Scala analysis: enn45
Detempered Ennealimmal[45], TM reduced
Generated by Scala: https://www.huygens-fokker.org/scala/
SHOW
0: 1/1 0.000000 unison, perfect prime 1: 49/48 35.696812 slendro diesis, septimal 1/6-tone 2: 25/24 70.672427 classic chromatic semitone, minor chroma 3: 21/20 84.467193 minor semitone 4: 15/14 119.442808 major diatonic semitone 5: 27/25 133.237575 large limma, BP small semitone, Zarlino semitone 6: 54/49 168.213190 Zalzal's mujannab 7: 9/8 203.910002 major whole tone 8: 245/216 218.100524 9: 81/70 252.680383 Al-Hwarizmi's lute middle finger 10: 7/6 266.870906 septimal minor third 11: 25/21 301.846520 BP second, quasi-equal minor third 12: 175/144 337.543332 13: 49/40 351.338099 larger approximation to neutral third 14: 5/4 386.313714 major third 15: 63/50 400.108480 quasi-equal major third 16: 9/7 435.084095 septimal major third, BP third 17: 21/16 470.780907 narrow fourth 18: 250/189 484.250233 19: 27/20 519.551289 acute fourth 20: 49/36 533.741811 Arabic lute acute fourth 21: 25/18 568.717426 classic augmented fourth 22: 486/343 603.297285 23: 10/7 617.487807 Euler's tritone 24: 35/24 653.184619 septimal semi-diminished fifth 25: 72/49 666.258189 Arabic lute grave fifth 26: 3/2 701.955001 perfect fifth 27: 49/32 737.651813 28: 54/35 750.725382 septimal semi-augmented fifth 29: 63/40 786.422194 narrow minor sixth 30: 100/63 799.891520 quasi-equal minor sixth 31: 81/50 835.192576 acute minor sixth 32: 81/49 870.168191 two (septimal major third, BP third) 33: 5/3 884.358713 major sixth, BP sixth 34: 245/144 920.055525 35: 12/7 933.129094 septimal major sixth 36: 7/4 968.825906 harmonic seventh 37: 25/14 1003.801521 middle minor seventh 38: 9/5 1017.596288 just minor seventh, BP seventh 39: 90/49 1052.571903 40: 50/27 1066.762425 grave major seventh 41: 189/100 1102.063481 42: 27/14 1137.039096 septimal major seventh 43: 35/18 1151.229619 septimal semi-diminished octave 44: 125/63 1186.205233 45: 2/1 1200.000000 octave
SHOW/INTERVAL
0: 126/125 13.7948 septimal semicomma, Starling comma 1: 49/48 35.6968 slendro diesis, septimal 1/6-tone 2: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 3: 126/125 13.7948 septimal semicomma, Starling comma 4: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 5: 126/125 13.7948 septimal semicomma, Starling comma 6: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 7: 49/48 35.6968 slendro diesis, septimal 1/6-tone 8: 245/243 14.1905 minor BP diesis, Sensamagic comma 9: 8748/8575 34.5799 10: 245/243 14.1905 minor BP diesis, Sensamagic comma 11: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 12: 49/48 35.6968 slendro diesis, septimal 1/6-tone 13: 126/125 13.7948 septimal semicomma, Starling comma 14: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 15: 126/125 13.7948 septimal semicomma, Starling comma 16: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 17: 49/48 35.6968 slendro diesis, septimal 1/6-tone 18: 4000/3969 13.4693 small septimal comma 19: 5103/5000 35.3011 20: 245/243 14.1905 minor BP diesis, Sensamagic comma 21: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 22: 8748/8575 34.5799 23: 245/243 14.1905 minor BP diesis, Sensamagic comma 24: 49/48 35.6968 slendro diesis, septimal 1/6-tone 25: 1728/1715 13.0736 Orwell comma 26: 49/48 35.6968 slendro diesis, septimal 1/6-tone 27: 49/48 35.6968 slendro diesis, septimal 1/6-tone 28: 1728/1715 13.0736 Orwell comma 29: 49/48 35.6968 slendro diesis, septimal 1/6-tone 30: 4000/3969 13.4693 small septimal comma 31: 5103/5000 35.3011 32: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 33: 245/243 14.1905 minor BP diesis, Sensamagic comma 34: 49/48 35.6968 slendro diesis, septimal 1/6-tone 35: 1728/1715 13.0736 Orwell comma 36: 49/48 35.6968 slendro diesis, septimal 1/6-tone 37: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 38: 126/125 13.7948 septimal semicomma, Starling comma 39: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 40: 245/243 14.1905 minor BP diesis, Sensamagic comma 41: 5103/5000 35.3011 42: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 43: 245/243 14.1905 minor BP diesis, Sensamagic comma 44: 50/49 34.9756 Erlich's decatonic comma, tritonic diesis 45: 126/125 13.7948 septimal semicomma, Starling comma
SHOW INTERVALS
Interval class, Number of incidences, Size: 1: 3 1728/1715 13.074 cents Orwell comma 1: 2 4000/3969 13.469 cents small septimal comma 1: 6 126/125 13.795 cents septimal semicomma, Starling comma 1: 7 245/243 14.191 cents minor BP diesis, Sensamagic comma 1: 2 8748/8575 34.580 cents 1: 12 50/49 34.976 cents Erlich's decatonic comma, tritonic diesis 1: 3 5103/5000 35.301 cents 1: 10 49/48 35.697 cents slendro diesis, septimal 1/6-tone 2: 21 36/35 48.770 cents septimal diesis, 1/4-tone 2: 8 250/243 49.166 cents maximal diesis, Porcupine comma 2: 4 1029/1000 49.492 cents keega 2: 3 12005/11664 49.887 cents 2: 1 17496/16807 69.555 cents septimal major diesis 2: 2 729/700 70.277 cents 2: 5 25/24 70.672 cents classic chromatic semitone, minor chroma 2: 1 2401/2304 71.394 cents two (slendro diesis, septimal 1/6-tone) 3: 1 3200/3087 62.240 cents 3: 2 648/625 62.565 cents major diesis 3: 6 28/27 62.961 cents Archytas' 1/3-tone 3: 9 360/343 83.746 cents 3: 2 12500/11907 84.142 cents 3: 22 21/20 84.467 cents minor semitone 3: 3 6125/5832 84.863 cents 4: 7 1296/1225 97.541 cents two (septimal diesis, 1/4-tone) 4: 9 200/189 97.937 cents 4: 3 1323/1250 98.262 cents 4: 8 343/324 98.658 cents 4: 1 6561/6125 119.047 cents BP major link 4: 14 15/14 119.443 cents major diatonic semitone 4: 3 343/320 120.164 cents 5: 5 2592/2401 132.516 cents 5: 1 10000/9261 132.912 cents 5: 20 27/25 133.238 cents large limma, BP small semitone, Zarlino semitone 5: 18 175/162 133.633 cents 5: 1 16807/15552 134.355 cents 6: 7 160/147 146.707 cents 6: 1 3402/3125 147.032 cents 6: 10 49/45 147.428 cents BP minor semitone 6: 12 54/49 168.213 cents Zalzal's mujannab 6: 5 625/567 168.609 cents BP great semitone, major BP chroma 6: 8 441/400 168.934 cents two (minor semitone) 6: 2 8575/7776 169.330 cents 7: 9 972/875 182.008 cents 7: 24 10/9 182.404 cents minor whole tone 7: 3 2401/2160 183.125 cents 7: 1 2700/2401 203.189 cents 7: 7 9/8 203.910 cents major whole tone 7: 1 4375/3888 204.306 cents 8: 2 384/343 195.477 cents 8: 5 28/25 196.198 cents middle second 8: 2 2450/2187 196.594 cents 8: 7 1944/1715 216.984 cents 8: 8 500/441 217.379 cents 8: 8 567/500 217.705 cents 8: 13 245/216 218.101 cents 9: 17 8/7 231.174 cents septimal whole tone 9: 2 2500/2187 231.570 cents 9: 8 343/300 231.895 cents 9: 1 19440/16807 251.959 cents 9: 9 81/70 252.680 cents Al-Hwarizmi's lute middle finger 9: 6 125/108 253.076 cents semi-augmented whole tone 9: 1 9261/8000 253.402 cents 9: 1 12005/10368 253.797 cents 10: 1 69984/60025 265.754 cents 10: 9 400/343 266.150 cents 10: 4 729/625 266.475 cents two (large limma, BP small semitone, Zarlino semitone) 10: 31 7/6 266.871 cents septimal minor third 11: 6 288/245 279.944 cents 11: 3 2000/1701 280.340 cents 11: 5 147/125 280.666 cents 11: 4 1715/1458 281.061 cents 11: 6 1458/1225 301.451 cents 11: 14 25/21 301.847 cents BP second, quasi-equal minor third 11: 2 11907/10000 302.172 cents 11: 5 343/288 302.568 cents 12: 2 2880/2401 314.920 cents 12: 27 6/5 315.641 cents minor third 12: 6 875/729 316.037 cents 12: 1 84035/69984 316.758 cents 12: 2 2916/2401 336.426 cents two (Zalzal's mujannab) 12: 2 243/200 337.148 cents acute minor third 12: 5 175/144 337.543 cents 13: 1 10368/8575 328.715 cents 13: 2 1600/1323 329.111 cents 13: 2 756/625 329.436 cents 13: 4 98/81 329.832 cents 13: 17 60/49 350.617 cents smaller approximation to neutral third 13: 1 15309/12500 350.942 cents 13: 2 6250/5103 351.013 cents 13: 16 49/40 351.338 cents larger approximation to neutral third 14: 12 216/175 364.412 cents 14: 10 100/81 364.807 cents grave major third 14: 1 3087/2500 365.133 cents 14: 4 2401/1944 365.529 cents 14: 1 104976/84035 385.197 cents 14: 2 2187/1750 385.918 cents 14: 15 5/4 386.314 cents major third 15: 11 432/343 399.387 cents 15: 4 5000/3969 399.783 cents 15: 19 63/50 400.108 cents quasi-equal major third 15: 11 1225/972 400.504 cents 16: 2 7776/6125 413.182 cents 16: 9 80/63 413.578 cents wide major third 16: 1 3969/3125 413.903 cents 16: 6 343/270 414.299 cents 16: 19 9/7 435.084 cents septimal major third, BP third 16: 4 625/486 435.480 cents 16: 4 1029/800 435.805 cents 17: 2 15552/12005 448.158 cents 17: 3 4000/3087 448.553 cents 17: 11 162/125 448.879 cents 17: 20 35/27 449.275 cents septimal semi-diminished fourth, 9/4-tone 17: 3 450/343 470.060 cents 17: 6 21/16 470.781 cents narrow fourth 18: 4 64/49 462.348 cents 2 septatones or septatonic major third 18: 4 98/75 463.069 cents 18: 1 8575/6561 463.465 cents 18: 13 324/245 483.854 cents 18: 10 250/189 484.250 cents 18: 6 1323/1000 484.576 cents 18: 7 1715/1296 484.971 cents 19: 1 5832/4375 497.649 cents 19: 24 4/3 498.045 cents perfect fourth 19: 2 2401/1800 498.766 cents 19: 3 3240/2401 518.830 cents 19: 10 27/20 519.551 cents acute fourth 19: 5 875/648 519.947 cents 20: 4 11664/8575 532.625 cents 20: 16 200/147 533.021 cents 20: 6 1701/1250 533.346 cents 20: 19 49/36 533.742 cents Arabic lute acute fourth 21: 10 48/35 546.815 cents septimal semi-augmented fourth 21: 3 1000/729 547.211 cents 21: 3 343/250 547.537 cents 21: 2 12005/8748 547.932 cents 21: 1 23328/16807 567.600 cents 21: 10 243/175 568.322 cents 21: 14 25/18 568.717 cents classic augmented fourth 21: 2 2401/1728 569.439 cents 22: 8 480/343 581.791 cents 22: 1 50000/35721 582.187 cents 22: 25 7/5 582.512 cents septimal or Huygens' tritone, BP fourth 22: 2 6125/4374 582.908 cents 22: 3 486/343 603.297 cents 22: 1 625/441 603.693 cents two (BP second, quasi-equal minor third) 22: 2 567/400 604.018 cents 22: 3 1225/864 604.414 cents 23: 3 1728/1225 595.586 cents 23: 2 800/567 595.982 cents 23: 1 882/625 596.307 cents 23: 3 343/243 596.703 cents 23: 2 8748/6125 617.092 cents 23: 25 10/7 617.488 cents Euler's tritone 23: 1 35721/25000 617.813 cents 23: 8 343/240 618.209 cents 24: 2 3456/2401 630.561 cents 24: 14 36/25 631.283 cents classic diminished fifth 24: 10 350/243 631.678 cents 24: 1 16807/11664 632.400 cents 24: 2 17496/12005 652.068 cents 24: 3 500/343 652.463 cents 24: 3 729/500 652.789 cents 24: 10 35/24 653.185 cents septimal semi-diminished fifth 25: 19 72/49 666.258 cents Arabic lute grave fifth 25: 6 2500/1701 666.654 cents 25: 16 147/100 666.979 cents 25: 4 8575/5832 667.375 cents 26: 5 1296/875 680.053 cents 26: 10 40/27 680.449 cents grave fifth 26: 3 2401/1620 681.170 cents 26: 2 3600/2401 701.234 cents two (smaller approximation to neutral third) 26: 24 3/2 701.955 cents perfect fifth 26: 1 4375/2916 702.351 cents 27: 7 2592/1715 715.029 cents 27: 6 2000/1323 715.424 cents 27: 10 189/125 715.750 cents 27: 13 245/162 716.146 cents 27: 1 13122/8575 736.535 cents 27: 4 75/49 736.931 cents BP fifth 27: 4 49/32 737.652 cents 28: 6 32/21 729.219 cents wide fifth 28: 3 343/225 729.940 cents 28: 20 54/35 750.725 cents septimal semi-augmented fifth 28: 11 125/81 751.121 cents 28: 3 3087/2000 751.447 cents 28: 2 12005/7776 751.842 cents 29: 4 1600/1029 764.195 cents 29: 4 972/625 764.520 cents 29: 19 14/9 764.916 cents septimal minor sixth 29: 6 540/343 785.701 cents 29: 1 6250/3969 786.097 cents 29: 9 63/40 786.422 cents narrow minor sixth 29: 2 6125/3888 786.818 cents 30: 11 1944/1225 799.496 cents 30: 19 100/63 799.892 cents quasi-equal minor sixth 30: 4 3969/2500 800.217 cents two (quasi-equal major third) 30: 11 343/216 800.613 cents 31: 15 8/5 813.686 cents minor sixth 31: 2 3500/2187 814.082 cents 31: 1 84035/52488 814.803 cents 31: 4 3888/2401 834.471 cents 31: 1 5000/3087 834.867 cents 31: 10 81/50 835.193 cents acute minor sixth 31: 12 175/108 835.588 cents 32: 16 80/49 848.662 cents smaller approximation to neutral sixth 32: 2 5103/3125 848.987 cents 32: 1 25000/15309 849.058 cents 32: 17 49/30 849.383 cents larger approximation to neutral sixth 32: 4 81/49 870.168 cents two (septimal major third, BP third) 32: 2 625/378 870.564 cents 32: 2 1323/800 870.889 cents 32: 1 8575/5184 871.285 cents 33: 5 288/175 862.457 cents 33: 2 400/243 862.852 cents grave major sixth 33: 2 2401/1458 863.574 cents 33: 1 139968/84035 883.242 cents 33: 6 1458/875 883.963 cents 33: 27 5/3 884.359 cents major sixth, BP sixth 33: 2 2401/1440 885.080 cents 34: 5 576/343 897.432 cents 34: 2 20000/11907 897.828 cents 34: 14 42/25 898.153 cents quasi-equal major sixth 34: 6 1225/729 898.549 cents two (septimal semi-diminished fourth, 9/4-tone) 34: 4 2916/1715 918.939 cents 34: 5 250/147 919.334 cents 34: 3 1701/1000 919.660 cents 34: 6 245/144 920.056 cents 35: 31 12/7 933.129 cents septimal major sixth 35: 4 1250/729 933.525 cents 35: 9 343/200 933.850 cents 35: 1 60025/34992 934.246 cents 36: 1 20736/12005 946.203 cents 36: 1 16000/9261 946.598 cents 36: 6 216/125 946.924 cents semi-augmented sixth 36: 9 140/81 947.320 cents 36: 1 16807/9720 948.041 cents 36: 8 600/343 968.105 cents 36: 2 2187/1250 968.430 cents 36: 17 7/4 968.826 cents harmonic seventh 37: 13 432/245 981.899 cents 37: 8 1000/567 982.295 cents 37: 8 441/250 982.621 cents 37: 7 1715/972 983.016 cents 37: 2 2187/1225 1003.406 cents 37: 5 25/14 1003.802 cents middle minor seventh 37: 2 343/192 1004.523 cents 38: 1 7776/4375 995.694 cents 38: 7 16/9 996.090 cents Pythagorean minor seventh 38: 1 2401/1350 996.811 cents 38: 3 4320/2401 1016.875 cents 38: 24 9/5 1017.596 cents just minor seventh, BP seventh 38: 9 875/486 1017.992 cents 39: 2 15552/8575 1030.670 cents 39: 8 800/441 1031.066 cents 39: 5 1134/625 1031.391 cents 39: 12 49/27 1031.787 cents 39: 10 90/49 1052.572 cents 39: 1 3125/1701 1052.968 cents 39: 7 147/80 1053.293 cents 40: 1 31104/16807 1065.645 cents 40: 18 324/175 1066.367 cents 40: 20 50/27 1066.762 cents grave major seventh 40: 1 9261/5000 1067.088 cents 40: 5 2401/1296 1067.484 cents two (Arabic lute acute fourth) 41: 3 640/343 1079.836 cents 41: 14 28/15 1080.557 cents grave major seventh 41: 1 12250/6561 1080.953 cents 41: 8 648/343 1101.342 cents 41: 3 2500/1323 1101.738 cents 41: 9 189/100 1102.063 cents 41: 7 1225/648 1102.459 cents 42: 3 11664/6125 1115.137 cents 42: 22 40/21 1115.533 cents acute major seventh 42: 2 11907/6250 1115.858 cents 42: 9 343/180 1116.254 cents 42: 6 27/14 1137.039 cents septimal major seventh 42: 2 625/324 1137.435 cents octave - major diesis 42: 1 3087/1600 1137.760 cents 43: 1 4608/2401 1128.606 cents 43: 5 48/25 1129.328 cents classic diminished octave 43: 2 1400/729 1129.723 cents 43: 1 16807/8748 1130.445 cents 43: 3 23328/12005 1150.113 cents 43: 4 2000/1029 1150.508 cents 43: 8 243/125 1150.834 cents octave - maximal diesis 43: 21 35/18 1151.230 cents septimal semi-diminished octave 44: 10 96/49 1164.303 cents 44: 3 10000/5103 1164.699 cents 44: 12 49/25 1165.024 cents BP eighth 44: 2 8575/4374 1165.420 cents 44: 7 486/245 1185.809 cents 44: 6 125/63 1186.205 cents 44: 2 3969/2000 1186.531 cents 44: 3 1715/864 1186.926 cents Highest number of different intervals for one interval class: 8 Average number of different intervals per interval class: 6.68182 = 147/22
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 32 33 34 35 36 37 38 39 40 41 42 43 44 45 0.0 : 35.7 70.7 84.5 119.4 133.2 168.2 203.9 218.1 252.7 266.9 301.8 337.5 351.3 386.3 400.1 435.1 470.8 484.3 519.6 533.7 568.7 603.3 617.5 653.2 666.3 702.0 737.7 750.7 786.4 799.9 835.2 870.2 884.4 920.1 933.1 968.8 1003.8 1017.6 1052.6 1066.8 1102.1 1137.0 1151.2 1186.2 1200.0 35.7 : 35.0 48.8 83.7 97.5 132.5 168.2 182.4 217.0 231.2 266.1 301.8 315.6 350.6 364.4 399.4 435.1 448.6 483.9 498.0 533.0 567.6 581.8 617.5 630.6 666.3 702.0 715.0 750.7 764.2 799.5 834.5 848.7 884.4 897.4 933.1 968.1 981.9 1016.9 1031.1 1066.4 1101.3 1115.5 1150.5 1164.3 1200.0 70.7 : 13.8 48.8 62.6 97.5 133.2 147.4 182.0 196.2 231.2 266.9 280.7 315.6 329.4 364.4 400.1 413.6 448.9 463.1 498.0 532.6 546.8 582.5 595.6 631.3 667.0 680.1 715.7 729.2 764.5 799.5 813.7 849.4 862.5 898.2 933.1 946.9 981.9 996.1 1031.4 1066.4 1080.6 1115.5 1129.3 1165.0 1200.0 84.5 : 35.0 48.8 83.7 119.4 133.6 168.2 182.4 217.4 253.1 266.9 301.8 315.6 350.6 386.3 399.8 435.1 449.3 484.3 518.8 533.0 568.7 581.8 617.5 653.2 666.3 702.0 715.4 750.7 785.7 799.9 835.6 848.7 884.4 919.3 933.1 968.1 982.3 1017.6 1052.6 1066.8 1101.7 1115.5 1151.2 1186.2 1200.0 119.4 : 13.8 48.8 84.5 98.7 133.2 147.4 182.4 218.1 231.9 266.9 280.7 315.6 351.3 364.8 400.1 414.3 449.3 483.9 498.0 533.7 546.8 582.5 618.2 631.3 667.0 680.4 715.7 750.7 764.9 800.6 813.7 849.4 884.4 898.2 933.1 947.3 982.6 1017.6 1031.8 1066.8 1080.6 1116.3 1151.2 1165.0 1200.0 133.2 : 35.0 70.7 84.9 119.4 133.6 168.6 204.3 218.1 253.1 266.9 301.8 337.5 351.0 386.3 400.5 435.5 470.1 484.3 519.9 533.0 568.7 604.4 617.5 653.2 666.7 702.0 736.9 751.1 786.8 799.9 835.6 870.6 884.4 919.3 933.5 968.8 1003.8 1018.0 1053.0 1066.8 1102.5 1137.4 1151.2 1186.2 1200.0 168.2 : 35.7 49.9 84.5 98.7 133.6 169.3 183.1 218.1 231.9 266.9 302.6 316.0 351.3 365.5 400.5 435.1 449.3 485.0 498.0 533.7 569.4 582.5 618.2 631.7 667.0 702.0 716.1 751.8 764.9 800.6 835.6 849.4 884.4 898.5 933.9 968.8 983.0 1018.0 1031.8 1067.5 1102.5 1116.3 1151.2 1165.0 1200.0 203.9 : 14.2 48.8 63.0 97.9 133.6 147.4 182.4 196.2 231.2 266.9 280.3 315.6 329.8 364.8 399.4 413.6 449.3 462.3 498.0 533.7 546.8 582.5 596.0 631.3 666.3 680.4 716.1 729.2 764.9 799.9 813.7 848.7 862.9 898.2 933.1 947.3 982.3 996.1 1031.8 1066.8 1080.6 1115.5 1129.3 1164.3 1200.0 218.1 : 34.6 48.8 83.7 119.4 133.2 168.2 182.0 217.0 252.7 266.1 301.5 315.6 350.6 385.2 399.4 435.1 448.2 483.9 519.6 532.6 568.3 581.8 617.1 652.1 666.3 702.0 715.0 750.7 785.7 799.5 834.5 848.7 884.0 918.9 933.1 968.1 981.9 1017.6 1052.6 1066.4 1101.3 1115.1 1150.1 1185.8 1200.0 252.7 : 14.2 49.2 84.9 98.7 133.6 147.4 182.4 218.1 231.6 266.9 281.1 316.0 350.6 364.8 400.5 413.6 449.3 485.0 498.0 533.7 547.2 582.5 617.5 631.7 667.4 680.4 716.1 751.1 764.9 799.9 814.1 849.4 884.4 898.5 933.5 947.3 983.0 1018.0 1031.8 1066.8 1080.6 1115.5 1151.2 1165.4 1200.0 266.9 : 35.0 70.7 84.5 119.4 133.2 168.2 203.9 217.4 252.7 266.9 301.8 336.4 350.6 386.3 399.4 435.1 470.8 483.9 519.6 533.0 568.3 603.3 617.5 653.2 666.3 702.0 736.9 750.7 785.7 799.9 835.2 870.2 884.4 919.3 933.1 968.8 1003.8 1017.6 1052.6 1066.4 1101.3 1137.0 1151.2 1185.8 1200.0 301.8 : 35.7 49.5 84.5 98.3 133.2 168.9 182.4 217.7 231.9 266.9 301.5 315.6 351.3 364.4 400.1 435.8 448.9 484.6 498.0 533.3 568.3 582.5 618.2 631.3 667.0 702.0 715.7 750.7 764.9 800.2 835.2 849.4 884.4 898.2 933.9 968.8 982.6 1017.6 1031.4 1066.4 1102.1 1116.3 1150.8 1165.0 1200.0 337.5 : 13.8 48.8 62.6 97.5 133.2 146.7 182.0 196.2 231.2 265.8 279.9 315.6 328.7 364.4 400.1 413.2 448.9 462.3 497.6 532.6 546.8 582.5 595.6 631.3 666.3 680.1 715.0 729.2 764.5 799.5 813.7 848.7 862.5 898.2 933.1 946.9 981.9 995.7 1030.7 1066.4 1080.6 1115.1 1129.3 1164.3 1200.0 351.3 : 35.0 48.8 83.7 119.4 132.9 168.2 182.4 217.4 252.0 266.1 301.8 314.9 350.6 386.3 399.4 435.1 448.6 483.9 518.8 533.0 568.7 581.8 617.5 652.5 666.3 701.2 715.4 750.7 785.7 799.9 834.9 848.7 884.4 919.3 933.1 968.1 981.9 1016.9 1052.6 1066.8 1101.3 1115.5 1150.5 1186.2 1200.0 386.3 : 13.8 48.8 84.5 97.9 133.2 147.4 182.4 217.0 231.2 266.9 279.9 315.6 351.3 364.4 400.1 413.6 448.9 483.9 498.0 533.7 546.8 582.5 617.5 631.3 666.3 680.4 715.7 750.7 764.9 799.9 813.7 849.4 884.4 898.2 933.1 946.9 981.9 1017.6 1031.8 1066.4 1080.6 1115.5 1151.2 1165.0 1200.0 400.1 : 35.0 70.7 84.1 119.4 133.6 168.6 203.2 217.4 253.1 266.1 301.8 337.5 350.6 386.3 399.8 435.1 470.1 484.3 519.9 533.0 568.7 603.7 617.5 652.5 666.7 702.0 736.9 751.1 786.1 799.9 835.6 870.6 884.4 919.3 933.1 968.1 1003.8 1018.0 1052.6 1066.8 1101.7 1137.4 1151.2 1186.2 1200.0 435.1 : 35.7 49.2 84.5 98.7 133.6 168.2 182.4 218.1 231.2 266.9 302.6 315.6 351.3 364.8 400.1 435.1 449.3 485.0 498.0 533.7 568.7 582.5 617.5 631.7 667.0 702.0 716.1 751.1 764.9 800.6 835.6 849.4 884.4 898.2 933.1 968.8 983.0 1017.6 1031.8 1066.8 1102.5 1116.3 1151.2 1165.0 1200.0 470.8 : 13.5 48.8 63.0 97.9 132.5 146.7 182.4 195.5 231.2 266.9 279.9 315.6 329.1 364.4 399.4 413.6 449.3 462.3 498.0 533.0 546.8 581.8 596.0 631.3 666.3 680.4 715.4 729.2 764.9 799.9 813.7 848.7 862.5 897.4 933.1 947.3 981.9 996.1 1031.1 1066.8 1080.6 1115.5 1129.3 1164.3 1200.0 484.3 : 35.3 49.5 84.5 119.0 133.2 168.9 182.0 217.7 253.4 266.5 302.2 315.6 350.9 385.9 400.1 435.8 448.9 484.6 519.6 533.3 568.3 582.5 617.8 652.8 667.0 702.0 715.7 751.4 786.4 800.2 835.2 849.0 884.0 919.7 933.9 968.4 982.6 1017.6 1053.3 1067.1 1102.1 1115.9 1150.8 1186.5 1200.0 519.6 : 14.2 49.2 83.7 97.9 133.6 146.7 182.4 218.1 231.2 266.9 280.3 315.6 350.6 364.8 400.5 413.6 449.3 484.3 498.0 533.0 547.2 582.5 617.5 631.7 666.7 680.4 716.1 751.1 764.9 799.9 813.7 848.7 884.4 898.5 933.1 947.3 982.3 1018.0 1031.8 1066.8 1080.6 1115.5 1151.2 1164.7 1200.0 533.7 : 35.0 69.6 83.7 119.4 132.5 168.2 203.9 217.0 252.7 266.1 301.5 336.4 350.6 386.3 399.4 435.1 470.1 483.9 518.8 533.0 568.3 603.3 617.5 652.5 666.3 702.0 736.9 750.7 785.7 799.5 834.5 870.2 884.4 918.9 933.1 968.1 1003.8 1017.6 1052.6 1066.4 1101.3 1137.0 1150.5 1185.8 1200.0 568.7 : 34.6 48.8 84.5 97.5 133.2 168.9 182.0 217.7 231.2 266.5 301.5 315.6 351.3 364.4 400.1 435.1 448.9 483.9 498.0 533.3 568.3 582.5 617.5 631.3 667.0 702.0 715.7 750.7 764.5 799.5 835.2 849.4 884.0 898.2 933.1 968.8 982.6 1017.6 1031.4 1066.4 1102.1 1115.5 1150.8 1165.0 1200.0 603.3 : 14.2 49.9 63.0 98.7 134.4 147.4 183.1 196.6 231.9 266.9 281.1 316.8 329.8 365.5 400.5 414.3 449.3 463.5 498.8 533.7 547.9 582.9 596.7 632.4 667.4 681.2 716.1 729.9 764.9 800.6 814.8 849.4 863.6 898.5 934.2 948.0 983.0 996.8 1031.8 1067.5 1081.0 1116.3 1130.4 1165.4 1200.0 617.5 : 35.7 48.8 84.5 120.2 133.2 168.9 182.4 217.7 252.7 266.9 302.6 315.6 351.3 386.3 400.1 435.1 449.3 484.6 519.6 533.7 568.7 582.5 618.2 653.2 667.0 702.0 715.7 750.7 786.4 800.6 835.2 849.4 884.4 920.1 933.9 968.8 982.6 1017.6 1053.3 1066.8 1102.1 1116.3 1151.2 1185.8 1200.0 653.2 : 13.1 48.8 84.5 97.5 133.2 146.7 182.0 217.0 231.2 266.9 279.9 315.6 350.6 364.4 399.4 413.6 448.9 483.9 498.0 533.0 546.8 582.5 617.5 631.3 666.3 680.1 715.0 750.7 764.9 799.5 813.7 848.7 884.4 898.2 933.1 946.9 981.9 1017.6 1031.1 1066.4 1080.6 1115.5 1150.1 1164.3 1200.0 666.3 : 35.7 71.4 84.5 120.2 133.6 168.9 203.9 218.1 253.8 266.9 302.6 337.5 351.3 386.3 400.5 435.8 470.8 485.0 519.9 533.7 569.4 604.4 618.2 653.2 667.0 702.0 737.7 751.8 786.4 800.6 835.6 871.3 885.1 920.1 933.9 968.8 1004.5 1018.0 1053.3 1067.5 1102.5 1137.0 1151.2 1186.9 1200.0 702.0 : 35.7 48.8 84.5 97.9 133.2 168.2 182.4 218.1 231.2 266.9 301.8 315.6 350.6 364.8 400.1 435.1 449.3 484.3 498.0 533.7 568.7 582.5 617.5 631.3 666.3 702.0 716.1 750.7 764.9 799.9 835.6 849.4 884.4 898.2 933.1 968.8 982.3 1017.6 1031.8 1066.8 1101.3 1115.5 1151.2 1164.3 1200.0 737.7 : 13.1 48.8 62.2 97.5 132.5 146.7 182.4 195.5 231.2 266.1 279.9 314.9 329.1 364.4 399.4 413.6 448.6 462.3 498.0 533.0 546.8 581.8 595.6 630.6 666.3 680.4 715.0 729.2 764.2 799.9 813.7 848.7 862.5 897.4 933.1 946.6 981.9 996.1 1031.1 1065.6 1079.8 1115.5 1128.6 1164.3 1200.0 750.7 : 35.7 49.2 84.5 119.4 133.6 169.3 182.4 218.1 253.1 266.9 301.8 316.0 351.3 386.3 400.5 435.5 449.3 485.0 519.9 533.7 568.7 582.5 617.5 653.2 667.4 702.0 716.1 751.1 786.8 800.6 835.6 849.4 884.4 920.1 933.5 968.8 983.0 1018.0 1052.6 1066.8 1102.5 1115.5 1151.2 1186.9 1200.0 786.4 : 13.5 48.8 83.7 97.9 133.6 146.7 182.4 217.4 231.2 266.1 280.3 315.6 350.6 364.8 399.8 413.6 449.3 484.3 498.0 533.0 546.8 581.8 617.5 631.7 666.3 680.4 715.4 751.1 764.9 799.9 813.7 848.7 884.4 897.8 933.1 947.3 982.3 1016.9 1031.1 1066.8 1079.8 1115.5 1151.2 1164.3 1200.0 799.9 : 35.3 70.3 84.5 120.2 133.2 168.9 203.9 217.7 252.7 266.9 302.2 337.1 351.3 386.3 400.1 435.8 470.8 484.6 519.6 533.3 568.3 604.0 618.2 652.8 667.0 702.0 737.7 751.4 786.4 800.2 835.2 870.9 884.4 919.7 933.9 968.8 1003.4 1017.6 1053.3 1066.4 1102.1 1137.8 1150.8 1186.5 1200.0 835.2 : 35.0 49.2 84.9 97.9 133.6 168.6 182.4 217.4 231.6 266.9 301.8 316.0 351.0 364.8 400.5 435.5 449.3 484.3 498.0 533.0 568.7 582.9 617.5 631.7 666.7 702.4 716.1 751.1 764.9 799.9 835.6 849.1 884.4 898.5 933.5 968.1 982.3 1018.0 1031.1 1066.8 1102.5 1115.5 1151.2 1164.7 1200.0 870.2 : 14.2 49.9 63.0 98.7 133.6 147.4 182.4 196.6 231.9 266.9 281.1 316.0 329.8 365.5 400.5 414.3 449.3 463.1 498.0 533.7 547.9 582.5 596.7 631.7 667.4 681.2 716.1 729.9 764.9 800.6 814.1 849.4 863.6 898.5 933.1 947.3 983.0 996.1 1031.8 1067.5 1080.6 1116.3 1129.7 1165.0 1200.0 884.4 : 35.7 48.8 84.5 119.4 133.2 168.2 182.4 217.7 252.7 266.9 301.8 315.6 351.3 386.3 400.1 435.1 448.9 483.9 519.6 533.7 568.3 582.5 617.5 653.2 667.0 702.0 715.7 750.7 786.4 799.9 835.2 849.4 884.4 918.9 933.1 968.8 981.9 1017.6 1053.3 1066.4 1102.1 1115.5 1150.8 1185.8 1200.0 920.1 : 13.1 48.8 83.7 97.5 132.5 146.7 182.0 217.0 231.2 266.1 279.9 315.6 350.6 364.4 399.4 413.2 448.2 483.9 498.0 532.6 546.8 581.8 617.5 631.3 666.3 680.1 715.0 750.7 764.2 799.5 813.7 848.7 883.2 897.4 933.1 946.2 981.9 1017.6 1030.7 1066.4 1079.8 1115.1 1150.1 1164.3 1200.0 933.1 : 35.7 70.7 84.5 119.4 133.6 168.9 203.9 218.1 253.1 266.9 302.6 337.5 351.3 386.3 400.1 435.1 470.8 485.0 519.6 533.7 568.7 604.4 618.2 653.2 667.0 702.0 737.7 751.1 786.4 800.6 835.6 870.2 884.4 920.1 933.1 968.8 1004.5 1017.6 1053.3 1066.8 1102.1 1137.0 1151.2 1186.9 1200.0 968.8 : 35.0 48.8 83.7 97.9 133.2 168.2 182.4 217.4 231.2 266.9 301.8 315.6 350.6 364.4 399.4 435.1 449.3 483.9 498.0 533.0 568.7 582.5 617.5 631.3 666.3 702.0 715.4 750.7 764.9 799.9 834.5 848.7 884.4 897.4 933.1 968.8 981.9 1017.6 1031.1 1066.4 1101.3 1115.5 1151.2 1164.3 1200.0 1003.8: 13.8 48.8 63.0 98.3 133.2 147.4 182.4 196.2 231.9 266.9 280.7 315.6 329.4 364.4 400.1 414.3 448.9 463.1 498.0 533.7 547.5 582.5 596.3 631.3 667.0 680.4 715.7 729.9 764.9 799.5 813.7 849.4 862.5 898.2 933.9 946.9 982.6 996.1 1031.4 1066.4 1080.6 1116.3 1129.3 1165.0 1200.0 1017.6: 35.0 49.2 84.5 119.4 133.6 168.6 182.4 218.1 253.1 266.9 301.8 315.6 350.6 386.3 400.5 435.1 449.3 484.3 519.9 533.7 568.7 582.5 617.5 653.2 666.7 702.0 716.1 751.1 785.7 799.9 835.6 848.7 884.4 920.1 933.1 968.8 982.3 1017.6 1052.6 1066.8 1102.5 1115.5 1151.2 1186.2 1200.0 1052.6: 14.2 49.5 84.5 98.7 133.6 147.4 183.1 218.1 231.9 266.9 280.7 315.6 351.3 365.5 400.1 414.3 449.3 485.0 498.8 533.7 547.5 582.5 618.2 631.7 667.0 681.2 716.1 750.7 764.9 800.6 813.7 849.4 885.1 898.2 933.9 947.3 982.6 1017.6 1031.8 1067.5 1080.6 1116.3 1151.2 1165.0 1200.0 1066.8: 35.3 70.3 84.5 119.4 133.2 168.9 203.9 217.7 252.7 266.5 301.5 337.1 351.3 385.9 400.1 435.1 470.8 484.6 519.6 533.3 568.3 604.0 617.5 652.8 667.0 702.0 736.5 750.7 786.4 799.5 835.2 870.9 884.0 919.7 933.1 968.4 1003.4 1017.6 1053.3 1066.4 1102.1 1137.0 1150.8 1185.8 1200.0 1102.1: 35.0 49.2 84.1 97.9 133.6 168.6 182.4 217.4 231.2 266.1 301.8 316.0 350.6 364.8 399.8 435.5 449.3 484.3 498.0 533.0 568.7 582.2 617.5 631.7 666.7 701.2 715.4 751.1 764.2 799.9 835.6 848.7 884.4 897.8 933.1 968.1 982.3 1018.0 1031.1 1066.8 1101.7 1115.5 1150.5 1164.7 1200.0 1137.0: 14.2 49.2 63.0 98.7 133.6 147.4 182.4 196.2 231.2 266.9 281.1 315.6 329.8 364.8 400.5 414.3 449.3 463.1 498.0 533.7 547.2 582.5 596.7 631.7 666.3 680.4 716.1 729.2 764.9 800.6 813.7 849.4 862.9 898.2 933.1 947.3 983.0 996.1 1031.8 1066.8 1080.6 1115.5 1129.7 1165.0 1200.0 1151.2: 35.0 48.8 84.5 119.4 133.2 168.2 182.0 217.0 252.7 266.9 301.5 315.6 350.6 386.3 400.1 435.1 448.9 483.9 519.6 533.0 568.3 582.5 617.5 652.1 666.3 702.0 715.0 750.7 786.4 799.5 835.2 848.7 884.0 918.9 933.1 968.8 981.9 1017.6 1052.6 1066.4 1101.3 1115.5 1150.8 1185.8 1200.0 1186.2: 13.8 49.5 84.5 98.3 133.2 147.0 182.0 217.7 231.9 266.5 280.7 315.6 351.3 365.1 400.1 413.9 448.9 484.6 498.0 533.3 547.5 582.5 617.1 631.3 667.0 680.1 715.7 751.4 764.5 800.2 813.7 849.0 884.0 898.2 933.9 946.9 982.6 1017.6 1031.4 1066.4 1080.6 1115.9 1150.8 1165.0 1200.0 1200.0
SHOW/SPAN INTERVALS
Interval class, Interval span, Span size, Gap to prev. class: 1: 13.0736 .. 35.6968 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents 2: 48.7704 .. 71.3936 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents 3: 62.2397 .. 84.8629 cents 84035/82944, 22.6232 cents 819200/823543,-9.1539 cents 4: 97.5408 .. 120.1640 cents 84035/82944, 22.6232 cents 7558272/7503125, 12.6778 cents 5: 132.5164 .. 134.3545 cents 40353607/40310784, 1.8382 cents 829440/823543, 12.3524 cents 6: 146.7069 .. 169.3301 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 7: 182.0080 .. 204.3058 cents 3828125/3779136, 22.2978 cents 7558272/7503125, 12.6778 cents 8: 195.4773 .. 218.1005 cents 84035/82944, 22.6232 cents 1492992/1500625,-8.8285 cents 9: 231.1741 .. 253.7973 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents 10: 265.7540 .. 266.8709 cents 420175/419904, 1.1170 cents 725594112/720600125, 11.9566 cents 11: 279.9445 .. 302.5677 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents 12: 314.9201 .. 337.5433 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 13: 328.7149 .. 351.3381 cents 84035/82944, 22.6232 cents 1492992/1500625,-8.8285 cents 14: 364.4117 .. 386.3137 cents 875/864, 21.9020 cents 1728/1715, 13.0736 cents 15: 399.3873 .. 400.5042 cents 420175/419904, 1.1170 cents 1728/1715, 13.0736 cents 16: 413.1820 .. 435.8053 cents 84035/82944, 22.6232 cents 7558272/7503125, 12.6778 cents 17: 448.1577 .. 470.7809 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 18: 462.3482 .. 484.9714 cents 84035/82944, 22.6232 cents 1024/1029,-8.4327 cents 19: 497.6492 .. 519.9470 cents 3828125/3779136, 22.2978 cents 7558272/7503125, 12.6778 cents 20: 532.6249 .. 533.7418 cents 420175/419904, 1.1170 cents 7558272/7503125, 12.6778 cents 21: 546.8154 .. 569.4386 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents 22: 581.7910 .. 604.4142 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 23: 595.5858 .. 618.2090 cents 84035/82944, 22.6232 cents 1492992/1500625,-8.8285 cents 24: 630.5614 .. 653.1846 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 25: 666.2582 .. 667.3751 cents 420175/419904, 1.1170 cents 1728/1715, 13.0736 cents 26: 680.0530 .. 702.3508 cents 3828125/3779136, 22.2978 cents 7558272/7503125, 12.6778 cents 27: 715.0286 .. 737.6518 cents 84035/82944, 22.6232 cents 7558272/7503125, 12.6778 cents 28: 729.2191 .. 751.8423 cents 84035/82944, 22.6232 cents 1024/1029,-8.4327 cents 29: 764.1947 .. 786.8180 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 30: 799.4958 .. 800.6127 cents 420175/419904, 1.1170 cents 7558272/7503125, 12.6778 cents 31: 813.6863 .. 835.5883 cents 875/864, 21.9020 cents 1728/1715, 13.0736 cents 32: 848.6619 .. 871.2851 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents 33: 862.4567 .. 885.0799 cents 84035/82944, 22.6232 cents 1492992/1500625,-8.8285 cents 34: 897.4323 .. 920.0555 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 35: 933.1291 .. 934.2460 cents 420175/419904, 1.1170 cents 1728/1715, 13.0736 cents 36: 946.2027 .. 968.8259 cents 84035/82944, 22.6232 cents 725594112/720600125, 11.9566 cents 37: 981.8995 .. 1004.5227 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents 38: 995.6942 .. 1017.9920 cents 3828125/3779136, 22.2978 cents 1492992/1500625,-8.8285 cents 39: 1030.6699 .. 1053.2931 cents 84035/82944, 22.6232 cents 7558272/7503125, 12.6778 cents 40: 1065.6455 .. 1067.4836 cents 40353607/40310784, 1.8382 cents 829440/823543, 12.3524 cents 41: 1079.8360 .. 1102.4592 cents 84035/82944, 22.6232 cents 829440/823543, 12.3524 cents 42: 1115.1371 .. 1137.7603 cents 84035/82944, 22.6232 cents 7558272/7503125, 12.6778 cents 43: 1128.6064 .. 1151.2296 cents 84035/82944, 22.6232 cents 819200/823543,-9.1539 cents 44: 1164.3032 .. 1186.9264 cents 84035/82944, 22.6232 cents 1728/1715, 13.0736 cents
SHOW DATA
Number of notes : 45 -- Interval properties -- Smallest interval : 1728/1715, 13.0736 cents, class 1 Average step (divided formal octave): 26.6667 cents Largest one step interval : 49/48, 35.6968 cents Average / Smallest step : 2.039739 Largest / Average step : 1.338630 Largest / Smallest step : 2.730456 Median interval of one step : 50/49, 34.9756 cents, amount: 12 Most common interval of one step : 50/49, 34.9756 cents, amount: 12 Least squares average step : 26.94446 cents, oct.: 1212.50082 cents Scale is not proper Step pattern alph. order: ABCBCBADEDBACBCBAFGDBEDAHAAHAFGBDAHABCBDGBDBC Step pattern size order : HFCFCFHDEDFHCFCFHBGDFEDHAHHAHBGFDHAHFCFDGFDFC Scale is a Constant Structure, by a margin of 6.59457 cents Scale diversity : 1.174059 Lumma stability : 0.381038 Lumma impropriety factor : 0.066096 Number of different interval sizes : 294 = 6.68182 / class Number of one step interval sizes : 8 Highest interval variety : 8 Mean interval variety : 6.68182 = 147/22 Median interval variety : 4 Lowest interval variety : 4 Smallest interval difference : 78125000/78121827, 0.0703 cents Most common intervals : 7/6, 266.8709 cents & inv., amount: 31 Most common triad is 0.0 266.871 933.129 cents, amount: 19 Number of recognisable fifths : 63, average 709.7916 cents Number of appreciable fifths : 27, average 701.9162 cents Scale contains a complete diamond : 9 21 49 Length of longest harmonic part : 2 at degree 0 Length of longest subharmonic part : 2 at degree 5 Formal octave complements present : 9 = 20.0000% Limited transpositions with margin 22.6232 cents: 5 10 15 20 25 30 35 40 Limited inverse transpositions with margin 22.6232 cents: 2 7 12 17 22 27 32 37 42 -- Rational properties -- Prime limit : 7 Odd number limit : 84035 (O: 84035 U: 84035) Highest odd numerator or denominator: 343 Scale harmonicity : 0.008868 Average absolute harmonicity : 0.074970 Specific harmonicity : 0.063085 Fundamental : 1/7408800, -22.8208 octaves, 0.0000 Hz. Guide tone : 11907000, 23.5053 octaves, 3115175606.039 Hz. Exponens Consonantiae : 8.821658E+13, 46.32612 octaves Euler's gradus suavitatis : 75 Sum of Mann's harmonic distance : 2627.0, average 58.37778 Mersenne's string divisions : too high to compute Sum of van Prooijen's expressibility: 67.04948, average 1.48999 Sum of Tenney's harmonic distance : 131.26344, average 2.91697 Vogel's harmonic complexity : 47.04444 Wille's k value : 5672362 Wilson's harmonic complexity : 84 Rectangular lattice diameter : 18 Triangular lattice diameter : 8 Lattice compactness : 4539.51620, average 4.38601 Lattice compactness (without 2's) : 3671.34630, average 3.54719 Number of different primes : 4 Prime exponents' range, average, count, tones@limit: 2: -5 .. 3 -1.02222 76 1 3: -3 .. 5 0.55556 83 2 5: -2 .. 3 0.31111 44 9 7: -3 .. 2 -0.02222 45 33 Average exponent except 2's : 38 / 45 = 0.84444 Average absolute exponent except 2's: 172 / 45 = 3.82222 Scale is JI-epimorphic with val: <45 71 104 126| = patent
FIT/MODE
45: 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 1 1 1 1 1 1 1 1 1 1 1 1 1 1 SP B ME I SD: 10.5584 c. M: 17.6518 c. 46: 1 1 1 1 1 1 2 0 1 1 1 2 0 2 0 1 2 0 2 0 2 1 0 2 0 2 1 1 1 0 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 N D3 S SD: 9.7659 c. M: 18.4985 c. 47: 1 2 0 1 1 1 2 0 2 0 2 1 1 1 0 2 1 1 1 1 1 1 1 1 1 1 2 0 2 0 1 2 0 2 0 2 1 1 1 1 1 1 1 1 1 N D3 SD: 9.3197 c. M: 18.1713 c. 48: 1 2 0 2 0 2 1 1 1 1 1 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 1 1 1 1 N B D3 S SD: 7.2375 c. M: 12.6518 c. 49: 1 2 0 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 1 1 1 1 N D3 S SD: 7.0365 c. M:-11.4645 c. 50: 1 2 1 1 1 1 1 1 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 1 1 2 0 2 0 2 1 1 1 1 N D3 SD: 6.9425 c. M: 11.9100 c. 52: 2 1 1 1 1 1 2 0 2 1 1 2 0 2 0 2 1 1 2 0 2 1 1 1 1 1 2 1 1 1 1 2 0 2 0 2 2 0 2 0 2 1 1 1 1 N D3 S SD: 6.6719 c. M:-11.5831 c. 53: 2 1 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 0 2 1 1 2 0 2 0 2 2 0 2 0 2 1 1 2 0 2 1 1 1 1 2 1 1 1 1 N D3 S SD: 6.3641 c. M: 11.0625 c. 54: 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 2 1 1 1 1 P B ME S SD: 6.1881 c. M:-9.5646 c. 57: 2 1 1 2 0 2 2 0 2 1 1 2 1 1 1 2 1 1 2 0 2 2 0 2 1 1 2 1 1 1 2 1 1 2 0 2 2 0 2 1 1 2 1 1 1 N B D3 S SD: 5.7541 c. M: 7.6230 c. 60: 2 2 0 2 1 1 2 1 2 0 2 2 1 1 1 2 2 0 2 1 1 2 1 2 0 2 2 1 1 1 2 2 0 2 1 1 2 1 2 0 2 2 1 1 1 N B D3 SD: 5.7319 c. M:-9.8318 c. 62: 2 2 0 2 1 2 2 0 2 1 2 1 1 2 1 1 2 1 2 1 1 2 1 2 0 2 2 1 2 0 2 2 1 2 0 2 2 1 1 1 2 2 0 2 1 N SD: 5.5524 c. M: 9.2941 c. 63: 2 2 0 2 1 2 2 0 2 1 2 2 0 2 1 2 2 0 2 1 2 2 0 2 1 2 2 0 2 1 2 2 0 2 1 2 2 0 2 1 2 2 0 2 1 N B D3 SD: 5.2096 c. M: 8.5767 c. 66: 2 2 1 2 0 2 2 1 2 1 2 2 0 2 1 2 2 1 2 0 2 2 1 2 1 2 2 0 2 1 2 2 1 2 0 2 2 1 2 1 2 2 0 2 1 N B D3 S SD: 5.1014 c. M:-8.4154 c. 68: 2 2 1 2 1 2 2 0 2 1 2 2 1 2 1 2 2 0 2 1 2 2 1 2 1 2 2 1 2 0 2 2 1 2 1 2 2 1 2 0 2 2 1 2 1 N S SD: 5.0897 c. M:-8.2574 c. 69: 2 2 1 2 1 2 2 1 2 0 2 2 1 2 1 2 2 1 2 1 2 2 1 2 0 2 2 1 2 1 2 2 1 2 1 2 2 1 2 0 2 2 1 2 1 N B D3 SD: 5.0377 c. M:-8.5991 c. 71: 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 0 3 2 0 3 0 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 N SD: 4.8182 c. M: 8.1964 c. 72: 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 2 2 1 2 1 P B ME S SD: 2.4037 c. M: 4.3185 c. 99: 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 3 3 1 3 1 N B DE S SD: 1.3449 c. M:-2.7633 c. 171: 5 5 2 5 2 5 5 2 5 2 5 5 2 5 2 5 5 2 5 2 5 5 2 5 2 5 5 2 5 2 5 5 2 5 2 5 5 2 5 2 5 5 2 5 2 N B DE S SD: 0.3494 c. M: 0.8097 c. 441: 13 13 5 13 5 13 13 5 13 5 13 13 5 13 5 13 13 5 13 5 13 13 5 13 5 13 13 5 13 5 13 13 5 13 5 13 13 5 13 5 13 13 5 13 5 N B DE S SD: 0.2749 c. M:-0.7843 c. 612: 18 18 7 18 7 18 18 7 18 7 18 18 7 18 7 18 18 7 18 7 18 18 7 18 7 18 18 7 18 7 18 18 7 18 7 18 18 7 18 7 18 18 7 18 7 N B DE S SD: 0.2526 c. M:-0.6243 c. 764: 23 22 9 22 9 22 23 9 22 9 22 23 9 22 9 22 23 8 23 9 22 22 9 23 8 23 23 8 23 8 23 22 9 23 8 23 22 9 22 9 23 22 9 22 9 N SD: 0.2882 c. M:-0.5681 c. 783: 23 23 9 23 9 23 23 9 23 9 23 23 9 23 9 23 23 9 23 9 23 23 9 23 9 23 23 9 23 9 23 23 9 23 9 23 23 9 23 9 23 23 9 23 9 N B DE S SD: 0.2562 c. M:-0.5341 c. 836: 25 24 10 24 10 24 25 10 24 10 24 25 10 24 10 24 25 9 25 10 24 24 10 25 9 25 25 9 25 9 25 24 10 25 9 25 24 10 24 10 25 24 10 24 10 N SD: 0.2585 c. M: 0.5593 c. 935: 28 27 11 27 11 27 28 11 27 11 27 28 11 27 11 27 28 10 28 11 27 27 11 28 10 28 28 10 28 10 28 27 11 28 10 28 27 11 27 11 28 27 11 27 11 N SD: 0.1991 c. M: 0.4000 c. 1007: 30 29 12 29 12 29 30 12 29 12 29 30 12 29 12 29 30 11 30 12 29 29 12 30 11 30 30 11 30 11 30 29 12 30 11 30 29 12 29 12 30 29 12 29 12 N SD: 0.2191 c. M: 0.5051 c. 1034: 31 30 12 30 12 30 31 12 30 12 30 31 12 30 12 30 31 11 31 12 30 30 12 31 11 31 31 11 31 11 31 30 12 31 11 31 30 12 30 12 31 30 12 30 12 N SD: 0.2331 c. M:-0.4526 c. 1106: 33 32 13 32 13 32 33 13 32 13 32 33 13 32 13 32 33 12 33 13 32 32 13 33 12 33 33 12 33 12 33 32 13 33 12 33 32 13 32 13 33 32 13 32 13 N SD: 0.1512 c. M: 0.3443 c. 1205: 36 35 14 35 14 35 36 14 35 14 35 36 14 35 14 35 36 13 36 14 35 35 14 36 13 36 36 13 36 13 36 35 14 36 13 36 35 14 35 14 36 35 14 35 14 N SD: 0.1716 c. M:-0.3432 c. 1277: 38 37 15 37 15 37 38 15 37 15 37 38 15 37 15 37 38 14 38 15 37 37 15 38 14 38 38 14 38 14 38 37 15 38 14 38 37 15 37 15 38 37 15 37 15 N SD: 0.1320 c. M: 0.3035 c. 1376: 41 40 16 40 16 40 41 16 40 16 40 41 16 40 16 40 41 15 41 16 40 40 16 41 15 41 41 15 41 15 41 40 16 41 15 41 40 16 40 16 41 40 16 40 16 N SD: 0.1351 c. M:-0.2725 c. 1448: 43 42 17 42 17 42 43 17 42 17 42 43 17 42 17 42 43 16 43 17 42 42 17 43 16 43 43 16 43 16 43 42 17 43 16 43 42 17 42 17 43 42 17 42 17 N SD: 0.1311 c. M: 0.2936 c. 1547: 46 45 18 45 18 45 46 18 45 18 45 46 18 45 18 45 46 17 46 18 45 45 18 46 17 46 46 17 46 17 46 45 18 46 17 46 45 18 45 18 46 45 18 45 18 N SD: 0.1183 c. M:-0.2308 c. 1578: 47 46 18 46 18 46 47 19 45 19 46 47 18 46 18 46 47 18 46 19 46 45 19 47 17 47 47 17 47 18 46 46 19 47 17 47 46 18 46 19 46 46 19 46 18 N SD: 0.1153 c. M: 0.2555 c. 1677: 50 49 19 49 19 49 50 20 48 20 49 50 19 49 19 49 50 19 49 20 49 48 20 50 18 50 50 18 50 19 49 49 20 50 18 50 49 19 49 20 49 49 20 49 19 N SD: 0.1007 c. M:-0.2026 c. 1718: 51 50 20 50 20 50 51 20 50 20 50 51 20 50 20 50 51 19 51 20 50 50 20 51 19 51 51 19 51 19 51 50 20 51 19 51 50 20 50 20 51 50 20 50 20 N SD: 0.1158 c. M: 0.1990 c. 1749: 52 51 20 51 20 51 52 21 50 21 51 52 20 51 20 51 52 20 51 21 51 50 21 52 19 52 52 19 52 20 51 51 21 52 19 52 51 20 51 21 51 51 21 51 20 N SD: 0.1038 c. M: 0.2098 c. 1848: 55 54 21 54 21 54 55 22 53 22 54 55 21 54 21 54 55 21 54 22 54 53 22 55 20 55 55 20 55 21 54 54 22 55 20 55 54 21 54 22 54 54 22 54 21 N SD: 0.0761 c. M:-0.1654 c. 2019: 60 59 23 59 23 59 60 24 58 24 59 60 23 59 23 59 60 23 59 24 59 58 24 60 22 60 60 22 60 23 59 59 24 60 22 60 59 23 59 24 59 59 24 59 23 N SD: 0.0668 c. M:-0.1480 c. 2190: 65 64 25 64 25 64 65 26 63 26 64 65 25 64 25 64 65 25 64 26 64 63 26 65 24 65 65 24 65 25 64 64 26 65 24 65 64 25 64 26 64 64 26 64 25 N SD: 0.0703 c. M: 0.1457 c. 2460: 73 72 28 72 28 72 73 29 71 29 72 73 28 72 28 72 73 28 72 29 72 71 29 73 27 73 73 27 73 28 72 72 29 73 27 73 72 28 72 29 72 72 29 72 28 N SD: 0.0735 c. M:-0.1400 c. 2612: 78 76 30 76 30 76 78 31 75 31 76 78 30 76 30 76 78 29 77 31 76 75 31 78 28 78 78 28 78 29 77 76 31 78 28 78 76 30 76 31 77 76 31 76 30 N SD: 0.0746 c. M:-0.1736 c. 2684: 80 78 31 78 31 78 80 32 77 32 78 80 31 78 31 78 80 30 79 32 78 77 32 80 29 80 80 29 80 30 79 78 32 80 29 80 78 31 78 32 79 78 32 78 31 N SD: 0.0606 c. M: 0.1676 c. 2783: 83 81 32 81 32 81 83 33 80 33 81 83 32 81 32 81 83 31 82 33 81 80 33 83 30 83 83 30 83 31 82 81 33 83 30 83 81 32 81 33 82 81 33 81 32 N SD: 0.0495 c. M:-0.1132 c. 2855: 85 83 33 83 33 83 85 34 82 34 83 85 33 83 33 83 85 32 84 34 83 82 34 85 31 85 85 31 85 32 84 83 34 85 31 85 83 33 83 34 84 83 34 83 33 N SD: 0.0534 c. M: 0.1449 c. 2954: 88 86 34 86 34 86 88 35 85 35 86 88 34 86 34 86 88 33 87 35 86 85 35 88 32 88 88 32 88 33 87 86 35 88 32 88 86 34 86 35 87 86 35 86 34 N SD: 0.0285 c. M:-0.0598 c. 3125: 93 91 36 91 36 91 93 37 90 37 91 93 36 91 36 91 93 35 92 37 91 90 37 93 34 93 93 34 93 35 92 91 37 93 34 93 91 36 91 37 92 91 37 91 36 N SD: 0.0156 c. M: 0.0333 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: 4.5983 cents 4 .. 8 match: 4 H SD: 0.0000 cents 5 .. 10 match: 5 H SD: 4.7786 cents 6 .. 12 match: 6 H SD: 2.3605 cents 7 .. 14 match: 7 H SD: 2.0739 cents 8 .. 16 match: 8 H SD: 2.8545 cents 9 .. 18 match: 9 H SD: 3.4129 cents 10 .. 20 match: 10 H SD: 3.0678 cents 11 .. 22 match: 11 H SD: 3.9450 cents 12 .. 24 match: 12 H SD: 1.5874 cents 13 .. 26 match: 13 H SD: 1.9513 cents 14 .. 28 match: 14 H SD: 1.3424 cents 15 .. 30 match: 15 H SD: 2.4988 cents 16 .. 32 match: 16 H SD: 2.3718 cents 17 .. 34 match: 17 H SD: 2.2253 cents 18 .. 36 match: 18 H SD: 2.0083 cents 19 .. 38 match: 19 H SD: 1.6743 cents 20 .. 40 match: 20 H SD: 1.7721 cents 21 .. 42 match: 21 H SD: 1.8398 cents 22 .. 44 match: 22 H SD: 2.3586 cents 23 .. 46 match: 23 H SD: 1.8519 cents 24 .. 48 match: 24 H SD: 1.4847 cents 25 .. 50 match: 25 H SD: 2.0239 cents 26 .. 52 match: 26 H SD: 1.5935 cents 27 .. 54 match: 27 H SD: 1.9786 cents 28 .. 56 match: 27 S SD: 1.4182 cents 29 .. 58 match: 28 S SD: 1.6961 cents 30 .. 60 match: 28 SD: 1.7786 cents 31 .. 62 match: 29 SD: 1.5608 cents 32 .. 64 match: 31 S SD: 1.6247 cents 33 .. 66 match: 29 SD: 1.9162 cents 34 .. 68 match: 31 S SD: 1.7215 cents 35 .. 70 match: 31 SD: 1.5879 cents 36 .. 72 match: 34 SD: 1.2436 cents 37 .. 74 match: 35 SD: 1.3399 cents 38 .. 76 match: 33 SD: 1.2886 cents 39 .. 78 match: 35 SD: 1.3037 cents 40 .. 80 match: 36 SD: 1.2051 cents 41 .. 82 match: 35 SD: 1.2673 cents 42 .. 84 match: 38 SD: 1.0902 cents 43 .. 86 match: 36 SD: 1.2621 cents 44 .. 88 match: 35 SD: 1.2197 cents 45 .. 90 match: 35 SD: 1.3341 cents 46 .. 92 match: 40 SD: 1.0802 cents 47 .. 94 match: 37 SD: 1.1496 cents 48 .. 96 match: 34 SD: 0.9724 cents 49 .. 98 match: 39 SD: 0.9718 cents 50 .. 100 match: 34 SD: 1.0948 cents 51 .. 102 match: 38 SD: 1.0448 cents 52 .. 104 match: 39 SD: 0.9395 cents 53 .. 106 match: 39 SD: 0.9477 cents 54 .. 108 match: 37 SD: 1.0243 cents 55 .. 110 match: 38 SD: 0.9031 cents 56 .. 112 match: 38 SD: 0.8548 cents 57 .. 114 match: 42 SD: 0.8900 cents 58 .. 116 match: 39 SD: 0.9197 cents 59 .. 118 match: 40 SD: 0.9131 cents 60 .. 120 match: 40 SD: 0.7902 cents 61 .. 122 match: 42 SD: 0.8056 cents 62 .. 124 match: 39 SD: 0.9131 cents 63 .. 126 match: 37 SD: 0.8581 cents 64 .. 128 match: 41 SD: 0.8119 cents 65 .. 130 match: 40 SD: 0.8647 cents 66 .. 132 match: 40 SD: 0.7088 cents 67 .. 134 match: 38 SD: 0.8194 cents 68 .. 136 match: 40 SD: 0.7290 cents 69 .. 138 match: 40 SD: 0.8218 cents 70 .. 140 match: 42 SD: 0.7100 cents 71 .. 142 match: 42 SD: 0.8165 cents 72 .. 144 match: 42 SD: 0.6883 cents 73 .. 146 match: 43 SD: 0.7628 cents 74 .. 148 match: 42 SD: 0.6476 cents 76 .. 152 match: 43 SD: 0.7494 cents 77 .. 154 match: 42 SD: 0.6190 cents 78 .. 156 match: 41 SD: 0.7015 cents 79 .. 158 match: 43 SD: 0.6961 cents 80 .. 160 match: 42 SD: 0.5538 cents 81 .. 162 match: 44 SD: 0.6507 cents 82 .. 164 match: 41 SD: 0.7567 cents 83 .. 166 match: 45 SD: 0.6342 cents 84 .. 168 match: 42 SD: 0.5270 cents 85 .. 170 match: 42 SD: 0.6117 cents 86 .. 172 match: 41 SD: 0.6787 cents 87 .. 174 match: 44 SD: 0.5978 cents 88 .. 176 match: 43 SD: 0.5303 cents 89 .. 178 match: 44 SD: 0.5002 cents 90 .. 180 match: 43 SD: 0.5812 cents 91 .. 182 match: 43 SD: 0.6437 cents 92 .. 184 match: 43 SD: 0.5835 cents 93 .. 186 match: 43 SD: 0.6484 cents 94 .. 188 match: 44 SD: 0.5479 cents 96 .. 192 match: 45 SD: 0.4612 cents 98 .. 196 match: 44 SD: 0.4749 cents 100 .. 200 match: 44 SD: 0.4780 cents 105 .. 210 match: 43 SD: 0.5061 cents 106 .. 212 match: 44 SD: 0.5311 cents 108 .. 216 match: 43 SD: 0.4638 cents 109 .. 218 match: 44 SD: 0.4985 cents 111 .. 222 match: 45 SD: 0.4485 cents 115 .. 230 match: 45 SD: 0.4290 cents 120 .. 240 match: 45 SD: 0.4076 cents 126 .. 252 match: 45 SD: 0.3769 cents 136 .. 272 match: 45 SD: 0.3452 cents 157 .. 314 match: 45 SD: 0.3377 cents 158 .. 316 match: 45 SD: 0.3252 cents 164 .. 328 match: 45 SD: 0.2866 cents 177 .. 354 match: 45 SD: 0.2664 cents 185 .. 370 match: 45 SD: 0.2414 cents 192 .. 384 match: 45 SD: 0.2350 cents 196 .. 392 match: 45 SD: 0.2251 cents 223 .. 446 match: 45 SD: 0.2249 cents 224 .. 448 match: 45 SD: 0.2020 cents 240 .. 480 match: 45 SD: 0.1962 cents 247 .. 494 match: 45 SD: 0.1942 cents 262 .. 524 match: 45 SD: 0.1880 cents 266 .. 532 match: 45 SD: 0.1813 cents 280 .. 560 match: 45 SD: 0.1772 cents 284 .. 568 match: 45 SD: 0.1725 cents 288 .. 576 match: 45 SD: 0.1497 cents 335 .. 670 match: 45 SD: 0.1354 cents 336 .. 672 match: 45 SD: 0.1279 cents 378 .. 756 match: 45 SD: 0.1265 cents 384 .. 768 match: 45 SD: 0.1256 cents 400 .. 800 match: 45 SD: 0.1176 cents 424 .. 848 match: 45 SD: 0.1093 cents 432 .. 864 match: 45 SD: 0.1053 cents 463 .. 926 match: 45 SD: 0.1044 cents 473 .. 946 match: 45 SD: 0.1040 cents 479 .. 958 match: 45 SD: 0.1019 cents 480 .. 960 match: 45 SD: 0.0938 cents 520 .. 1040 match: 45 SD: 0.0865 cents 528 .. 1056 match: 45 SD: 0.0859 cents 560 .. 1120 match: 45 SD: 0.0772 cents 576 .. 1152 match: 45 SD: 0.0722 cents