 62.9609 Archytas' 1/3-tone 29: 64/63 27.2641 septimal comma, Archytas' comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 10 81/80 21.506 cents syntonic comma, Didymus comma 1: 7 64/63 27.264 cents septimal comma, Archytas' comma 1: 7 28/27 62.961 cents Archytas' 1/3-tone 1: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 5 36/35 48.770 cents septimal diesis, 1/4-tone 2: 5 21/20 84.467 cents minor semitone 2: 9 256/243 90.225 cents limma, Pythagorean minor second 2: 10 135/128 92.179 cents major chroma, major limma 3: 10 16/15 111.731 cents minor diatonic semitone 3: 5 2187/2048 113.685 cents apotome 3: 2 16384/15309 117.489 cents 3: 5 15/14 119.443 cents major diatonic semitone 3: 2 7168/6561 153.186 cents 3: 5 35/32 155.140 cents septimal neutral second 4: 3 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 4: 2 1024/945 138.995 cents 4: 5 243/224 140.949 cents Archytas' 2/3-tone 4: 2 448/405 174.692 cents 4: 5 567/512 176.646 cents 4: 2 65536/59049 180.450 cents Pythagorean diminished third 4: 10 10/9 182.404 cents minor whole tone 5: 4 4096/3645 201.956 cents narrow diminished third 5: 21 9/8 203.910 cents major whole tone 5: 2 640/567 209.668 cents 5: 2 280/243 245.365 cents 6: 2 256/225 223.463 cents Neapolitan diminished third 6: 6 729/640 225.416 cents acute major second 6: 7 8/7 231.174 cents septimal whole tone 6: 7 7/6 266.871 cents septimal minor third 6: 4 2560/2187 272.629 cents grave minor third 6: 3 75/64 274.582 cents classic augmented second 7: 3 81/70 252.680 cents Al-Hwarizmi's lute middle finger 7: 3 189/160 288.377 cents 7: 17 32/27 294.135 cents Pythagorean minor third 7: 6 1215/1024 296.089 cents wide augmented second 8: 10 6/5 315.641 cents minor third 8: 3 19683/16384 317.595 cents Pythagorean augmented second 8: 4 2048/1701 321.399 cents 8: 3 135/112 323.353 cents septimal wide minor third 8: 4 896/729 357.096 cents 8: 3 315/256 359.050 cents 8: 2 100/81 364.807 cents grave major third 9: 1 243/200 337.148 cents acute minor third 9: 4 128/105 342.905 cents septimal neutral third 9: 3 2187/1792 344.859 cents 9: 4 56/45 378.602 cents septimal narrow major third 9: 3 5103/4096 380.556 cents 9: 4 8192/6561 384.360 cents Pythagorean diminished fourth 9: 10 5/4 386.314 cents major third 10: 8 512/405 405.866 cents narrow diminished fourth 10: 13 81/64 407.820 cents Pythagorean major third 10: 4 80/63 413.578 cents wide major third 10: 4 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 11: 4 32/25 427.373 cents classic diminished fourth 11: 2 6561/5120 429.326 cents acute major third 11: 7 9/7 435.084 cents septimal major third, BP third 11: 7 21/16 470.781 cents narrow fourth 11: 8 320/243 476.539 cents grave fourth 11: 1 675/512 478.492 cents wide augmented third 12: 1 729/560 456.590 cents 12: 1 1701/1280 492.287 cents 12: 25 4/3 498.045 cents perfect fourth 12: 2 10935/8192 499.999 cents fourth + schisma, 5-limit approximation to ET fourth 13: 10 27/20 519.551 cents acute fourth 13: 1 177147/131072 521.505 cents Pythagorean augmented third 13: 6 256/189 525.309 cents 13: 1 1215/896 527.263 cents 13: 6 112/81 561.006 cents 13: 1 2835/2048 562.960 cents 13: 4 25/18 568.717 cents classic augmented fourth 14: 5 48/35 546.815 cents septimal semi-augmented fourth 14: 1 19683/14336 548.769 cents 14: 5 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 14: 1 45927/32768 584.466 cents 14: 7 1024/729 588.270 cents Pythagorean diminished fifth 14: 10 45/32 590.224 cents diatonic tritone 15: 10 64/45 609.776 cents 2nd tritone 15: 7 729/512 611.730 cents Pythagorean tritone 15: 1 65536/45927 615.534 cents 15: 5 10/7 617.488 cents Euler's tritone 15: 1 28672/19683 651.231 cents 15: 5 35/24 653.185 cents septimal semi-diminished fifth 16: 4 36/25 631.283 cents classic diminished fifth 16: 1 4096/2835 637.040 cents 16: 6 81/56 638.994 cents 16: 1 1792/1215 672.737 cents 16: 6 189/128 674.691 cents 16: 1 262144/177147 678.495 cents Pythagorean diminished sixth 16: 10 40/27 680.449 cents grave fifth 17: 2 16384/10935 700.001 cents fifth - schisma, 5-limit approximation to ET fifth 17: 25 3/2 701.955 cents perfect fifth 17: 1 2560/1701 707.713 cents 17: 1 1120/729 743.410 cents 18: 1 1024/675 721.508 cents narrow diminished sixth 18: 8 243/160 723.461 cents acute fifth 18: 7 32/21 729.219 cents wide fifth 18: 7 14/9 764.916 cents septimal minor sixth 18: 2 10240/6561 770.674 cents grave minor sixth 18: 4 25/16 772.627 cents classic augmented fifth 19: 4 54/35 750.725 cents septimal semi-augmented fifth 19: 4 63/40 786.422 cents narrow minor sixth 19: 13 128/81 792.180 cents Pythagorean minor sixth 19: 8 405/256 794.134 cents wide augmented fifth 20: 10 8/5 813.686 cents minor sixth 20: 4 6561/4096 815.640 cents Pythagorean augmented fifth 20: 3 8192/5103 819.444 cents 20: 4 45/28 821.398 cents septimale wide minor sixth 20: 3 3584/2187 855.141 cents 20: 4 105/64 857.095 cents septimal neutral sixth 20: 1 400/243 862.852 cents grave major sixth 21: 2 81/50 835.193 cents acute minor sixth 21: 3 512/315 840.950 cents 21: 4 729/448 842.904 cents 21: 3 224/135 876.647 cents narrow septimal major sixth 21: 4 1701/1024 878.601 cents 21: 3 32768/19683 882.405 cents Pythagorean diminished seventh 21: 10 5/3 884.359 cents major sixth, BP sixth 22: 6 2048/1215 903.911 cents narrow diminished seventh 22: 17 27/16 905.865 cents Pythagorean major sixth 22: 3 320/189 911.623 cents 22: 3 140/81 947.320 cents 23: 3 128/75 925.418 cents diminished seventh 23: 4 2187/1280 927.371 cents acute major sixth 23: 7 12/7 933.129 cents septimal major sixth 23: 7 7/4 968.826 cents harmonic seventh 23: 6 1280/729 974.584 cents grave minor seventh 23: 2 225/128 976.537 cents augmented sixth 24: 2 243/140 954.635 cents 24: 2 567/320 990.332 cents 24: 21 16/9 996.090 cents Pythagorean minor seventh 24: 4 3645/2048 998.044 cents wide augmented sixth 25: 10 9/5 1017.596 cents just minor seventh, BP seventh 25: 2 59049/32768 1019.550 cents Pythagorean augmented sixth 25: 5 1024/567 1023.354 cents 25: 2 405/224 1025.308 cents 25: 5 448/243 1059.051 cents 25: 2 945/512 1061.005 cents 25: 3 50/27 1066.762 cents grave major seventh 26: 5 64/35 1044.860 cents septimal neutral seventh 26: 2 6561/3584 1046.814 cents 26: 5 28/15 1080.557 cents grave major seventh 26: 2 15309/8192 1082.511 cents 26: 5 4096/2187 1086.315 cents Pythagorean diminished octave 26: 10 15/8 1088.269 cents classic major seventh 27: 10 256/135 1107.821 cents octave - major chroma 27: 9 243/128 1109.775 cents Pythagorean major seventh 27: 5 40/21 1115.533 cents acute major seventh 27: 5 35/18 1151.230 cents septimal semi-diminished octave 28: 5 48/25 1129.328 cents classic diminished octave 28: 7 27/14 1137.039 cents septimal major seventh 28: 7 63/32 1172.736 cents octave - septimal comma 28: 10 160/81 1178.494 cents octave - syntonic comma Highest number of different intervals for one interval class: 7 Average number of different intervals per interval class: 5.42857 = 38/7
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 : 63.0 90.2 111.7 182.4 203.9 266.9 294.1 315.6 386.3 407.8 470.8 498.0 561.0 588.3 609.8 680.4 702.0 764.9 792.2 813.7 884.4 905.9 968.8 996.1 1017.6 1088.3 1109.8 1172.7 1200.0 63.0 : 27.3 48.8 119.4 140.9 203.9 231.2 252.7 323.4 344.9 407.8 435.1 498.0 525.3 546.8 617.5 639.0 702.0 729.2 750.7 821.4 842.9 905.9 933.1 954.6 1025.3 1046.8 1109.8 1137.0 1200.0 90.2 : 21.5 92.2 113.7 176.6 203.9 225.4 296.1 317.6 380.6 407.8 470.8 498.0 519.6 590.2 611.7 674.7 702.0 723.5 794.1 815.6 878.6 905.9 927.4 998.0 1019.6 1082.5 1109.8 1172.7 1200.0 111.7 : 70.7 92.2 155.1 182.4 203.9 274.6 296.1 359.0 386.3 449.3 476.5 498.0 568.7 590.2 653.2 680.4 702.0 772.6 794.1 857.1 884.4 905.9 976.5 998.0 1061.0 1088.3 1151.2 1178.5 1200.0 182.4 : 21.5 84.5 111.7 133.2 203.9 225.4 288.4 315.6 378.6 405.9 427.4 498.0 519.6 582.5 609.8 631.3 702.0 723.5 786.4 813.7 835.2 905.9 927.4 990.3 1017.6 1080.6 1107.8 1129.3 1200.0 203.9 : 63.0 90.2 111.7 182.4 203.9 266.9 294.1 357.1 384.4 405.9 476.5 498.0 561.0 588.3 609.8 680.4 702.0 764.9 792.2 813.7 884.4 905.9 968.8 996.1 1059.1 1086.3 1107.8 1178.5 1200.0 266.9 : 27.3 48.8 119.4 140.9 203.9 231.2 294.1 321.4 342.9 413.6 435.1 498.0 525.3 546.8 617.5 639.0 702.0 729.2 750.7 821.4 842.9 905.9 933.1 996.1 1023.4 1044.9 1115.5 1137.0 1200.0 294.1 : 21.5 92.2 113.7 176.6 203.9 266.9 294.1 315.6 386.3 407.8 470.8 498.0 519.6 590.2 611.7 674.7 702.0 723.5 794.1 815.6 878.6 905.9 968.8 996.1 1017.6 1088.3 1109.8 1172.7 1200.0 315.6 : 70.7 92.2 155.1 182.4 245.4 272.6 294.1 364.8 386.3 449.3 476.5 498.0 568.7 590.2 653.2 680.4 702.0 772.6 794.1 857.1 884.4 947.3 974.6 996.1 1066.8 1088.3 1151.2 1178.5 1200.0 386.3 : 21.5 84.5 111.7 174.7 202.0 223.5 294.1 315.6 378.6 405.9 427.4 498.0 519.6 582.5 609.8 631.3 702.0 723.5 786.4 813.7 876.6 903.9 925.4 996.1 1017.6 1080.6 1107.8 1129.3 1200.0 407.8 : 63.0 90.2 153.2 180.4 202.0 272.6 294.1 357.1 384.4 405.9 476.5 498.0 561.0 588.3 609.8 680.4 702.0 764.9 792.2 855.1 882.4 903.9 974.6 996.1 1059.1 1086.3 1107.8 1178.5 1200.0 470.8 : 27.3 90.2 117.5 139.0 209.7 231.2 294.1 321.4 342.9 413.6 435.1 498.0 525.3 546.8 617.5 639.0 702.0 729.2 792.2 819.4 841.0 911.6 933.1 996.1 1023.4 1044.9 1115.5 1137.0 1200.0 498.0 : 63.0 90.2 111.7 182.4 203.9 266.9 294.1 315.6 386.3 407.8 470.8 498.0 519.6 590.2 611.7 674.7 702.0 764.9 792.2 813.7 884.4 905.9 968.8 996.1 1017.6 1088.3 1109.8 1172.7 1200.0 561.0 : 27.3 48.8 119.4 140.9 203.9 231.2 252.7 323.4 344.9 407.8 435.1 456.6 527.3 548.8 611.7 639.0 702.0 729.2 750.7 821.4 842.9 905.9 933.1 954.6 1025.3 1046.8 1109.8 1137.0 1200.0 588.3 : 21.5 92.2 113.7 176.6 203.9 225.4 296.1 317.6 380.6 407.8 429.3 500.0 521.5 584.5 611.7 674.7 702.0 723.5 794.1 815.6 878.6 905.9 927.4 998.0 1019.6 1082.5 1109.8 1172.7 1200.0 609.8 : 70.7 92.2 155.1 182.4 203.9 274.6 296.1 359.0 386.3 407.8 478.5 500.0 563.0 590.2 653.2 680.4 702.0 772.6 794.1 857.1 884.4 905.9 976.5 998.0 1061.0 1088.3 1151.2 1178.5 1200.0 680.4 : 21.5 84.5 111.7 133.2 203.9 225.4 288.4 315.6 337.1 407.8 429.3 492.3 519.6 582.5 609.8 631.3 702.0 723.5 786.4 813.7 835.2 905.9 927.4 990.3 1017.6 1080.6 1107.8 1129.3 1200.0 702.0 : 63.0 90.2 111.7 182.4 203.9 266.9 294.1 315.6 386.3 407.8 470.8 498.0 561.0 588.3 609.8 680.4 702.0 764.9 792.2 813.7 884.4 905.9 968.8 996.1 1059.1 1086.3 1107.8 1178.5 1200.0 764.9 : 27.3 48.8 119.4 140.9 203.9 231.2 252.7 323.4 344.9 407.8 435.1 498.0 525.3 546.8 617.5 639.0 702.0 729.2 750.7 821.4 842.9 905.9 933.1 996.1 1023.4 1044.9 1115.5 1137.0 1200.0 792.2 : 21.5 92.2 113.7 176.6 203.9 225.4 296.1 317.6 380.6 407.8 470.8 498.0 519.6 590.2 611.7 674.7 702.0 723.5 794.1 815.6 878.6 905.9 968.8 996.1 1017.6 1088.3 1109.8 1172.7 1200.0 813.7 : 70.7 92.2 155.1 182.4 203.9 274.6 296.1 359.0 386.3 449.3 476.5 498.0 568.7 590.2 653.2 680.4 702.0 772.6 794.1 857.1 884.4 947.3 974.6 996.1 1066.8 1088.3 1151.2 1178.5 1200.0 884.4 : 21.5 84.5 111.7 133.2 203.9 225.4 288.4 315.6 378.6 405.9 427.4 498.0 519.6 582.5 609.8 631.3 702.0 723.5 786.4 813.7 876.6 903.9 925.4 996.1 1017.6 1080.6 1107.8 1129.3 1200.0 905.9 : 63.0 90.2 111.7 182.4 203.9 266.9 294.1 357.1 384.4 405.9 476.5 498.0 561.0 588.3 609.8 680.4 702.0 764.9 792.2 855.1 882.4 903.9 974.6 996.1 1059.1 1086.3 1107.8 1178.5 1200.0 968.8 : 27.3 48.8 119.4 140.9 203.9 231.2 294.1 321.4 342.9 413.6 435.1 498.0 525.3 546.8 617.5 639.0 702.0 729.2 792.2 819.4 841.0 911.6 933.1 996.1 1023.4 1044.9 1115.5 1137.0 1200.0 996.1 : 21.5 92.2 113.7 176.6 203.9 266.9 294.1 315.6 386.3 407.8 470.8 498.0 519.6 590.2 611.7 674.7 702.0 764.9 792.2 813.7 884.4 905.9 968.8 996.1 1017.6 1088.3 1109.8 1172.7 1200.0 1017.6: 70.7 92.2 155.1 182.4 245.4 272.6 294.1 364.8 386.3 449.3 476.5 498.0 568.7 590.2 653.2 680.4 743.4 770.7 792.2 862.9 884.4 947.3 974.6 996.1 1066.8 1088.3 1151.2 1178.5 1200.0 1088.3: 21.5 84.5 111.7 174.7 202.0 223.5 294.1 315.6 378.6 405.9 427.4 498.0 519.6 582.5 609.8 672.7 700.0 721.5 792.2 813.7 876.6 903.9 925.4 996.1 1017.6 1080.6 1107.8 1129.3 1200.0 1109.8: 63.0 90.2 153.2 180.4 202.0 272.6 294.1 357.1 384.4 405.9 476.5 498.0 561.0 588.3 651.2 678.5 700.0 770.7 792.2 855.1 882.4 903.9 974.6 996.1 1059.1 1086.3 1107.8 1178.5 1200.0 1172.7: 27.3 90.2 117.5 139.0 209.7 231.2 294.1 321.4 342.9 413.6 435.1 498.0 525.3 588.3 615.5 637.0 707.7 729.2 792.2 819.4 841.0 911.6 933.1 996.1 1023.4 1044.9 1115.5 1137.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 21.5063 .. 70.6724 cents 250/243, 49.1661 cents 81/80, 21.5063 cents 2: 48.7704 .. 92.1787 cents 525/512, 43.4083 cents 864/875,-21.9020 cents 3: 111.7313 .. 155.1396 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 4: 133.2376 .. 182.4037 cents 250/243, 49.1661 cents 864/875,-21.9020 cents 5: 201.9563 .. 245.3646 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 6: 223.4626 .. 274.5824 cents 16875/16384, 51.1199 cents 864/875,-21.9020 cents 7: 252.6804 .. 296.0887 cents 525/512, 43.4083 cents 864/875,-21.9020 cents 8: 315.6413 .. 364.8074 cents 250/243, 49.1661 cents 2048/2025, 19.5526 cents 9: 337.1476 .. 386.3137 cents 250/243, 49.1661 cents 19683/20000,-27.6598 cents 10: 405.8663 .. 449.2746 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 11: 427.3726 .. 478.4924 cents 16875/16384, 51.1199 cents 864/875,-21.9020 cents 12: 456.5904 .. 499.9987 cents 525/512, 43.4083 cents 864/875,-21.9020 cents 13: 519.5513 .. 568.7174 cents 250/243, 49.1661 cents 2048/2025, 19.5526 cents 14: 546.8154 .. 590.2237 cents 525/512, 43.4083 cents 864/875,-21.9020 cents 15: 609.7763 .. 653.1846 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 16: 631.2826 .. 680.4487 cents 250/243, 49.1661 cents 864/875,-21.9020 cents 17: 700.0013 .. 743.4096 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 18: 721.5076 .. 772.6274 cents 16875/16384, 51.1199 cents 864/875,-21.9020 cents 19: 750.7254 .. 794.1337 cents 525/512, 43.4083 cents 864/875,-21.9020 cents 20: 813.6863 .. 862.8524 cents 250/243, 49.1661 cents 2048/2025, 19.5526 cents 21: 835.1926 .. 884.3587 cents 250/243, 49.1661 cents 19683/20000,-27.6598 cents 22: 903.9113 .. 947.3196 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 23: 925.4176 .. 976.5374 cents 16875/16384, 51.1199 cents 864/875,-21.9020 cents 24: 954.6354 .. 998.0437 cents 525/512, 43.4083 cents 864/875,-21.9020 cents 25: 1017.5963 .. 1066.7624 cents 250/243, 49.1661 cents 2048/2025, 19.5526 cents 26: 1044.8604 .. 1088.2687 cents 525/512, 43.4083 cents 864/875,-21.9020 cents 27: 1107.8213 .. 1151.2296 cents 525/512, 43.4083 cents 2048/2025, 19.5526 cents 28: 1129.3276 .. 1178.4937 cents 250/243, 49.1661 cents 864/875,-21.9020 cents
SHOW DATA
Number of notes : 29 -- Interval properties -- Smallest interval : 81/80, 21.5063 cents, class 1 Average step (divided formal octave): 41.3793 cents Largest one step interval : 25/24, 70.6724 cents Average / Smallest step : 1.924056 Largest / Average step : 1.707917 Largest / Smallest step : 3.286128 Median interval of one step : 64/63, 27.2641 cents, amount: 7 Most common interval of one step : 81/80, 21.5063 cents, amount: 10 Least squares average step : 41.59415 cents, oct.: 1206.23022 cents Scale is not proper Step pattern alph. order: ABCDCABCDCABABCDCABCDCABCDCAB Step pattern size order : CBADACBADACBCBADACBADACBADACB Scale is a Constant Structure, by a margin of 7.31577 cents Scale diversity : 1.344549 Lumma stability : 0.215076 Lumma impropriety factor : 0.301624 Number of different interval sizes : 152 = 5.42857 / class Number of one step interval sizes : 4 Highest interval variety : 7 Mean interval variety : 5.42857 = 38/7 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 32805/32768, 1.9537 cents Most common intervals : 4/3, 498.0450 cents & inv., amount: 25 Most common triad is 0.0 498.045 701.955 cents, amount: 21 Number of recognisable fifths : 28, average 702.0211 cents Scale contains two identical disjunct "tetrachords" of 13 notes Scale contains a complete diamond : 1 3 9 27 81 243 All steps are superparticular (epimoric) Length of longest harmonic part : 1 at degree 0 Length of longest subharmonic part : 1 at degree 0 Formal octave complements present : 19 = 65.5172% Scale is differentially coherent in interval class 1 -- Rational properties -- Prime limit : 7 Odd number limit : 177147 (O: 177147 U: 177147) Highest odd numerator or denominator: 729 Scale harmonicity : 0.014405 Average absolute harmonicity : 0.117507 Specific harmonicity : 0.102311 Fundamental : 1/466560, -18.8317 octaves, 0.0006 Hz. Guide tone : 8709120, 23.0541 octaves, 2278528443.274 Hz. Exponens Consonantiae : 4.063327E+12, 41.88580 octaves Euler's gradus suavitatis : 54 Sum of Mann's harmonic distance : 1933.5, average 66.67241 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 36.42334, average 1.25598 Sum of Tenney's harmonic distance : 72.58990, average 2.50310 Vogel's harmonic complexity : 30.65517 Wille's k value : 442867 Wilson's harmonic complexity : 50 Rectangular lattice diameter : 14 Triangular lattice diameter : 11 Lattice compactness : 2598.63165, average 5.97387 Lattice compactness (without 2's) : 1422.52424, average 3.27017 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -7 .. 10 0.82759 100 1 3: -6 .. 5 -0.62069 62 11 5: -1 .. 1 0.00000 10 10 7: 0 .. 1 0.24138 7 7 Average exponent except 2's :-11 / 29 =-0.37931 Average absolute exponent except 2's: 79 / 29 = 2.72414 Scale is weakly epimorphic with val: <29 46 66 81| Scale is JI-epimorphic with val: <29 46 67 81| = patent
FIT/MODE
29: 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: 13.1357 c. M: 23.0749 c. 30: 2 0 1 2 0 2 0 1 2 0 2 0 2 1 0 2 1 1 1 0 2 1 1 1 0 2 1 1 1 N SD: 11.1846 c. M:-18.0450 c. 31: 2 0 1 2 0 2 1 0 2 1 1 1 1 1 1 2 0 2 0 1 2 0 2 1 0 2 1 1 1 N D3 SD: 10.7469 c. M: 19.0704 c. 32: 2 0 1 2 0 2 1 0 2 1 2 0 2 1 0 2 1 1 1 1 2 0 2 1 0 2 1 1 1 N SD: 10.5203 c. M:-16.7191 c. 33: 2 0 1 2 1 1 1 1 2 0 2 1 1 1 1 2 0 2 1 0 2 1 2 0 1 2 1 1 1 N D3 SD: 10.2294 c. M: 17.4977 c. 34: 2 1 0 2 1 2 0 1 2 1 1 1 2 1 0 2 1 2 0 1 2 1 1 1 1 2 0 2 1 N T3 SD: 9.8353 c. M: 15.8847 c. 35: 2 1 0 2 1 2 1 0 2 1 2 1 1 1 1 2 0 2 1 1 2 0 2 1 1 2 0 2 1 N D3 SD: 9.5415 c. M:-16.2407 c. 37: 2 1 0 3 0 2 1 1 2 1 2 0 2 1 1 2 1 2 0 1 2 1 2 1 0 3 0 2 1 N SD: 9.2822 c. M:-15.7056 c. 38: 2 1 1 2 0 2 1 1 2 1 2 1 2 1 0 3 0 2 1 1 2 1 2 1 0 2 1 2 1 N SD: 8.8692 c. M: 14.5845 c. 39: 2 1 1 2 1 2 1 0 3 0 2 1 2 1 1 2 1 2 1 0 3 0 2 1 1 2 1 2 1 N SD: 8.6069 c. M: 14.9798 c. 40: 2 1 1 2 1 2 1 1 2 1 2 1 2 1 0 3 0 3 0 1 3 0 2 1 1 2 1 2 1 N SD: 8.6576 c. M:-15.6413 c. 41: 2 1 1 2 1 2 1 1 2 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 1 2 1 2 1 P M ME S SD: 4.1433 c. M: 7.2780 c. 53: 3 1 1 3 1 3 1 1 3 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 1 3 1 3 1 N M DE S SD: 2.5114 c. M:-5.0318 c. 94: 5 2 2 5 2 5 2 2 5 2 5 2 5 2 2 5 2 5 2 2 5 2 5 2 2 5 2 5 2 N M DE S SD: 2.1434 c. M: 3.8530 c. 118: 6 3 2 7 2 6 3 2 7 2 6 3 6 3 2 7 2 6 3 2 7 2 6 3 2 7 2 6 3 N SD: 1.3953 c. M: 3.2444 c. 130: 7 3 2 8 2 7 3 2 8 2 7 3 7 3 2 8 2 7 3 2 8 2 7 3 2 8 2 7 3 N SD: 1.4855 c. M:-2.6282 c. 171: 9 4 3 10 3 9 4 3 10 3 9 4 9 4 3 10 3 9 4 3 10 3 9 4 3 10 3 9 4 N SD: 0.5514 c. M:-1.2037 c. 347: 18 8 6 21 6 18 8 6 21 6 18 8 18 8 6 21 6 18 8 6 21 6 18 8 6 21 6 18 8 N SD: 0.6616 c. M: 1.1308 c. 388: 20 9 7 23 7 20 9 7 23 7 20 9 20 9 7 23 7 20 9 7 23 7 20 9 7 23 7 20 9 N SD: 0.5363 c. M: 1.2121 c. 395: 21 9 7 23 7 21 9 7 23 7 21 9 21 9 7 23 7 21 9 7 23 7 21 9 7 23 7 21 9 N SD: 0.5789 c. M:-1.0971 c. 400: 21 9 7 24 7 21 9 7 24 7 21 9 21 9 7 24 7 21 9 7 24 7 21 9 7 24 7 21 9 N SD: 0.4119 c. M: 0.7763 c. 441: 23 10 8 26 8 23 10 8 26 8 23 10 23 10 8 26 8 23 10 8 26 8 23 10 8 26 8 23 10 N SD: 0.2459 c. M: 0.5149 c. 571: 30 13 10 34 10 30 13 10 34 10 30 13 30 13 10 34 10 30 13 10 34 10 30 13 10 34 10 30 13 N SD: 0.2415 c. M:-0.4620 c. 612: 32 14 11 36 11 32 14 11 36 11 32 14 32 14 11 36 11 32 14 11 36 11 32 14 11 36 11 32 14 N SD: 0.1044 c. M: 0.2216 c. 665: 35 15 12 39 12 35 15 12 39 12 35 15 35 15 12 39 12 35 15 12 39 12 35 15 12 39 12 35 15 N SD: 0.1301 c. M:-0.1971 c. 1106: 58 25 20 65 20 58 25 20 65 20 58 25 58 25 20 65 20 58 25 20 65 20 58 25 20 65 20 58 25 N SD: 0.1006 c. M: 0.2049 c. 1183: 62 27 21 70 21 62 27 21 70 21 62 27 62 27 21 70 21 62 27 21 70 21 62 27 21 70 21 62 27 N SD: 0.1114 c. M:-0.1937 c. 1236: 65 28 22 73 22 65 28 22 73 22 65 28 65 28 22 73 22 65 28 22 73 22 65 28 22 73 22 65 28 N SD: 0.0901 c. M:-0.1591 c. 1277: 67 29 23 75 23 67 29 23 75 23 67 29 67 29 23 75 23 67 29 23 75 23 67 29 23 75 23 67 29 N SD: 0.0577 c. M: 0.1042 c. 1848: 97 42 33 109 33 97 42 33 109 33 97 42 97 42 33 109 33 97 42 33 109 33 97 42 33 109 33 97 42 N SD: 0.0367 c. M:-0.0708 c. 2460: 129 56 44 145 44 129 56 44 145 44 129 56 129 56 44 145 44 129 56 44 145 44 129 56 44 145 44 129 56 N SD: 0.0286 c. M: 0.0530 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: 1.1516 cents 6 .. 12 match: 6 H SD: 5.2944 cents 7 .. 14 match: 7 H SD: 7.3648 cents 8 .. 16 match: 8 H SD: 3.5670 cents 9 .. 18 match: 9 H SD: 4.7216 cents 10 .. 20 match: 10 H SD: 2.7850 cents 11 .. 22 match: 11 H SD: 6.2721 cents 12 .. 24 match: 12 H SD: 3.7828 cents 13 .. 26 match: 13 H SD: 4.8103 cents 14 .. 28 match: 14 H SD: 5.2969 cents 15 .. 30 match: 14 S SD: 2.7252 cents 16 .. 32 match: 15 S SD: 2.5094 cents 17 .. 34 match: 17 H SD: 4.2648 cents 18 .. 36 match: 16 S SD: 3.2814 cents 19 .. 38 match: 17 S SD: 2.9334 cents 20 .. 40 match: 18 S SD: 2.7819 cents 21 .. 42 match: 20 SD: 3.4031 cents 22 .. 44 match: 18 SD: 3.1514 cents 23 .. 46 match: 22 SD: 3.0260 cents 24 .. 48 match: 20 SD: 2.3396 cents 25 .. 50 match: 20 SD: 2.5516 cents 26 .. 52 match: 21 SD: 2.2554 cents 27 .. 54 match: 21 SD: 2.1885 cents 28 .. 56 match: 20 SD: 2.4820 cents 29 .. 58 match: 24 SD: 1.9996 cents 30 .. 60 match: 24 SD: 1.9564 cents 31 .. 62 match: 23 SD: 1.9250 cents 32 .. 64 match: 25 SD: 1.8404 cents 33 .. 66 match: 24 SD: 1.8609 cents 34 .. 68 match: 20 SD: 1.9780 cents 35 .. 70 match: 24 SD: 1.7390 cents 36 .. 72 match: 25 SD: 1.6341 cents 37 .. 74 match: 24 SD: 1.8504 cents 38 .. 76 match: 26 SD: 1.7953 cents 39 .. 78 match: 25 SD: 1.6989 cents 40 .. 80 match: 27 SD: 1.6160 cents 41 .. 82 match: 25 SD: 1.4593 cents 42 .. 84 match: 25 SD: 1.2875 cents 43 .. 86 match: 26 SD: 1.7007 cents 44 .. 88 match: 27 SD: 1.5601 cents 45 .. 90 match: 27 SD: 1.1972 cents 46 .. 92 match: 25 SD: 1.5575 cents 47 .. 94 match: 26 SD: 1.3349 cents 48 .. 96 match: 28 SD: 1.1213 cents 49 .. 98 match: 28 SD: 1.3180 cents 50 .. 100 match: 26 SD: 1.1896 cents 51 .. 102 match: 26 SD: 1.5083 cents 52 .. 104 match: 27 SD: 1.1865 cents 54 .. 108 match: 28 SD: 0.9675 cents 57 .. 114 match: 28 SD: 1.0582 cents 58 .. 116 match: 28 SD: 1.1773 cents 59 .. 118 match: 28 SD: 1.0929 cents 60 .. 120 match: 29 SD: 0.8409 cents 62 .. 124 match: 28 SD: 1.1521 cents 63 .. 126 match: 29 SD: 1.1235 cents 64 .. 128 match: 29 SD: 0.9276 cents 66 .. 132 match: 28 SD: 1.1008 cents 67 .. 134 match: 28 SD: 1.1270 cents 69 .. 138 match: 29 SD: 1.0926 cents 70 .. 140 match: 29 SD: 0.9766 cents 71 .. 142 match: 29 SD: 0.8045 cents 76 .. 152 match: 29 SD: 0.8004 cents 79 .. 158 match: 29 SD: 0.7493 cents 80 .. 160 match: 29 SD: 0.7241 cents 89 .. 178 match: 29 SD: 0.7038 cents 90 .. 180 match: 29 SD: 0.6006 cents 108 .. 216 match: 29 SD: 0.5257 cents 120 .. 240 match: 29 SD: 0.5100 cents 128 .. 256 match: 29 SD: 0.4468 cents 135 .. 270 match: 29 SD: 0.3615 cents 168 .. 336 match: 29 SD: 0.3411 cents 180 .. 360 match: 29 SD: 0.3078 cents 185 .. 370 match: 29 SD: 0.2934 cents 208 .. 416 match: 29 SD: 0.2886 cents 210 .. 420 match: 29 SD: 0.2793 cents 216 .. 432 match: 29 SD: 0.2715 cents 222 .. 444 match: 29 SD: 0.2713 cents 224 .. 448 match: 29 SD: 0.2691 cents 225 .. 450 match: 29 SD: 0.2409 cents 240 .. 480 match: 29 SD: 0.2050 cents 295 .. 590 match: 29 SD: 0.1998 cents 297 .. 594 match: 29 SD: 0.1865 cents 320 .. 640 match: 29 SD: 0.1774 cents 324 .. 648 match: 29 SD: 0.1547 cents 360 .. 720 match: 29 SD: 0.1452 cents 384 .. 768 match: 29 SD: 0.1358 cents 432 .. 864 match: 29 SD: 0.1005 cents 540 .. 1080 match: 29 SD: 0.0917 cents 576 .. 1152 match: 29 SD: 0.0881 cents 600 .. 1200 match: 29 SD: 0.0852 cents