Scala analysis: woz31
2401/2400 norm reduced 31
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: 21/20 84.467193 minor semitone 3: 15/14 119.442808 major diatonic semitone 4: 49/45 147.428097 BP minor semitone 5: 28/25 196.198479 middle second 6: 8/7 231.174094 septimal whole tone 7: 7/6 266.870906 septimal minor third 8: 6/5 315.641287 minor third 9: 49/40 351.338099 larger approximation to neutral third 10: 5/4 386.313714 major third 11: 9/7 435.084095 septimal major third, BP third 12: 64/49 462.348187 2 septatones or septatonic major third 13: 4/3 498.044999 perfect fourth 14: 48/35 546.815381 septimal semi-augmented fourth 15: 7/5 582.512193 septimal or Huygens' tritone, BP 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: 49/32 737.651813 20: 14/9 764.915905 septimal minor sixth 21: 8/5 813.686286 minor sixth 22: 49/30 849.383098 larger approximation to 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: 90/49 1052.571903 28: 28/15 1080.557192 grave major seventh 29: 40/21 1115.532807 acute major seventh 30: 49/25 1165.024385 BP eighth 31: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 36/35 48.7704 septimal diesis, 1/4-tone 3: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 4: 686/675 27.9853 senga 5: 36/35 48.7704 septimal diesis, 1/4-tone 6: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 36/35 48.7704 septimal diesis, 1/4-tone 9: 49/48 35.6968 slendro diesis, septimal 1/6-tone 10: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 11: 36/35 48.7704 septimal diesis, 1/4-tone 12: 64/63 27.2641 septimal comma, Archytas' comma 13: 49/48 35.6968 slendro diesis, septimal 1/6-tone 14: 36/35 48.7704 septimal diesis, 1/4-tone 15: 49/48 35.6968 slendro diesis, septimal 1/6-tone 16: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 17: 49/48 35.6968 slendro diesis, septimal 1/6-tone 18: 36/35 48.7704 septimal diesis, 1/4-tone 19: 49/48 35.6968 slendro diesis, septimal 1/6-tone 20: 64/63 27.2641 septimal comma, Archytas' comma 21: 36/35 48.7704 septimal diesis, 1/4-tone 22: 49/48 35.6968 slendro diesis, septimal 1/6-tone 23: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 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: 36/35 48.7704 septimal diesis, 1/4-tone 28: 686/675 27.9853 senga 29: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 30: 1029/1000 49.4916 keega 31: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 2 64/63 27.264 cents septimal comma, Archytas' comma 1: 2 686/675 27.985 cents senga 1: 8 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 9 49/48 35.697 cents slendro diesis, septimal 1/6-tone 1: 9 36/35 48.770 cents septimal diesis, 1/4-tone 1: 1 1029/1000 49.492 cents keega 2: 4 28/27 62.961 cents Archytas' 1/3-tone 2: 7 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 2 256/245 76.034 cents septimal minor semitone 2: 2 392/375 76.756 cents 2: 5 360/343 83.746 cents 2: 11 21/20 84.467 cents minor semitone 3: 1 1225/1152 106.369 cents 3: 1 2560/2401 111.010 cents 3: 10 16/15 111.731 cents minor diatonic semitone 3: 1 2401/2250 112.452 cents 3: 14 15/14 119.443 cents major diatonic semitone 3: 4 343/320 120.164 cents 4: 5 160/147 146.707 cents 4: 7 49/45 147.428 cents BP minor semitone 4: 2 375/343 154.418 cents BP major semitone, minor BP chroma 4: 8 35/32 155.140 cents septimal neutral second 4: 3 192/175 160.502 cents septimal 4/5-tone 4: 1 686/625 161.223 cents 4: 4 54/49 168.213 cents Zalzal's mujannab 4: 1 441/400 168.934 cents two (minor semitone) 5: 7 10/9 182.404 cents minor whole tone 5: 1 2401/2160 183.125 cents 5: 2 125/112 190.115 cents classic augmented semitone 5: 2 1715/1536 190.836 cents 5: 4 384/343 195.477 cents 5: 8 28/25 196.198 cents middle second 5: 1 2700/2401 203.189 cents 5: 6 9/8 203.910 cents major whole tone 6: 2 245/216 218.101 cents 6: 16 8/7 231.174 cents septimal whole tone 6: 6 343/300 231.895 cents 6: 5 225/196 238.886 cents two (major diatonic semitone) 6: 2 147/128 239.607 cents 7: 5 400/343 266.150 cents 7: 17 7/6 266.871 cents septimal minor third 7: 1 2401/2048 275.304 cents 7: 3 288/245 279.944 cents 7: 3 147/125 280.666 cents 7: 2 405/343 287.656 cents 8: 1 2401/2025 294.856 cents two (BP minor semitone) 8: 8 25/21 301.847 cents BP second, quasi-equal minor third 8: 4 343/288 302.568 cents 8: 2 2880/2401 314.920 cents 8: 16 6/5 315.641 cents minor third 9: 1 98/81 329.832 cents 9: 2 175/144 337.543 cents 9: 2 128/105 342.905 cents septimal neutral third 9: 2 1372/1125 343.627 cents 9: 14 60/49 350.617 cents smaller approximation to neutral third 9: 10 49/40 351.338 cents larger approximation to neutral third 10: 2 1280/1029 377.881 cents 10: 6 56/45 378.602 cents septimal narrow major third 10: 15 5/4 386.314 cents major third 10: 1 2401/1920 387.035 cents 10: 1 784/625 392.397 cents two (middle second) 10: 3 432/343 399.387 cents 10: 3 63/50 400.108 cents quasi-equal major third 11: 3 80/63 413.578 cents wide major third 11: 3 343/270 414.299 cents 11: 3 125/98 421.289 cents 11: 5 245/192 422.011 cents 11: 1 3072/2401 426.651 cents 11: 6 32/25 427.373 cents classic diminished fourth 11: 9 9/7 435.084 cents septimal major third, BP third 11: 1 1029/800 435.805 cents 12: 2 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 12: 2 125/96 456.986 cents classic augmented third 12: 7 64/49 462.348 cents 2 septatones or septatonic major third 12: 8 98/75 463.069 cents 12: 4 450/343 470.060 cents 12: 8 21/16 470.781 cents narrow fourth 13: 1 3200/2401 497.324 cents 13: 15 4/3 498.045 cents perfect fourth 13: 1 2401/1800 498.766 cents 13: 6 75/56 505.757 cents marvelous fourth 13: 2 343/256 506.478 cents 13: 1 2304/1715 511.119 cents 13: 3 168/125 511.840 cents 13: 2 27/20 519.551 cents acute fourth 14: 4 200/147 533.021 cents 14: 9 49/36 533.742 cents Arabic lute acute fourth 14: 2 175/128 541.453 cents 14: 10 48/35 546.815 cents septimal semi-augmented fourth 14: 2 343/250 547.537 cents 14: 4 135/98 554.527 cents 15: 5 25/18 568.717 cents classic augmented fourth 15: 6 480/343 581.791 cents 15: 18 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 15: 2 45/32 590.224 cents diatonic tritone 16: 2 64/45 609.776 cents 2nd tritone 16: 18 10/7 617.488 cents Euler's tritone 16: 6 343/240 618.209 cents 16: 5 36/25 631.283 cents classic diminished fifth 17: 4 196/135 645.473 cents 17: 2 500/343 652.463 cents 17: 10 35/24 653.185 cents septimal semi-diminished fifth 17: 2 256/175 658.547 cents 17: 9 72/49 666.258 cents Arabic lute grave fifth 17: 4 147/100 666.979 cents 18: 2 40/27 680.449 cents grave fifth 18: 3 125/84 688.160 cents 18: 1 1715/1152 688.881 cents 18: 2 512/343 693.522 cents 3 septatones or septatonic fifth 18: 6 112/75 694.243 cents marvelous fifth 18: 1 3600/2401 701.234 cents two (smaller approximation to neutral third) 18: 15 3/2 701.955 cents perfect fifth 18: 1 2401/1600 702.676 cents two (larger approximation to neutral third) 19: 8 32/21 729.219 cents wide fifth 19: 4 343/225 729.940 cents 19: 8 75/49 736.931 cents BP fifth 19: 7 49/32 737.652 cents 19: 2 192/125 743.014 cents classic diminished sixth 19: 2 54/35 750.725 cents septimal semi-augmented fifth 20: 1 1600/1029 764.195 cents 20: 9 14/9 764.916 cents septimal minor sixth 20: 6 25/16 772.627 cents classic augmented fifth 20: 1 2401/1536 773.349 cents 20: 5 384/245 777.989 cents 20: 3 196/125 778.711 cents 20: 3 540/343 785.701 cents 20: 3 63/40 786.422 cents narrow minor sixth 21: 3 100/63 799.892 cents quasi-equal minor sixth 21: 3 343/216 800.613 cents 21: 1 625/392 807.603 cents 21: 1 3840/2401 812.965 cents 21: 15 8/5 813.686 cents minor sixth 21: 6 45/28 821.398 cents septimale wide minor sixth 21: 2 1029/640 822.119 cents 22: 10 80/49 848.662 cents smaller approximation to neutral sixth 22: 14 49/30 849.383 cents larger approximation to neutral sixth 22: 2 1125/686 856.373 cents 22: 2 105/64 857.095 cents septimal neutral sixth 22: 2 288/175 862.457 cents 22: 1 81/49 870.168 cents two (septimal major third, BP third) 23: 16 5/3 884.359 cents major sixth, BP sixth 23: 2 2401/1440 885.080 cents 23: 4 576/343 897.432 cents 23: 8 42/25 898.153 cents quasi-equal major sixth 23: 1 4050/2401 905.144 cents 24: 2 686/405 912.344 cents 24: 3 250/147 919.334 cents 24: 3 245/144 920.056 cents 24: 1 4096/2401 924.696 cents 4 septatones or septatonic major sixth 24: 17 12/7 933.129 cents septimal major sixth 24: 5 343/200 933.850 cents 25: 2 256/147 960.393 cents 25: 5 392/225 961.114 cents 25: 6 600/343 968.105 cents 25: 16 7/4 968.826 cents harmonic seventh 25: 2 432/245 981.899 cents 26: 6 16/9 996.090 cents Pythagorean minor seventh 26: 1 2401/1350 996.811 cents 26: 8 25/14 1003.802 cents middle minor seventh 26: 4 343/192 1004.523 cents 26: 2 3072/1715 1009.164 cents 26: 2 224/125 1009.885 cents 26: 1 4320/2401 1016.875 cents 26: 7 9/5 1017.596 cents just minor seventh, BP seventh 27: 1 800/441 1031.066 cents 27: 4 49/27 1031.787 cents 27: 1 625/343 1038.777 cents 27: 3 175/96 1039.498 cents 27: 8 64/35 1044.860 cents septimal neutral seventh 27: 2 686/375 1045.582 cents 27: 7 90/49 1052.572 cents 27: 5 147/80 1053.293 cents 28: 4 640/343 1079.836 cents 28: 14 28/15 1080.557 cents grave major seventh 28: 1 4500/2401 1087.548 cents 28: 10 15/8 1088.269 cents classic major seventh 28: 1 2401/1280 1088.990 cents 28: 1 2304/1225 1093.631 cents two (septimal semi-augmented fourth) 29: 11 40/21 1115.533 cents acute major seventh 29: 5 343/180 1116.254 cents 29: 2 375/196 1123.244 cents 29: 2 245/128 1123.966 cents 29: 7 48/25 1129.328 cents classic diminished octave 29: 4 27/14 1137.039 cents septimal major seventh 30: 1 2000/1029 1150.508 cents 30: 9 35/18 1151.230 cents septimal semi-diminished octave 30: 9 96/49 1164.303 cents 30: 8 49/25 1165.024 cents BP eighth 30: 2 675/343 1172.015 cents 30: 2 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: 6.33333 = 19/3
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 84.5 119.4 147.4 196.2 231.2 266.9 315.6 351.3 386.3 435.1 462.3 498.0 546.8 582.5 617.5 653.2 702.0 737.7 764.9 813.7 849.4 884.4 933.1 968.8 1003.8 1052.6 1080.6 1115.5 1165.0 1200.0 35.7 : 48.8 83.7 111.7 160.5 195.5 231.2 279.9 315.6 350.6 399.4 426.7 462.3 511.1 546.8 581.8 617.5 666.3 702.0 729.2 778.0 813.7 848.7 897.4 933.1 968.1 1016.9 1044.9 1079.8 1129.3 1164.3 1200.0 84.5 : 35.0 63.0 111.7 146.7 182.4 231.2 266.9 301.8 350.6 377.9 413.6 462.3 498.0 533.0 568.7 617.5 653.2 680.4 729.2 764.9 799.9 848.7 884.4 919.3 968.1 996.1 1031.1 1080.6 1115.5 1151.2 1200.0 119.4 : 28.0 76.8 111.7 147.4 196.2 231.9 266.9 315.6 342.9 378.6 427.4 463.1 498.0 533.7 582.5 618.2 645.5 694.2 729.9 764.9 813.7 849.4 884.4 933.1 961.1 996.1 1045.6 1080.6 1116.3 1165.0 1200.0 147.4 : 48.8 83.7 119.4 168.2 203.9 238.9 287.7 314.9 350.6 399.4 435.1 470.1 505.8 554.5 590.2 617.5 666.3 702.0 736.9 785.7 821.4 856.4 905.1 933.1 968.1 1017.6 1052.6 1088.3 1137.0 1172.0 1200.0 196.2 : 35.0 70.7 119.4 155.1 190.1 238.9 266.1 301.8 350.6 386.3 421.3 457.0 505.8 541.5 568.7 617.5 653.2 688.2 736.9 772.6 807.6 856.4 884.4 919.3 968.8 1003.8 1039.5 1088.3 1123.2 1151.2 1200.0 231.2 : 35.7 84.5 120.2 155.1 203.9 231.2 266.9 315.6 351.3 386.3 422.0 470.8 506.5 533.7 582.5 618.2 653.2 702.0 737.7 772.6 821.4 849.4 884.4 933.9 968.8 1004.5 1053.3 1088.3 1116.3 1165.0 1200.0 266.9 : 48.8 84.5 119.4 168.2 195.5 231.2 279.9 315.6 350.6 386.3 435.1 470.8 498.0 546.8 582.5 617.5 666.3 702.0 736.9 785.7 813.7 848.7 898.2 933.1 968.8 1017.6 1052.6 1080.6 1129.3 1164.3 1200.0 315.6 : 35.7 70.7 119.4 146.7 182.4 231.2 266.9 301.8 337.5 386.3 422.0 449.3 498.0 533.7 568.7 617.5 653.2 688.2 736.9 764.9 799.9 849.4 884.4 920.1 968.8 1003.8 1031.8 1080.6 1115.5 1151.2 1200.0 351.3 : 35.0 83.7 111.0 146.7 195.5 231.2 266.1 301.8 350.6 386.3 413.6 462.3 498.0 533.0 581.8 617.5 652.5 701.2 729.2 764.2 813.7 848.7 884.4 933.1 968.1 996.1 1044.9 1079.8 1115.5 1164.3 1200.0 386.3 : 48.8 76.0 111.7 160.5 196.2 231.2 266.9 315.6 351.3 378.6 427.4 463.1 498.0 546.8 582.5 617.5 666.3 694.2 729.2 778.7 813.7 849.4 898.2 933.1 961.1 1009.9 1044.9 1080.6 1129.3 1165.0 1200.0 435.1 : 27.3 63.0 111.7 147.4 182.4 218.1 266.9 302.6 329.8 378.6 414.3 449.3 498.0 533.7 568.7 617.5 645.5 680.4 729.9 764.9 800.6 849.4 884.4 912.3 961.1 996.1 1031.8 1080.6 1116.3 1151.2 1200.0 462.3 : 35.7 84.5 120.2 155.1 190.8 239.6 275.3 302.6 351.3 387.0 422.0 470.8 506.5 541.5 590.2 618.2 653.2 702.7 737.7 773.3 822.1 857.1 885.1 933.9 968.8 1004.5 1053.3 1089.0 1124.0 1172.7 1200.0 498.0 : 48.8 84.5 119.4 155.1 203.9 239.6 266.9 315.6 351.3 386.3 435.1 470.8 505.8 554.5 582.5 617.5 667.0 702.0 737.7 786.4 821.4 849.4 898.2 933.1 968.8 1017.6 1053.3 1088.3 1137.0 1164.3 1200.0 546.8 : 35.7 70.7 106.4 155.1 190.8 218.1 266.9 302.6 337.5 386.3 422.0 457.0 505.8 533.7 568.7 618.2 653.2 688.9 737.7 772.6 800.6 849.4 884.4 920.1 968.8 1004.5 1039.5 1088.3 1115.5 1151.2 1200.0 582.5 : 35.0 70.7 119.4 155.1 182.4 231.2 266.9 301.8 350.6 386.3 421.3 470.1 498.0 533.0 582.5 617.5 653.2 702.0 736.9 764.9 813.7 848.7 884.4 933.1 968.8 1003.8 1052.6 1079.8 1115.5 1164.3 1200.0 617.5 : 35.7 84.5 120.2 147.4 196.2 231.9 266.9 315.6 351.3 386.3 435.1 463.1 498.0 547.5 582.5 618.2 667.0 702.0 729.9 778.7 813.7 849.4 898.2 933.9 968.8 1017.6 1044.9 1080.6 1129.3 1165.0 1200.0 653.2 : 48.8 84.5 111.7 160.5 196.2 231.2 279.9 315.6 350.6 399.4 427.4 462.3 511.8 546.8 582.5 631.3 666.3 694.2 743.0 778.0 813.7 862.5 898.2 933.1 981.9 1009.2 1044.9 1093.6 1129.3 1164.3 1200.0 702.0 : 35.7 63.0 111.7 147.4 182.4 231.2 266.9 301.8 350.6 378.6 413.6 463.1 498.0 533.7 582.5 617.5 645.5 694.2 729.2 764.9 813.7 849.4 884.4 933.1 960.4 996.1 1044.9 1080.6 1115.5 1151.2 1200.0 737.7 : 27.3 76.0 111.7 146.7 195.5 231.2 266.1 314.9 342.9 377.9 427.4 462.3 498.0 546.8 581.8 609.8 658.5 693.5 729.2 778.0 813.7 848.7 897.4 924.7 960.4 1009.2 1044.9 1079.8 1115.5 1164.3 1200.0 764.9 : 48.8 84.5 119.4 168.2 203.9 238.9 287.7 315.6 350.6 400.1 435.1 470.8 519.6 554.5 582.5 631.3 666.3 702.0 750.7 786.4 821.4 870.2 897.4 933.1 981.9 1017.6 1052.6 1088.3 1137.0 1172.7 1200.0 813.7 : 35.7 70.7 119.4 155.1 190.1 238.9 266.9 301.8 351.3 386.3 422.0 470.8 505.8 533.7 582.5 617.5 653.2 702.0 737.7 772.6 821.4 848.7 884.4 933.1 968.8 1003.8 1039.5 1088.3 1124.0 1151.2 1200.0 849.4 : 35.0 83.7 119.4 154.4 203.2 231.2 266.1 315.6 350.6 386.3 435.1 470.1 498.0 546.8 581.8 617.5 666.3 702.0 736.9 785.7 813.0 848.7 897.4 933.1 968.1 1003.8 1052.6 1088.3 1115.5 1164.3 1200.0 884.4 : 48.8 84.5 119.4 168.2 196.2 231.2 280.7 315.6 351.3 400.1 435.1 463.1 511.8 546.8 582.5 631.3 667.0 702.0 750.7 778.0 813.7 862.5 898.2 933.1 968.8 1017.6 1053.3 1080.6 1129.3 1165.0 1200.0 933.1 : 35.7 70.7 119.4 147.4 182.4 231.9 266.9 302.6 351.3 386.3 414.3 463.1 498.0 533.7 582.5 618.2 653.2 702.0 729.2 764.9 813.7 849.4 884.4 920.1 968.8 1004.5 1031.8 1080.6 1116.3 1151.2 1200.0 968.8 : 35.0 83.7 111.7 146.7 196.2 231.2 266.9 315.6 350.6 378.6 427.4 462.3 498.0 546.8 582.5 617.5 666.3 693.5 729.2 778.0 813.7 848.7 884.4 933.1 968.8 996.1 1044.9 1080.6 1115.5 1164.3 1200.0 1003.8: 48.8 76.8 111.7 161.2 196.2 231.9 280.7 315.6 343.6 392.4 427.4 463.1 511.8 547.5 582.5 631.3 658.5 694.2 743.0 778.7 813.7 849.4 898.2 933.9 961.1 1009.9 1045.6 1080.6 1129.3 1165.0 1200.0 1052.6: 28.0 63.0 112.5 147.4 183.1 231.9 266.9 294.9 343.6 378.6 414.3 463.1 498.8 533.7 582.5 609.8 645.5 694.2 729.9 764.9 800.6 849.4 885.1 912.3 961.1 996.8 1031.8 1080.6 1116.3 1151.2 1200.0 1080.6: 35.0 84.5 119.4 155.1 203.9 238.9 266.9 315.6 350.6 386.3 435.1 470.8 505.8 554.5 581.8 617.5 666.3 702.0 736.9 772.6 821.4 857.1 884.4 933.1 968.8 1003.8 1052.6 1088.3 1123.2 1172.0 1200.0 1115.5: 49.5 84.5 120.2 168.9 203.9 231.9 280.7 315.6 351.3 400.1 435.8 470.8 519.6 546.8 582.5 631.3 667.0 702.0 737.7 786.4 822.1 849.4 898.2 933.9 968.8 1017.6 1053.3 1088.3 1137.0 1165.0 1200.0 1165.0: 35.0 70.7 119.4 154.4 182.4 231.2 266.1 301.8 350.6 386.3 421.3 470.1 497.3 533.0 581.8 617.5 652.5 688.2 736.9 772.6 799.9 848.7 884.4 919.3 968.1 1003.8 1038.8 1087.5 1115.5 1150.5 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 27.2641 .. 49.4916 cents 64827/64000, 22.2275 cents 64/63, 27.2641 cents 2: 62.9609 .. 84.4672 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 3: 106.3692 .. 120.1640 cents 126/125, 13.7948 cents 875/864, 21.9020 cents 4: 146.7069 .. 168.9344 cents 64827/64000, 22.2275 cents 51200/50421, 26.5429 cents 5: 182.4037 .. 203.9100 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 6: 218.1005 .. 239.6068 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 7: 266.1497 .. 287.6560 cents 81/80, 21.5063 cents 51200/50421, 26.5429 cents 8: 294.8562 .. 315.6413 cents 2430/2401, 20.7851 cents 823543/820125, 7.2002 cents 9: 329.8318 .. 351.3381 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 10: 377.8810 .. 400.1085 cents 64827/64000, 22.2275 cents 51200/50421, 26.5429 cents 11: 413.5778 .. 435.8053 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 12: 449.2746 .. 470.7809 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 13: 497.3238 .. 519.5513 cents 64827/64000, 22.2275 cents 51200/50421, 26.5429 cents 14: 533.0206 .. 554.5269 cents 81/80, 21.5063 cents 4000/3969, 13.4693 cents 15: 568.7174 .. 590.2237 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 16: 609.7763 .. 631.2826 cents 81/80, 21.5063 cents 2048/2025, 19.5526 cents 17: 645.4731 .. 666.9794 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 18: 680.4487 .. 702.6762 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 19: 729.2191 .. 750.7254 cents 81/80, 21.5063 cents 51200/50421, 26.5429 cents 20: 764.1947 .. 786.4222 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 21: 799.8915 .. 822.1190 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 22: 848.6619 .. 870.1682 cents 81/80, 21.5063 cents 51200/50421, 26.5429 cents 23: 884.3587 .. 905.1438 cents 2430/2401, 20.7851 cents 245/243, 14.1905 cents 24: 912.3440 .. 933.8503 cents 81/80, 21.5063 cents 823543/820125, 7.2002 cents 25: 960.3932 .. 981.8995 cents 81/80, 21.5063 cents 51200/50421, 26.5429 cents 26: 996.0900 .. 1017.5963 cents 81/80, 21.5063 cents 245/243, 14.1905 cents 27: 1031.0656 .. 1053.2931 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 cents 28: 1079.8360 .. 1093.6308 cents 126/125, 13.7948 cents 51200/50421, 26.5429 cents 29: 1115.5328 .. 1137.0391 cents 81/80, 21.5063 cents 875/864, 21.9020 cents 30: 1150.5084 .. 1172.7359 cents 64827/64000, 22.2275 cents 4000/3969, 13.4693 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 : 1029/1000, 49.4916 cents Average / Smallest step : 1.419804 Largest / Average step : 1.278532 Largest / Smallest step : 1.815266 Median interval of one step : 49/48, 35.6968 cents, amount: 9 Least squares average step : 38.69803 cents, oct.: 1199.63881 cents Scale is strictly proper Step pattern alph. order: ABCDBCABACBEABACABAEBACBACBDCFC Step pattern size order : DECBECDEDCEADEDCDEDAEDCEDCEBCFC Scale is a Constant Structure, by a margin of 7.20020 cents Scale diversity : 1.307103 Rothenberg stability : 1.000000 = 1 Lumma stability : 0.470387 Number of different interval sizes : 190 = 6.33333 / class Number of one step interval sizes : 6 Highest interval variety : 8 Mean interval variety : 6.33333 = 19/3 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 2401/2400, 0.7212 cents Most common intervals : 7/5, 582.5122 cents & inv., amount: 18 Number of recognisable fifths : 29, average 697.9001 cents Number of appreciable fifths : 25, average 699.4296 cents Best fifths form a closed circle Best major thirds form a closed circle Best minor thirds form a closed circle Scale contains a complete diamond : 3 5 7 15 21 35 Length of longest harmonic part : 2 at degree 8 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 27 = 87.0968% Scale is n-1 differentially coherent in interval classes 1 and 2 combined Scale is n-1 differentially coherent in interval classes 2 and 3 combined -- Rational properties -- Prime limit : 7 Odd number limit : 2401 (O: 2401 U: 2401) Highest odd numerator or denominator: 49 Scale harmonicity : 0.011311 Average absolute harmonicity : 0.099511 Specific harmonicity : 0.078055 Fundamental : 1/352800, -18.4285 octaves, 0.0007 Hz. Guide tone : 705600, 19.4285 octaves, 184602998.876 Hz. Exponens Consonantiae : 2.489357E+11, 37.85698 octaves Euler's gradus suavitatis : 60 Sum of Mann's harmonic distance : 678.0, average 21.87097 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 35.13140, average 1.13327 Sum of Tenney's harmonic distance : 70.37688, average 2.27022 Vogel's harmonic complexity : 36.16129 Wille's k value : 270112 Wilson's harmonic complexity : 60 Rectangular lattice diameter : 12 Triangular lattice diameter : 6 Lattice compactness : 1913.35683, average 3.85757 Lattice compactness (without 2's) : 1180.52675, average 2.38009 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 6 0.19355 58 1 3: -2 .. 2 -0.06452 22 2 5: -2 .. 2 -0.12903 22 4 7: -2 .. 2 0.25806 32 24 Average exponent except 2's : 2 / 31 = 0.06452 Average absolute exponent except 2's: 76 / 31 = 2.45161 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: 4.6835 c. M: 9.2776 c. 57: 2 2 2 1 2 2 2 2 2 1 3 1 2 2 2 1 2 2 2 1 3 1 2 2 2 2 2 1 2 2 2 P D3 I SD: 5.3167 c. M: 7.3663 c. 58: 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 2 2 1 2 2 2 2 2 1 3 1 2 2 2 P D3 SD: 5.1486 c. M: 10.6981 c. 66: 2 3 2 1 3 2 2 2 2 2 3 1 2 3 2 2 2 3 2 1 3 2 2 2 2 2 3 1 2 3 2 P D3 I SD: 5.0359 c. M:-7.8299 c. 68: 2 3 2 1 3 2 2 3 2 2 3 1 2 3 2 2 2 3 2 1 3 2 2 3 2 2 3 1 2 3 2 N D3 I SD: 3.2027 c. M:-6.2516 c. 72: 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 2 2 3 2 2 3 2 2 3 2 2 3 2 2 3 2 SP M ME I SD: 2.3593 c. M:-4.3185 c. 99: 3 4 3 2 4 3 3 4 3 3 4 2 3 4 3 3 3 4 3 2 4 3 3 4 3 3 4 2 3 4 3 P D3 I SD: 1.2834 c. M: 2.2591 c. 130: 4 5 4 3 5 4 4 5 4 4 5 3 4 5 4 4 4 5 4 3 5 4 4 5 4 4 5 3 4 5 4 SP D3 I SD: 1.2644 c. M: 2.3523 c. 140: 4 6 4 3 6 4 4 6 4 4 6 3 4 6 4 4 4 6 4 3 6 4 4 6 4 4 6 3 4 6 4 P I SD: 1.1300 c. M: 2.0588 c. 171: 5 7 5 4 7 5 5 7 5 5 7 4 5 7 5 5 5 7 5 4 7 5 5 7 5 5 7 4 5 7 5 SP I SD: 0.3466 c. M:-0.8097 c. 270: 8 11 8 6 11 8 8 11 8 8 11 6 8 11 8 8 8 11 8 6 11 8 8 11 8 8 11 6 8 11 8 SP I SD: 0.3787 c. M:-0.7614 c. 441: 13 18 13 10 18 13 13 18 13 13 18 10 13 18 13 13 13 18 13 10 18 13 13 18 13 13 18 10 13 18 13 SP I SD: 0.2463 c. M:-0.4893 c. 612: 18 25 18 14 25 18 18 25 18 18 25 14 18 25 18 18 18 25 18 14 25 18 18 25 18 18 25 14 18 25 18 SP I SD: 0.2320 c. M: 0.4027 c. 935: 28 38 27 22 38 27 28 38 28 27 38 21 28 38 28 27 28 38 28 21 38 28 27 38 28 27 38 22 27 39 27 SP SD: 0.1715 c. M:-0.3232 c. 1106: 33 45 32 26 45 32 33 45 33 32 45 25 33 45 33 32 33 45 33 25 45 33 32 45 33 32 45 26 32 46 32 SP SD: 0.1176 c. M:-0.2559 c. 1236: 37 50 36 29 50 36 37 50 37 36 50 28 37 50 37 36 37 50 37 28 50 37 36 50 37 36 50 29 36 51 36 SP SD: 0.1202 c. M:-0.2255 c. 1277: 38 52 37 30 52 37 38 52 38 37 52 29 38 52 38 37 38 52 38 29 52 38 37 52 38 37 52 30 37 53 37 SP SD: 0.0963 c. M:-0.2066 c. 1376: 41 56 40 32 56 40 41 56 41 40 56 31 41 56 41 40 41 56 41 31 56 41 40 56 41 40 56 32 40 57 40 SP SD: 0.0707 c. M:-0.1389 c. 1407: 42 57 41 33 57 41 42 57 42 41 57 32 42 57 42 41 42 57 42 32 57 42 41 57 42 41 57 33 41 58 41 SP SD: 0.0734 c. M:-0.1241 c. 1547: 46 63 45 36 63 45 46 63 46 45 63 35 46 63 46 45 46 63 46 35 63 46 45 63 46 45 63 36 45 64 45 SP SD: 0.0480 c. M: 0.0835 c. 1848: 55 75 54 43 75 54 55 75 55 54 75 42 55 75 55 54 55 75 55 42 75 55 54 75 55 54 75 43 54 76 54 SP SD: 0.0450 c. M: 0.0946 c. 2019: 60 82 59 47 82 59 60 82 60 59 82 46 60 82 60 59 60 82 60 46 82 60 59 82 60 59 82 47 59 83 59 SP SD: 0.0425 c. M: 0.0912 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: 2.7590 cents 6 .. 12 match: 6 H SD: 0.5348 cents 7 .. 14 match: 7 H SD: 2.8116 cents 8 .. 16 match: 8 H SD: 1.8440 cents 9 .. 18 match: 9 H SD: 3.0420 cents 10 .. 20 match: 10 H SD: 2.8179 cents 11 .. 22 match: 11 H SD: 3.6003 cents 12 .. 24 match: 12 H SD: 2.2724 cents 13 .. 26 match: 13 H SD: 3.5772 cents 14 .. 28 match: 14 H SD: 2.7766 cents 15 .. 30 match: 15 H SD: 2.9252 cents 16 .. 32 match: 16 H SD: 3.0580 cents 17 .. 34 match: 17 H SD: 3.2469 cents 18 .. 36 match: 18 H SD: 2.1846 cents 19 .. 38 match: 19 H SD: 2.9631 cents 20 .. 40 match: 20 H SD: 2.2617 cents 21 .. 42 match: 21 H SD: 2.4130 cents 22 .. 44 match: 22 H SD: 2.3376 cents 23 .. 46 match: 23 H SD: 2.4309 cents 24 .. 48 match: 24 H SD: 1.6501 cents 25 .. 50 match: 24 S SD: 2.1322 cents 26 .. 52 match: 23 SD: 2.6632 cents 27 .. 54 match: 24 SD: 2.2289 cents 28 .. 56 match: 27 SD: 2.1171 cents 29 .. 58 match: 26 SD: 2.3135 cents 30 .. 60 match: 28 SD: 1.8929 cents 31 .. 62 match: 26 SD: 2.0767 cents 32 .. 64 match: 29 SD: 1.6990 cents 33 .. 66 match: 28 SD: 2.0306 cents 34 .. 68 match: 29 SD: 2.1242 cents 35 .. 70 match: 29 SD: 1.5319 cents 36 .. 72 match: 30 SD: 1.5449 cents 37 .. 74 match: 29 SD: 1.8903 cents 38 .. 76 match: 29 SD: 1.8161 cents 39 .. 78 match: 30 SD: 1.7036 cents 40 .. 80 match: 31 SD: 1.4415 cents 42 .. 84 match: 31 SD: 1.3036 cents 43 .. 86 match: 31 SD: 1.2496 cents 44 .. 88 match: 30 SD: 1.3514 cents 45 .. 90 match: 31 SD: 1.3237 cents 48 .. 96 match: 31 SD: 1.2652 cents 49 .. 98 match: 30 SD: 1.2265 cents 50 .. 100 match: 30 SD: 1.3726 cents 52 .. 104 match: 31 SD: 1.1747 cents 55 .. 110 match: 31 SD: 1.0685 cents 56 .. 112 match: 31 SD: 0.9465 cents 60 .. 120 match: 31 SD: 0.9297 cents 68 .. 136 match: 31 SD: 0.9117 cents 72 .. 144 match: 31 SD: 0.8886 cents 75 .. 150 match: 31 SD: 0.8512 cents 76 .. 152 match: 31 SD: 0.8166 cents 80 .. 160 match: 31 SD: 0.7823 cents 81 .. 162 match: 31 SD: 0.7439 cents 83 .. 166 match: 31 SD: 0.7396 cents 84 .. 168 match: 31 SD: 0.6095 cents 98 .. 196 match: 31 SD: 0.5429 cents 115 .. 230 match: 31 SD: 0.5052 cents 120 .. 240 match: 31 SD: 0.4991 cents 124 .. 248 match: 31 SD: 0.4720 cents 126 .. 252 match: 31 SD: 0.4427 cents 137 .. 274 match: 31 SD: 0.4390 cents 140 .. 280 match: 31 SD: 0.3597 cents 156 .. 312 match: 31 SD: 0.3567 cents 160 .. 320 match: 31 SD: 0.3532 cents 168 .. 336 match: 31 SD: 0.3372 cents 180 .. 360 match: 31 SD: 0.2992 cents 192 .. 384 match: 31 SD: 0.2790 cents 196 .. 392 match: 31 SD: 0.2603 cents 200 .. 400 match: 31 SD: 0.2492 cents 224 .. 448 match: 31 SD: 0.2473 cents 235 .. 470 match: 31 SD: 0.2418 cents 240 .. 480 match: 31 SD: 0.2077 cents 280 .. 560 match: 31 SD: 0.1663 cents 294 .. 588 match: 31 SD: 0.1651 cents 324 .. 648 match: 31 SD: 0.1620 cents 336 .. 672 match: 31 SD: 0.1371 cents 360 .. 720 match: 31 SD: 0.1319 cents 392 .. 784 match: 31 SD: 0.1306 cents 420 .. 840 match: 31 SD: 0.1182 cents 476 .. 952 match: 31 SD: 0.1094 cents 480 .. 960 match: 31 SD: 0.0947 cents 560 .. 1120 match: 31 SD: 0.0912 cents 576 .. 1152 match: 31 SD: 0.0856 cents 600 .. 1200 match: 31 SD: 0.0836 cents