| Rational version of 17wt-archagall_spinoff-8_9.scl, 1/1 at 1024 Interval class, Number of incidences, Size: 1: 1 400/387 57.200 cents 1: 1 797/771 57.419 cents 1: 1 272/263 58.253 cents 1: 1 1807/1747 58.460 cents 1: 1 2048/1975 62.836 cents 1: 1 531/512 63.082 cents 1: 1 707/680 67.411 cents 1: 1 1542/1483 67.541 cents 1: 1 1884/1807 72.243 cents 1: 1 387/371 73.097 cents 1: 1 1747/1671 77.001 cents 1: 1 251/240 77.584 cents 1: 1 263/251 80.851 cents 1: 1 371/354 81.204 cents 1: 1 1975/1884 81.664 cents 1: 1 1671/1594 81.672 cents 1: 1 1483/1414 82.484 cents 2: 1 1594/1483 124.960 cents 2: 1 1414/1315 125.663 cents 2: 1 2124/1975 125.917 cents 2: 1 400/371 130.297 cents 2: 1 1884/1747 130.703 cents 2: 1 1255/1161 134.783 cents 2: 1 1807/1671 135.462 cents 2: 1 557/514 139.091 cents 2: 1 272/251 139.103 cents 2: 1 1113/1024 144.285 cents 2: 1 512/471 144.500 cents 2: 1 1483/1360 149.894 cents 2: 1 771/707 150.025 cents 2: 1 1975/1807 153.907 cents 2: 1 129/118 154.301 cents 2: 1 263/240 158.434 cents 2: 1 1747/1594 158.674 cents 3: 1 1414/1255 206.514 cents 3: 1 1671/1483 206.632 cents 3: 1 2226/1975 207.121 cents 3: 1 797/707 207.443 cents 3: 1 177/157 207.582 cents 3: 1 628/557 207.705 cents 3: 1 1255/1113 207.881 cents 3: 1 1483/1315 208.147 cents 3: 1 200/177 211.501 cents 3: 1 1975/1747 212.368 cents 3: 1 1315/1161 215.634 cents 3: 1 1747/1542 216.092 cents 3: 1 17/15 216.687 cents 3: 1 2048/1807 216.743 cents 3: 1 1807/1594 217.134 cents 3: 1 1161/1024 217.383 cents 3: 1 771/680 217.435 cents 4: 1 1360/1161 273.886 cents 4: 1 1807/1542 274.552 cents 4: 1 75/64 274.582 cents classic augmented second 4: 1 797/680 274.854 cents 4: 1 2048/1747 275.203 cents 4: 1 1542/1315 275.688 cents 4: 1 2124/1807 279.825 cents 4: 1 2322/1975 280.218 cents 4: 1 1747/1483 283.633 cents 4: 1 707/600 284.097 cents 4: 1 1315/1113 288.731 cents 4: 1 371/314 288.786 cents 4: 1 1483/1255 288.997 cents 4: 1 1255/1062 289.084 cents 4: 1 1671/1414 289.116 cents 4: 1 1975/1671 289.369 cents 4: 1 942/797 289.377 cents 5: 1 1594/1315 333.107 cents 5: 1 96/79 337.418 cents 5: 1 2124/1747 338.285 cents 5: 1 1414/1161 341.297 cents 5: 1 1807/1483 342.093 cents 5: 1 314/257 346.795 cents 5: 1 1360/1113 346.984 cents 5: 1 1255/1024 352.166 cents 5: 1 2048/1671 352.205 cents 5: 1 1671/1360 356.526 cents 5: 1 1542/1255 356.538 cents 5: 1 2226/1807 361.029 cents 5: 1 387/314 361.883 cents 5: 1 1747/1414 366.117 cents 5: 1 1483/1200 366.581 cents 5: 1 1315/1062 369.935 cents 5: 1 1975/1594 371.041 cents 6: 1 1594/1255 413.957 cents 6: 1 1884/1483 414.336 cents 6: 1 202/159 414.394 cents 6: 1 1671/1315 414.779 cents 6: 1 502/395 415.002 cents 6: 1 708/557 415.286 cents 6: 1 200/157 419.083 cents 6: 1 2226/1747 419.489 cents 6: 1 1483/1161 423.781 cents 6: 1 1807/1414 424.577 cents 6: 1 680/531 428.187 cents 6: 1 1975/1542 428.460 cents 6: 1 1315/1024 433.017 cents 6: 1 1747/1360 433.528 cents 6: 1 1024/797 433.877 cents 6: 1 257/200 434.122 cents 6: 1 2322/1807 434.126 cents 7: 1 85/64 491.269 cents 7: 1 1024/771 491.296 cents 7: 1 514/387 491.322 cents 7: 1 2400/1807 491.325 cents 7: 1 797/600 491.541 cents 7: 1 1747/1315 491.780 cents 7: 1 1807/1360 491.988 cents 7: 1 2322/1747 492.586 cents 7: 1 707/531 495.598 cents 7: 1 1671/1255 495.629 cents 7: 1 526/395 495.852 cents 7: 1 1975/1483 496.001 cents 7: 1 742/557 496.490 cents 7: 1 1255/942 496.666 cents 7: 1 942/707 496.820 cents 7: 1 1483/1113 496.878 cents 7: 1 1062/797 496.959 cents 8: 1 1594/1161 548.740 cents 8: 1 2400/1747 549.786 cents 8: 1 1807/1315 550.240 cents 8: 1 544/395 554.105 cents 8: 1 354/257 554.377 cents 8: 1 707/512 558.680 cents 8: 1 2048/1483 558.837 cents 8: 1 471/340 564.231 cents 8: 1 514/371 564.419 cents 8: 1 2510/1807 568.909 cents 8: 1 774/557 569.587 cents 8: 1 1747/1255 572.631 cents 8: 1 557/400 573.213 cents 8: 1 1315/942 577.517 cents 8: 1 1483/1062 578.082 cents 8: 1 1113/797 578.162 cents 8: 1 1975/1414 578.485 cents 9: 1 2828/1975 621.515 cents 9: 1 1594/1113 621.838 cents 9: 1 2124/1483 621.918 cents 9: 1 1884/1315 622.483 cents 9: 1 800/557 626.787 cents 9: 1 2510/1747 627.369 cents 9: 1 557/387 630.413 cents 9: 1 1807/1255 631.091 cents 9: 1 371/257 635.581 cents 9: 1 680/471 635.769 cents 9: 1 1483/1024 641.163 cents 9: 1 1024/707 641.320 cents 9: 1 257/177 645.623 cents 9: 1 395/272 645.895 cents 9: 1 2630/1807 649.760 cents 9: 1 1747/1200 650.214 cents 9: 1 1161/797 651.260 cents 10: 1 797/531 703.041 cents 10: 1 2226/1483 703.122 cents 10: 1 707/471 703.180 cents 10: 1 1884/1255 703.334 cents 10: 1 557/371 703.510 cents 10: 1 2966/1975 703.999 cents 10: 1 395/263 704.148 cents 10: 1 2510/1671 704.371 cents 10: 1 1062/707 704.402 cents 10: 1 1747/1161 707.414 cents 10: 1 2720/1807 708.012 cents 10: 1 2630/1747 708.220 cents 10: 1 1200/797 708.459 cents 10: 1 1807/1200 708.675 cents 10: 1 387/257 708.678 cents 10: 1 771/512 708.704 cents 10: 1 128/85 708.731 cents 11: 1 1807/1161 765.874 cents 11: 1 400/257 765.878 cents 11: 1 797/512 766.123 cents 11: 1 2720/1747 766.472 cents 11: 1 2048/1315 766.983 cents 11: 1 3084/1975 771.540 cents 11: 1 531/340 771.813 cents 11: 1 2828/1807 775.423 cents 11: 1 2322/1483 776.219 cents 11: 1 1747/1113 780.511 cents 11: 1 157/100 780.917 cents 11: 1 557/354 784.714 cents 11: 1 395/251 784.998 cents 11: 1 2630/1671 785.221 cents 11: 1 159/101 785.606 cents 11: 1 1483/942 785.664 cents 11: 1 1255/797 786.043 cents 12: 1 3188/1975 828.959 cents 12: 1 2124/1315 830.065 cents 12: 1 2400/1483 833.419 cents 12: 1 2828/1747 833.883 cents 12: 1 628/387 838.117 cents 12: 1 1807/1113 838.971 cents 12: 1 1255/771 843.462 cents 12: 1 2720/1671 843.474 cents 12: 1 1671/1024 847.795 cents 12: 1 2048/1255 847.834 cents 12: 1 1113/680 853.016 cents 12: 1 257/157 853.205 cents 12: 1 2966/1807 857.907 cents 12: 1 1161/707 858.703 cents 12: 1 1747/1062 861.715 cents 12: 1 79/48 862.582 cents 12: 1 1315/797 866.893 cents 13: 1 797/471 910.623 cents 13: 1 3342/1975 910.631 cents 13: 1 2828/1671 910.884 cents 13: 1 2124/1255 910.916 cents 13: 1 2510/1483 911.003 cents 13: 1 628/371 911.214 cents 13: 1 2226/1315 911.269 cents 13: 1 1200/707 915.903 cents 13: 1 2966/1747 916.367 cents 13: 1 1975/1161 919.782 cents 13: 1 1807/1062 920.175 cents 13: 1 1315/771 924.312 cents 13: 1 1747/1024 924.797 cents 13: 1 1360/797 925.146 cents 13: 1 128/75 925.418 cents diminished seventh 13: 1 3084/1807 925.448 cents 13: 1 1161/680 926.114 cents 14: 1 1360/771 982.565 cents 14: 1 2048/1161 982.617 cents 14: 1 3188/1807 982.866 cents 14: 1 1807/1024 983.257 cents 14: 1 30/17 983.313 cents 14: 1 3084/1747 983.908 cents 14: 1 2322/1315 984.366 cents 14: 1 3494/1975 987.632 cents 14: 1 177/100 988.499 cents 14: 1 2630/1483 991.853 cents 14: 1 2226/1255 992.119 cents 14: 1 557/314 992.295 cents 14: 1 314/177 992.418 cents 14: 1 1414/797 992.557 cents 14: 1 1975/1113 992.879 cents 14: 1 2966/1671 993.368 cents 14: 1 1255/707 993.486 cents 15: 1 3188/1747 1041.326 cents 15: 1 480/263 1041.566 cents 15: 1 236/129 1045.699 cents 15: 1 3614/1975 1046.093 cents 15: 1 1414/771 1049.975 cents 15: 1 2720/1483 1050.106 cents 15: 1 471/256 1055.500 cents 15: 1 2048/1113 1055.715 cents 15: 1 251/136 1060.897 cents 15: 1 1028/557 1060.909 cents 15: 1 3342/1807 1064.538 cents 15: 1 2322/1255 1065.217 cents 15: 1 1747/942 1069.297 cents 15: 1 371/200 1069.703 cents 15: 1 1975/1062 1074.083 cents 15: 1 1315/707 1074.337 cents 15: 1 1483/797 1075.040 cents 16: 1 2828/1483 1117.516 cents 16: 1 3188/1671 1118.328 cents 16: 1 3768/1975 1118.336 cents 16: 1 708/371 1118.796 cents 16: 1 502/263 1119.149 cents 16: 1 480/251 1122.416 cents 16: 1 3342/1747 1122.999 cents 16: 1 742/387 1126.903 cents 16: 1 1807/942 1127.757 cents 16: 1 1483/771 1132.459 cents 16: 1 1360/707 1132.589 cents 16: 1 1024/531 1136.918 cents 16: 1 1975/1024 1137.164 cents 16: 1 3494/1807 1141.540 cents 16: 1 263/136 1141.747 cents 16: 1 1542/797 1142.581 cents 16: 1 387/200 1142.800 cents Highest number of different intervals for one interval class: 17 Average number of different intervals per interval class: 17.00000 = 17 | 139808/139807 = 2^5.17.251^-1.257.557^-1 = 1.00000715272 size is 0.012383 cents, 0.003106 savarts/eptamerides, or 0.006338 schismas 0.000576 syntonic commas ( 0 ) 0.000528 Pythagorean commas ( 0 ) 2.028828 MIDI tuning units 0.507207 MIDI pitch bend units 0.380040 Temperament units 0.310637 jots 0.017543 iotas 0.109383 Türk senti 0.008464 hekt 0.007533 Woolhouse units 0.006334 grads 0.006315 612-tone schismas 0.000743 moria 0.000633 diaschismas 0.000568 Sauveur commas 0.000547 53-tone commas 0.000454 septimal commas 0.000444 43-tone merides 0.000423 41-tone supracommas 0.000320 31-tone normal dieses 0.000302 minor dieses 0.000198 major dieses 0.000137 Pythagorean limmas 0.000106 secors 0.000065 1/3-comma mean whole tones 0.000064 1/4-comma mean whole tones 0.000063 1/5-comma mean whole tones 0.000063 1/6-comma mean whole tones 0.000010 octaves, 96907.174446 / octave | Interval class, Number of incidences, Size: 1: 1 400/387 57.200 cents 1: 1 797/771 57.419 cents 1: 1 272/263 58.253 cents 1: 1 1807/1747 58.460 cents 1: 1 2048/1975 62.836 cents 1: 1 531/512 63.082 cents 1: 1 707/680 67.411 cents 1: 1 1542/1483 67.541 cents 1: 1 1884/1807 72.243 cents 1: 1 387/371 73.097 cents 1: 1 1747/1671 77.001 cents 1: 1 251/240 77.584 cents 1: 1 263/251 80.851 cents 1: 1 371/354 81.204 cents 1: 1 1975/1884 81.664 cents 1: 1 1671/1594 81.672 cents 1: 1 1483/1414 82.484 cents 2: 1 1594/1483 124.960 cents 2: 1 1414/1315 125.663 cents 2: 1 2124/1975 125.917 cents 2: 1 400/371 130.297 cents 2: 1 1884/1747 130.703 cents 2: 1 1255/1161 134.783 cents 2: 1 1807/1671 135.462 cents 2: 1 557/514 139.091 cents 2: 1 272/251 139.103 cents 2: 1 1113/1024 144.285 cents 2: 1 512/471 144.500 cents 2: 1 1483/1360 149.894 cents 2: 1 771/707 150.025 cents 2: 1 1975/1807 153.907 cents 2: 1 129/118 154.301 cents 2: 1 263/240 158.434 cents 2: 1 1747/1594 158.674 cents 3: 1 1414/1255 206.514 cents 3: 1 1671/1483 206.632 cents 3: 1 2226/1975 207.121 cents 3: 1 797/707 207.443 cents 3: 1 177/157 207.582 cents 3: 1 628/557 207.705 cents 3: 1 1255/1113 207.881 cents 3: 1 1483/1315 208.147 cents 3: 1 200/177 211.501 cents 3: 1 1975/1747 212.368 cents | 1440179/1440000 = 2^-8.3^-2.5^-4.13.139.797 = 1.00012430556 size is 0.215189 cents, 0.053976 savarts/eptamerides, or 0.110143 schismas ( 1/9 ) 0.010006 syntonic commas 0.009173 Pythagorean commas 35.256506 MIDI tuning units 8.814127 MIDI pitch bend units 6.604252 Temperament units 5.398186 jots 0.304851 iotas 1.900833 Türk senti 0.147083 hekt 0.130906 Woolhouse units 0.110071 grads 0.109746 612-tone schismas 0.012911 moria 0.011006 diaschismas 0.009863 Sauveur commas 0.009504 53-tone commas 0.007893 septimal commas 0.007711 43-tone merides 0.007352 41-tone supracommas 0.005559 31-tone normal dieses 0.005241 minor dieses 0.003439 major dieses 0.002385 Pythagorean limmas 0.001844 secors 0.001135 1/3-comma mean whole tones 0.001114 1/4-comma mean whole tones 0.001102 1/5-comma mean whole tones 0.001094 1/6-comma mean whole tones 0.000179 octaves, 5576.502656 / octave | 464400/464399 = 2^4.3^3.5^2.13^-1.43.139^-1.257^-1 = 1.00000215332 size is 0.003728 cents, 0.000935 savarts/eptamerides, or 0.001908 schismas 0.000173 syntonic commas ( 0 ) 0.000159 Pythagorean commas ( 0 ) 0.610779 MIDI tuning units 0.152695 MIDI pitch bend units 0.114411 Temperament units 0.093517 jots 0.005281 iotas 0.032930 Türk senti 0.002548 hekt 0.002268 Woolhouse units 0.001907 grads 0.001901 612-tone schismas 0.000224 moria 0.000191 diaschismas 0.000171 Sauveur commas 0.000165 53-tone commas 0.000137 septimal commas 0.000134 43-tone merides 0.000127 41-tone supracommas 0.000096 31-tone normal dieses 0.000091 minor dieses 0.000060 major dieses 0.000041 Pythagorean limmas 0.000032 secors 0.000020 1/3-comma mean whole tones 0.000019 1/4-comma mean whole tones 0.000019 1/5-comma mean whole tones 0.000019 1/6-comma mean whole tones 0.000003 octaves, 321897.204092 / octave | 66049/66048 = 2^-9.3^-1.43^-1.257^2 = 1.00001514050 size is 0.026212 cents, 0.006575 savarts/eptamerides, or 0.013416 schismas 0.001219 syntonic commas ( 0 ) 0.001117 Pythagorean commas ( 0 ) 4.294502 MIDI tuning units 1.073625 MIDI pitch bend units 0.804446 Temperament units 0.657539 jots 0.037133 iotas 0.231535 Türk senti 0.017916 hekt 0.015945 Woolhouse units 0.013407 grads 0.013368 612-tone schismas 0.001573 moria 0.001341 diaschismas 0.001201 Sauveur commas 0.001158 53-tone commas 0.000961 septimal commas 0.000939 43-tone merides 0.000896 41-tone supracommas 0.000677 31-tone normal dieses 0.000638 minor dieses 0.000419 major dieses 0.000291 Pythagorean limmas 0.000225 secors 0.000138 1/3-comma mean whole tones 0.000136 1/4-comma mean whole tones 0.000134 1/5-comma mean whole tones 0.000133 1/6-comma mean whole tones 0.000022 octaves, 45781.331554 / octave | 65536/65535 = 2^16.3^-1.5^-1.17^-1.257^-1 = 1.00001525902 size is 0.026417 cents, 0.006626 savarts/eptamerides, or 0.013521 schismas 0.001228 syntonic commas ( 0 ) 0.001126 Pythagorean commas ( 0 ) 4.328118 MIDI tuning units 1.082030 MIDI pitch bend units 0.810743 Temperament units 0.662686 jots 0.037424 iotas 0.233348 Türk senti 0.018056 hekt 0.016070 Woolhouse units 0.013512 grads 0.013473 612-tone schismas 0.001585 moria 0.001351 diaschismas 0.001211 Sauveur commas 0.001167 53-tone commas 0.000969 septimal commas 0.000947 43-tone merides 0.000903 41-tone supracommas 0.000682 31-tone normal dieses 0.000643 minor dieses 0.000422 major dieses 0.000293 Pythagorean limmas 0.000226 secors 0.000139 1/3-comma mean whole tones 0.000137 1/4-comma mean whole tones 0.000135 1/5-comma mean whole tones 0.000134 1/6-comma mean whole tones 0.000022 octaves, 45425.747051 / octave | 1442840576/1442840405 = 2^25.5^-1.17^-1.43.257^-3 = 1.00000011852 size is 0.000205 cents, 0.000051 savarts/eptamerides, or 0.000105 schismas ( 0 ) 0.000010 syntonic commas ( 0 ) 0.000009 Pythagorean commas ( 0 ) 0.033617 MIDI tuning units 0.008404 MIDI pitch bend units 0.006297 Temperament units 0.005147 jots 0.000291 iotas 0.001812 Türk senti 0.000140 hekt 0.000125 Woolhouse units 0.000105 grads 0.000105 612-tone schismas 0.000012 moria 0.000010 diaschismas 0.000009 Sauveur commas 0.000009 53-tone commas 0.000008 septimal commas 0.000007 43-tone merides 0.000007 41-tone supracommas 0.000005 31-tone normal dieses 0.000005 minor dieses 0.000003 major dieses 0.000002 Pythagorean limmas 0.000002 secors 0.000001 1/3-comma mean whole tones 0.000001 1/4-comma mean whole tones 0.000001 1/5-comma mean whole tones 0.000001 1/6-comma mean whole tones 0.000000 octaves, 5848542.792471 / octave | 32896/32895 = 2^7.3^-2.5^-1.17^-1.43^-1.257 = 1.00003039976 size is 0.052628 cents, 0.013201 savarts/eptamerides, or 0.026937 schismas 0.002447 syntonic commas 0.002243 Pythagorean commas 8.622620 MIDI tuning units 2.155655 MIDI pitch bend units 1.615190 Temperament units 1.320225 jots 0.074557 iotas 0.464883 Türk senti 0.035972 hekt 0.032016 Woolhouse units 0.026920 grads 0.026840 612-tone schismas 0.003158 moria 0.002692 diaschismas 0.002412 Sauveur commas 0.002324 53-tone commas 0.001930 septimal commas 0.001886 43-tone merides 0.001798 41-tone supracommas 0.001360 31-tone normal dieses 0.001282 minor dieses 0.000841 major dieses 0.000583 Pythagorean limmas 0.000451 secors 0.000278 1/3-comma mean whole tones 0.000272 1/4-comma mean whole tones 0.000269 1/5-comma mean whole tones 0.000268 1/6-comma mean whole tones 0.000044 octaves, 22801.423076 / octave | 57825/57824 = 2^-5.3^2.5^2.13^-1.139^-1.257 = 1.00001729386 size is 0.029939 cents, 0.007510 savarts/eptamerides, or 0.015324 schismas 0.001392 syntonic commas ( 0 ) 0.001276 Pythagorean commas ( 0 ) 4.905280 MIDI tuning units 1.226320 MIDI pitch bend units 0.918858 Temperament units 0.751056 jots 0.042414 iotas 0.264465 Türk senti 0.020464 hekt 0.018213 Woolhouse units 0.015314 grads 0.015269 612-tone schismas 0.001796 moria 0.001531 diaschismas 0.001372 Sauveur commas 0.001322 53-tone commas 0.001098 septimal commas 0.001073 43-tone merides 0.001023 41-tone supracommas 0.000773 31-tone normal dieses 0.000729 minor dieses 0.000479 major dieses 0.000332 Pythagorean limmas 0.000257 secors 0.000158 1/3-comma mean whole tones 0.000155 1/4-comma mean whole tones 0.000153 1/5-comma mean whole tones 0.000152 1/6-comma mean whole tones 0.000025 octaves, 40080.889142 / octave | 30720/30719 = 2^11.3.5.13^-1.17^-1.139^-1 = 1.00003255314 size is 0.056356 cents, 0.014136 savarts/eptamerides, or 0.028846 schismas 0.002620 syntonic commas 0.002402 Pythagorean commas 9.233399 MIDI tuning units 2.308350 MIDI pitch bend units 1.729601 Temperament units 1.413742 jots 0.079838 iotas 0.497813 Türk senti 0.038520 hekt 0.034283 Woolhouse units 0.028827 grads 0.028742 612-tone schismas 0.003381 moria 0.002882 diaschismas 0.002583 Sauveur commas 0.002489 53-tone commas 0.002067 septimal commas 0.002019 43-tone merides 0.001926 41-tone supracommas 0.001456 31-tone normal dieses 0.001373 minor dieses 0.000901 major dieses 0.000625 Pythagorean limmas 0.000483 secors 0.000297 1/3-comma mean whole tones 0.000292 1/4-comma mean whole tones 0.000289 1/5-comma mean whole tones 0.000286 1/6-comma mean whole tones 0.000047 octaves, 21293.134811 / octave | 0.0 : 63.1 144.3 217.4 274.6 352.2 433.0 491.3 558.7 641.2 708.7 766.1 847.8 924.8 983.3 1055.5 1137.2 1200.0 63.1 : 81.2 154.3 211.5 289.1 369.9 428.2 495.6 578.1 645.6 703.0 784.7 861.7 920.2 992.4 1074.1 1136.9 1200.0 144.3 : 73.1 130.3 207.9 288.7 347.0 414.4 496.9 564.4 621.8 703.5 780.5 839.0 911.2 992.9 1055.7 1118.8 1200.0 217.4 : 57.2 134.8 215.6 273.9 341.3 423.8 491.3 548.7 630.4 707.4 765.9 838.1 919.8 982.6 1045.7 1126.9 1200.0 274.6 : 77.6 158.4 216.7 284.1 366.6 434.1 491.5 573.2 650.2 708.7 780.9 862.6 925.4 988.5 1069.7 1142.8 1200.0 352.2 : 80.9 139.1 206.5 289.0 356.5 414.0 495.6 572.6 631.1 703.3 785.0 847.8 910.9 992.1 1065.2 1122.4 1200.0 433.0 : 58.3 125.7 208.1 275.7 333.1 414.8 491.8 550.2 622.5 704.1 767.0 830.1 911.3 984.4 1041.6 1119.1 1200.0 491.3 : 67.4 149.9 217.4 274.9 356.5 433.5 492.0 564.2 645.9 708.7 771.8 853.0 926.1 983.3 1060.9 1141.7 1200.0 558.7 : 82.5 150.0 207.4 289.1 366.1 424.6 496.8 578.5 641.3 704.4 785.6 858.7 915.9 993.5 1074.3 1132.6 1200.0 641.2 : 67.5 125.0 206.6 283.6 342.1 414.3 496.0 558.8 621.9 703.1 776.2 833.4 911.0 991.9 1050.1 1117.5 1200.0 708.7 : 57.4 139.1 216.1 274.6 346.8 428.5 491.3 554.4 635.6 708.7 765.9 843.5 924.3 982.6 1050.0 1132.5 1200.0 766.1 : 81.7 158.7 217.1 289.4 371.0 433.9 497.0 578.2 651.3 708.5 786.0 866.9 925.1 992.6 1075.0 1142.6 1200.0 847.8 : 77.0 135.5 207.7 289.4 352.2 415.3 496.5 569.6 626.8 704.4 785.2 843.5 910.9 993.4 1060.9 1118.3 1200.0 924.8 : 58.5 130.7 212.4 275.2 338.3 419.5 492.6 549.8 627.4 708.2 766.5 833.9 916.4 983.9 1041.3 1123.0 1200.0 983.3 : 72.2 153.9 216.7 279.8 361.0 434.1 491.3 568.9 649.8 708.0 775.4 857.9 925.4 982.9 1064.5 1141.5 1200.0 1055.5: 81.7 144.5 207.6 288.8 361.9 419.1 496.7 577.5 635.8 703.2 785.7 853.2 910.6 992.3 1069.3 1127.8 1200.0 1137.2: 62.8 125.9 207.1 280.2 337.4 415.0 495.9 554.1 621.5 704.0 771.5 829.0 910.6 987.6 1046.1 1118.3 1200.0 1200.0 | Locations of 11/9: 5 : 0 - 5 diff. -4.758 5 : 2 - 7 diff. 0.424 5 : 3 - 8 diff. 6.111 5 : 5 - 10 diff. -9.131 5 : 7 - 12 diff. -9.118 5 : 9 - 14 diff. 5.314 5 : 10 - 15 diff. 0.613 5 : 12 - 17 diff. -4.797 5 : 13 - 18 diff. 9.123 5 : 16 - 21 diff. 9.990 Total of 10 = 58.82 % Covered degrees: 15 = 88.24 % More than once : 5 = 29.41 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 59.3785 cents Average absolute difference: 5.9379 cents Highest absolute difference: 9.9898 cents | Locations of 13/8: 12 : 0 - 12 diff. -7.268 12 : 2 - 14 diff. 1.556 12 : 3 - 15 diff. 2.410 12 : 5 - 17 diff. -7.306 12 : 6 - 18 diff. 10.463 12 : 9 - 21 diff. 7.109 12 : 10 - 22 diff. -2.934 12 : 12 - 24 diff. -2.946 12 : 13 - 25 diff. 6.645 12 : 16 - 28 diff. 11.569 Total of 10 = 58.82 % Covered degrees: 17 = 100.00 % More than once : 3 = 17.65 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 60.2054 cents Average absolute difference: 6.0205 cents Highest absolute difference: 11.5689 cents | Locations of 44/27: 12 : 0 - 12 diff. -2.342 12 : 2 - 14 diff. 6.481 12 : 3 - 15 diff. 7.336 12 : 5 - 17 diff. -2.381 12 : 7 - 19 diff. -7.563 12 : 10 - 22 diff. 1.991 12 : 12 - 24 diff. 1.979 12 : 13 - 25 diff. 11.570 12 : 15 - 27 diff. -7.752 Total of 9 = 52.94 % Covered degrees: 11 = 64.71 % More than once : 7 = 41.18 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 49.3960 cents Average absolute difference: 5.4884 cents Highest absolute difference: 11.5699 cents | Locations of 26/21: 5 : 1 - 6 diff. -0.188 5 : 4 - 9 diff. 3.166 5 : 8 - 13 diff. 3.630 5 : 11 - 16 diff. -1.294 5 : 14 - 19 diff. 8.718 5 : 15 - 20 diff. 7.864 Total of 6 = 35.29 % Covered degrees: 12 = 70.59 % More than once : 0 = 0.00 % Highest coverage: 1 Interval class patterns: 1 Total absolute difference : 24.8602 cents Average absolute difference: 4.1434 cents Highest absolute difference: 8.7183 cents | Locations of 17/14 3/2: 5-10: 2 - 7 - 12 diff. -10.854,-1.555 5-10: 3 - 8 - 13 diff. -5.167,-5.459 5-10: 6 - 11 - 16 diff. 3.023,-2.193 5-10: 9 - 14 - 19 diff. -5.964,-1.167 5-10: 10 - 15 - 20 diff. -10.666,-6.723 5-10: 13 - 18 - 23 diff. -2.155,-6.265 5-10: 16 - 21 - 26 diff. -1.289,-2.044 Total of 7 = 41.18 % Covered degrees: 15 = 88.24 % More than once : 6 = 35.29 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 64.5243 cents Average absolute difference: 9.2178 cents Highest absolute difference: 17.3892 cents | Locations of 16/13 3/2: 5-10: 0 - 5 - 10 diff. 7.306,-6.749 5-10: 1 - 6 - 11 diff. -10.463,-1.086 5-10: 4 - 9 - 14 diff. -7.109,-6.720 5-10: 5 - 10 - 15 diff. 2.934,-1.379 5-10: 7 - 12 - 17 diff. 2.946,-6.776 5-10: 8 - 13 - 18 diff. -6.645,-2.447 5-10: 11 - 16 - 21 diff. -11.569,-6.504 5-10: 12 - 17 - 22 diff. 7.268,-2.416 5-10: 14 - 19 - 24 diff. -1.556,-6.057 5-10: 15 - 20 - 25 diff. -2.410,-1.225 Total of 10 = 58.82 % Covered degrees: 17 = 100.00 % More than once : 11 = 64.71 % Highest coverage: 3 Interval class patterns: 1 Total absolute difference : 101.5646 cents Average absolute difference: 10.1565 cents Highest absolute difference: 18.0732 cents | Locations of 9/7 11/7 13/7: 6-11-15: 1 - 7 - 12 - 16 diff. 6.897,-2.222,-2.381 6-11-15: 4 - 10 - 15 - 19 diff. 0.962, 1.575, 1.999 6-11-15: 7 - 13 - 18 - 22 diff. 1.557, 10.679, 10.805 6-11-15: 8 - 14 - 19 - 23 diff. 10.507,-3.114,-2.635 6-11-15: 11 - 17 - 22 - 26 diff. 1.207,-3.551,-3.339 6-11-15: 14 - 20 - 25 - 29 diff. 0.958, 7.069, 7.163 Total of 6 = 35.29 % Covered degrees: 17 = 100.00 % More than once : 7 = 41.18 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 78.6188 cents Average absolute difference: 13.1031 cents Highest absolute difference: 23.0409 cents | Locations of 26/21 11/7 13/7: 5-11-15: 1 - 6 - 12 - 16 diff. -0.188,-2.222,-2.381 5-11-15: 4 - 9 - 15 - 19 diff. 3.166, 1.575, 1.999 5-11-15: 8 - 13 - 19 - 23 diff. 3.630,-3.114,-2.635 5-11-15: 11 - 16 - 22 - 26 diff. -1.294,-3.551,-3.339 5-11-15: 14 - 19 - 25 - 29 diff. 8.718, 7.069, 7.163 5-11-15: 15 - 20 - 26 - 30 diff. 7.864,-3.172, 2.405 Total of 6 = 35.29 % Covered degrees: 14 = 82.35 % More than once : 8 = 47.06 % Highest coverage: 3 Interval class patterns: 1 Total absolute difference : 65.4835 cents Average absolute difference: 10.9139 cents Highest absolute difference: 22.9510 cents | Locations of 9/8 16/13 4/3 3/2 64/39 16/9 2/1: 3-5-7-10-12-14-17: 1 - 4 - 6 - 8 - 11 - 13 - 15 - 18 diff. -7.591,-10.463, 2.447,-1.086,-4.198, 3.672, 0.000 3-5-7-10-12-14-17: 5 - 8 - 10 - 12 - 15 - 17 - 19 - 22 diff. -2.604, 2.934, 2.416,-1.379, 9.683, 3.971, 0.000 3-5-7-10-12-14-17: 8 - 11 - 13 - 15 - 18 - 20 - 22 - 25 diff. -3.533,-6.645, 1.225,-2.447,-1.186, 2.604, 0.000 3-5-7-10-12-14-17: 15 - 18 - 20 - 22 - 25 - 27 - 29 - 32 diff. -3.672,-2.410, 1.379,-1.225, 4.313, 3.795, 0.000 Total of 4 = 23.53 % Covered degrees: 13 = 76.47 % More than once : 9 = 52.94 % Highest coverage: 5 Interval class patterns: 1 Total absolute difference : 86.8748 cents Average absolute difference: 21.7187 cents Highest absolute difference: 29.4561 cents | Temperings of 13/12 11/9 4/3 3/2 13/8 16/9 2/1 0: 0.000: 5.7128 4.7580 -6.7759 6.7495 7.2676 -12.8330 0.0000 1: 63.082: 15.7284 22.5269 -2.4470 1.0864 21.1873 -3.6718 0.0000 2: 144.285: -8.2757 -0.4243 -1.1670 1.5548 -1.5562 -3.2111 0.0000 3: 217.383: -3.7894 -6.1110 -6.7232 5.4590 -2.4105 -13.4727 0.0000 4: 274.582: 19.8614 19.1731 -6.5043 6.7195 22.0542 -7.5908 0.0000 5: 352.166: 0.5305 9.1305 -2.4158 1.3789 7.3064 -3.9705 0.0000 6: 433.017: -12.9095 -14.3013 -6.2648 2.1928 -10.4625 -11.7238 0.0000 7: 491.269: 11.3217 9.1182 -6.0572 6.7759 12.4887 -12.7767 0.0000 8: 558.680: 11.4521 18.7090 -1.2248 2.4470 18.1754 -2.6037 0.0000 9: 641.163: -13.6130 -5.3145 -2.0441 1.1670 -7.1087 -4.2370 0.0000 10: 708.704: 0.5181 -0.6125 -6.7495 6.7232 2.9339 -13.5253 0.0000 11: 766.123: 20.1009 23.6333 -1.0864 6.5043 26.3657 -3.5334 0.0000 12: 847.795: -3.1109 4.7968 -1.5548 2.4158 2.9462 -2.7218 0.0000 13: 924.797: -7.8694 -9.1230 -5.4590 6.2648 -6.6446 -12.1822 0.0000 14: 983.257: 15.3347 13.6206 -6.7195 6.0572 17.3788 -13.2239 0.0000 15: 1055.500: 5.9274 14.4749 -1.3789 1.2248 12.6769 -3.7947 0.0000 16: 1137.164: -12.6553 -9.9898 -2.1928 2.0441 -11.5689 -8.4577 0.0000 17: 1200.000: 5.7128 4.7580 -6.7759 6.7495 7.2676 -12.8330 0.0000 Total abs. diff. : 168.7113 185.8176 66.7650 66.7650 190.5325 133.5300 0.0000 Average abs. diff.: 9.9242 10.9304 3.9274 3.9274 11.2078 7.8547 0.0000 Highest abs. diff.: 20.1009 23.6333 6.7759 6.7759 26.3657 13.5253 0.0000 | Locations of 13/11 3/2: 4-10: 1 - 5 - 11 diff. 0.125,-1.086 4-10: 2 - 6 - 12 diff. 0.479,-1.555 4-10: 4 - 8 - 14 diff. 5.112,-6.720 4-10: 5 - 9 - 15 diff. 0.212,-1.379 4-10: 8 - 12 - 18 diff. 0.094,-2.447 4-10: 9 - 13 - 19 diff. 5.577,-1.167 4-10: 11 - 15 - 21 diff. -0.167,-6.504 4-10: 12 - 16 - 22 diff. -0.159,-2.416 4-10: 14 - 18 - 24 diff. 9.385,-6.057 4-10: 15 - 19 - 25 diff. 0.424,-1.225 4-10: 16 - 20 - 26 diff. 8.991,-2.044 Total of 11 = 64.71 % Covered degrees: 15 = 88.24 % More than once : 11 = 64.71 % Highest coverage: 3 Interval class patterns: 1 Total absolute difference : 63.3262 cents Average absolute difference: 5.7569 cents Highest absolute difference: 15.4422 cents | Temperings of 3/2 7/4 9/4 0: 0.000: 6.7495 14.4310 13.4727 1: 63.082: 1.0864 23.5923 7.5908 2: 144.285: 1.5548 24.0530 3.9705 3: 217.383: 5.4590 13.7914 11.7238 4: 274.582: 6.7195 19.6733 12.7767 5: 352.166: 1.3789 23.2936 2.6037 6: 433.017: 2.1928 15.5403 4.2370 7: 491.269: 6.7759 14.4874 13.5253 8: 558.680: 2.4470 24.6604 3.5334 9: 641.163: 1.1670 23.0271 2.7218 10: 708.704: 6.7232 13.7388 12.1822 11: 766.123: 6.5043 23.7307 13.2239 12: 847.795: 2.4158 24.5423 3.7947 13: 924.797: 6.2648 15.0819 8.4577 14: 983.257: 6.0572 14.0402 12.8330 15: 1055.500: 1.2248 23.4694 3.6718 16: 1137.164: 2.0441 18.8064 3.2111 17: 1200.000: 6.7495 14.4310 13.4727 Total abs. diff. : 66.7650 329.9596 133.5300 Average abs. diff.: 3.9274 19.4094 7.8547 Highest abs. diff.: 6.7759 24.6604 13.5253 | Temperings of 7/6 3/2 11/6 0: 0.000: 7.7115 6.7495 6.1370 1: 63.082: 22.2134 1.0864 24.7197 2: 144.285: 21.8601 1.5548 6.3516 3: 217.383: 7.0155 5.4590 -3.6640 4: 274.582: 17.2264 6.7195 20.3401 5: 352.166: 22.1266 1.3789 15.8538 6: 433.017: 8.8171 2.1928 -7.7970 7: 491.269: 7.9831 6.7759 11.5339 8: 558.680: 22.2446 2.4470 24.9739 9: 641.163: 16.7623 1.1670 0.7427 10: 708.704: 7.6816 6.7232 0.6123 11: 766.123: 22.5059 6.5043 25.6774 12: 847.795: 22.4982 2.4158 11.5463 13: 924.797: 8.3324 6.2648 -8.0365 14: 983.257: 12.9538 6.0572 15.1753 15: 1055.500: 21.9146 1.2248 19.9338 16: 1137.164: 13.3475 2.0441 -3.2703 17: 1200.000: 7.7115 6.7495 6.1370 Total abs. diff. : 263.1946 66.7650 206.3657 Average abs. diff.: 15.4820 3.9274 12.1392 Highest abs. diff.: 22.5059 6.7759 25.6774 | Locations of 3/2 11/6: 10-15: 0 - 10 - 15 diff. -6.749,-6.137 10-15: 2 - 12 - 17 diff. -1.555,-6.352 10-15: 3 - 13 - 18 diff. -5.459, 3.664 10-15: 6 - 16 - 21 diff. -2.193, 7.797 10-15: 7 - 17 - 22 diff. -6.776,-11.534 10-15: 9 - 19 - 24 diff. -1.167,-0.743 10-15: 10 - 20 - 25 diff. -6.723,-0.612 10-15: 12 - 22 - 27 diff. -2.416,-11.546 10-15: 13 - 23 - 28 diff. -6.265, 8.037 10-15: 16 - 26 - 31 diff. -2.044, 3.270 Total of 10 = 58.82 % Covered degrees: 17 = 100.00 % More than once : 11 = 64.71 % Highest coverage: 3 Interval class patterns: 1 Total absolute difference : 101.0385 cents Average absolute difference: 10.1038 cents Highest absolute difference: 18.3098 cents | Locations of 9/7 11/7: 6-11: 1 - 7 - 12 diff. 6.897,-2.222 6-11: 4 - 10 - 15 diff. 0.962, 1.575 6-11: 7 - 13 - 18 diff. 1.557, 10.679 6-11: 8 - 14 - 19 diff. 10.507,-3.114 6-11: 11 - 17 - 22 diff. 1.207,-3.551 6-11: 14 - 20 - 25 diff. 0.958, 7.069 Total of 6 = 35.29 % Covered degrees: 14 = 82.35 % More than once : 4 = 23.53 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 50.2971 cents Average absolute difference: 8.3828 cents Highest absolute difference: 13.6206 cents | Locations of 4/3 3/2: 7-10: 0 - 7 - 10 diff. 6.776,-6.749 7-10: 1 - 8 - 11 diff. 2.447,-1.086 7-10: 2 - 9 - 12 diff. 1.167,-1.555 7-10: 3 - 10 - 13 diff. 6.723,-5.459 7-10: 4 - 11 - 14 diff. 6.504,-6.720 7-10: 5 - 12 - 15 diff. 2.416,-1.379 7-10: 6 - 13 - 16 diff. 6.265,-2.193 7-10: 7 - 14 - 17 diff. 6.057,-6.776 7-10: 8 - 15 - 18 diff. 1.225,-2.447 7-10: 9 - 16 - 19 diff. 2.044,-1.167 7-10: 10 - 17 - 20 diff. 6.749,-6.723 7-10: 11 - 18 - 21 diff. 1.086,-6.504 7-10: 12 - 19 - 22 diff. 1.555,-2.416 7-10: 13 - 20 - 23 diff. 5.459,-6.265 7-10: 14 - 21 - 24 diff. 6.720,-6.057 7-10: 15 - 22 - 25 diff. 1.379,-1.225 7-10: 16 - 23 - 26 diff. 2.193,-2.044 Total of 17 = 100.00 % Covered degrees: 17 = 100.00 % More than once : 17 = 100.00 % Highest coverage: 3 Interval class patterns: 1 Total absolute difference : 133.5300 cents Average absolute difference: 7.8547 cents Highest absolute difference: 13.5253 cents | Locations of 14/11 3/2: 6-10: 1 - 7 - 11 diff. -10.679,-1.086 6-10: 2 - 8 - 12 diff. 3.114,-1.555 6-10: 3 - 9 - 13 diff. -6.273,-5.459 6-10: 5 - 11 - 15 diff. 3.551,-1.379 6-10: 6 - 12 - 16 diff. 2.729,-2.193 6-10: 8 - 14 - 18 diff. -7.069,-2.447 6-10: 9 - 15 - 19 diff. 3.172,-1.167 6-10: 10 - 16 - 20 diff. -10.952,-6.723 6-10: 12 - 18 - 22 diff. 2.222,-2.416 6-10: 13 - 19 - 23 diff. -1.981,-6.265 6-10: 15 - 21 - 25 diff. -1.575,-1.225 6-10: 16 - 22 - 26 diff. 2.506,-2.044 Total of 12 = 70.59 % Covered degrees: 16 = 94.12 % More than once : 12 = 70.59 % Highest coverage: 3 Interval class patterns: 1 Total absolute difference : 89.7807 cents Average absolute difference: 7.4817 cents Highest absolute difference: 17.6751 cents | Locations of 23/18: 6 : 0 - 6 diff. -8.652 6 : 1 - 7 diff. -3.823 6 : 2 - 8 diff. 9.970 6 : 3 - 9 diff. 0.584 6 : 4 - 10 diff. -9.758 6 : 5 - 11 diff. 10.407 6 : 6 - 12 diff. 9.586 6 : 7 - 13 diff. -9.163 6 : 8 - 14 diff. -0.213 6 : 9 - 15 diff. 10.028 6 : 10 - 16 diff. -4.096 6 : 11 - 17 diff. -9.513 6 : 12 - 18 diff. 9.078 6 : 13 - 19 diff. 4.876 6 : 14 - 20 diff. -9.761 6 : 15 - 21 diff. 5.282 6 : 16 - 22 diff. 9.363 Total of 17 = 100.00 % Covered degrees: 17 = 100.00 % More than once : 17 = 100.00 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 124.1510 cents Average absolute difference: 7.3030 cents Highest absolute difference: 10.4072 cents | Locations of 23/18 3/2: 6-10: 0 - 6 - 10 diff. -8.652,-6.749 6-10: 1 - 7 - 11 diff. -3.823,-1.086 6-10: 2 - 8 - 12 diff. 9.970,-1.555 6-10: 3 - 9 - 13 diff. 0.584,-5.459 6-10: 4 - 10 - 14 diff. -9.758,-6.720 6-10: 5 - 11 - 15 diff. 10.407,-1.379 6-10: 6 - 12 - 16 diff. 9.586,-2.193 6-10: 7 - 13 - 17 diff. -9.163,-6.776 6-10: 8 - 14 - 18 diff. -0.213,-2.447 6-10: 9 - 15 - 19 diff. 10.028,-1.167 6-10: 10 - 16 - 20 diff. -4.096,-6.723 6-10: 11 - 17 - 21 diff. -9.513,-6.504 6-10: 12 - 18 - 22 diff. 9.078,-2.416 6-10: 13 - 19 - 23 diff. 4.876,-6.265 6-10: 14 - 20 - 24 diff. -9.761,-6.057 6-10: 15 - 21 - 25 diff. 5.282,-1.225 6-10: 16 - 22 - 26 diff. 9.363,-2.044 Total of 17 = 100.00 % Covered degrees: 17 = 100.00 % More than once : 17 = 100.00 % Highest coverage: 3 Interval class patterns: 1 Total absolute difference : 190.9160 cents Average absolute difference: 11.2304 cents Highest absolute difference: 16.4772 cents | Temperings of 18/13 23/13 0: 0.000: -4.7027 -4.4897 1: 63.082: 14.6995 4.6716 2: 144.285: 1.0367 5.1322 3: 217.383: -14.6420 -5.1294 4: 274.582: 9.8305 0.7525 5: 352.166: 9.2484 4.3728 6: 433.017: -13.1419 -3.3805 7: 491.269: 0.8484 -4.4334 8: 558.680: 15.1023 5.7396 9: 641.163: -4.5458 4.1064 10: 708.704: -9.0051 -5.1820 11: 766.123: 14.7800 4.8099 12: 847.795: 6.2051 5.6216 13: 924.797: -13.5966 -3.8389 14: 983.257: 5.5267 -4.8805 15: 1055.500: 14.1343 4.5486 16: 1137.164: -9.2775 -0.1143 17: 1200.000: -4.7027 -4.4897 Total abs. diff. : 160.3233 71.2039 Average abs. diff.: 9.4308 4.1885 Highest abs. diff.: 15.1023 5.7396 | 0: 1/1 0.000 unison, perfect prime 1: 531/512 63.082 2: 1113/1024 144.285 3: 1161/1024 217.383 4: 75/64 274.582 classic augmented second 5: 1255/1024 352.166 6: 1315/1024 433.017 7: 85/64 491.269 8: 707/512 558.680 9: 1483/1024 641.163 10: 771/512 708.704 11: 797/512 766.123 12: 1671/1024 847.795 13: 1747/1024 924.797 14: 1807/1024 983.257 15: 471/256 1055.500 16: 1975/1024 1137.164 17: 2/1 1200.000 octave | 30719/30720 = 2^-11.3^-1.5^-1.13.17.139 = 0.99996744792 size is -0.056356 cents, -0.014136 savarts/eptamerides, or -0.028846 schismas -0.002620 syntonic commas -0.002402 Pythagorean commas -9.233399 MIDI tuning units -2.308350 MIDI pitch bend units -1.729601 Temperament units -1.413742 jots -0.079838 iotas -0.497813 Türk senti -0.038520 hekt -0.034283 Woolhouse units -0.028827 grads -0.028742 612-tone schismas -0.003381 moria -0.002882 diaschismas -0.002583 Sauveur commas -0.002489 53-tone commas -0.002067 septimal commas -0.002019 43-tone merides -0.001926 41-tone supracommas -0.001456 31-tone normal dieses -0.001373 minor dieses -0.000901 major dieses -0.000625 Pythagorean limmas -0.000483 secors -0.000297 1/3-comma mean whole tones -0.000292 1/4-comma mean whole tones -0.000289 1/5-comma mean whole tones -0.000286 1/6-comma mean whole tones 0.000047 octaves, 21293.134811 / octave | Interval class, Number of incidences, Size: 1: 1 400/387 57.200 cents 1: 1 797/771 57.419 cents 1: 1 272/263 58.253 cents 1: 1 1807/1747 58.460 cents 1: 1 2048/1975 62.836 cents 1: 1 531/512 63.082 cents 1: 1 707/680 67.411 cents 1: 1 1542/1483 67.541 cents 1: 1 1884/1807 72.243 cents 1: 1 387/371 73.097 cents 1: 1 1747/1671 77.001 cents 1: 1 251/240 77.584 cents 1: 1 263/251 80.851 cents 1: 1 371/354 81.204 cents 1: 1 1975/1884 81.664 cents 1: 1 1671/1594 81.672 cents 1: 1 1483/1414 82.484 cents 2: 1 1594/1483 124.960 cents 2: 1 1414/1315 125.663 cents 2: 1 2124/1975 125.917 cents 2: 1 400/371 130.297 cents 2: 1 1884/1747 130.703 cents 2: 1 1255/1161 134.783 cents 2: 1 1807/1671 135.462 cents 2: 1 557/514 139.091 cents 2: 1 272/251 139.103 cents 2: 1 1113/1024 144.285 cents 2: 1 512/471 144.500 cents 2: 1 1483/1360 149.894 cents 2: 1 771/707 150.025 cents 2: 1 1975/1807 153.907 cents 2: 1 129/118 154.301 cents 2: 1 263/240 158.434 cents 2: 1 1747/1594 158.674 cents 3: 1 1414/1255 206.514 cents 3: 1 1671/1483 206.632 cents 3: 1 2226/1975 207.121 cents 3: 1 797/707 207.443 cents 3: 1 177/157 207.582 cents 3: 1 628/557 207.705 cents 3: 1 1255/1113 207.881 cents 3: 1 1483/1315 208.147 cents 3: 1 200/177 211.501 cents 3: 1 1975/1747 212.368 cents | 118/117 = 2.3^-2.13^-1.59 = 1.00854700855 size is 14.733996 cents, 3.695777 savarts/eptamerides, or 7.541505 schismas 0.685102 syntonic commas ( 13/19 ) 0.628047 Pythagorean commas 2414.017861 MIDI tuning units 603.504465 MIDI pitch bend units 452.194042 Temperament units 369.614561 jots 20.873161 iotas 130.150296 Türk senti 10.070793 hekt 8.963181 Woolhouse units 7.536567 grads 7.514338 612-tone schismas 0.884040 moria 0.753558 diaschismas 0.675308 Sauveur commas 0.650751 53-tone commas 0.540418 septimal commas 0.527968 43-tone merides 0.503412 41-tone supracommas 0.380628 31-tone normal dieses 0.358851 minor dieses 0.235498 major dieses 0.163303 Pythagorean limmas 0.126266 secors 0.077722 1/3-comma mean whole tones 0.076280 1/4-comma mean whole tones 0.075440 1/5-comma mean whole tones 0.074890 1/6-comma mean whole tones 0.012278 = 9/733 octaves, 81.444302 / octave | 15104/15093 = 2^8.3^-3.13^-1.43^-1.59 = 1.00072881468 size is 1.261289 cents, 0.316373 savarts/eptamerides, or 0.645583 schismas 0.058647 syntonic commas ( 1/17 ) 0.053763 Pythagorean commas ( 1/19 ) 206.649627 MIDI tuning units 51.662407 MIDI pitch bend units 38.709627 Temperament units 31.640491 jots 1.786826 iotas 11.141388 Türk senti 0.862100 hekt 0.767284 Woolhouse units 0.645160 grads 0.643258 612-tone schismas 0.075677 moria 0.064508 diaschismas 0.057809 Sauveur commas 0.055707 53-tone commas 0.046262 septimal commas 0.045196 43-tone merides 0.043094 41-tone supracommas 0.032583 31-tone normal dieses 0.030719 minor dieses 0.020160 major dieses 0.013979 Pythagorean limmas 0.010809 secors 0.006653 1/3-comma mean whole tones 0.006530 1/4-comma mean whole tones 0.006458 1/5-comma mean whole tones 0.006411 1/6-comma mean whole tones 0.001051 octaves, 951.407477 / octave | 1/1 : 531/512 1113/1024 1161/1024 75/64 1255/1024 1315/1024 85/64 707/512 1483/1024 771/512 797/512 1671/1024 1747/1024 1807/1024 471/256 1975/1024 2/1 531/512 : 371/354 129/118 200/177 1255/1062 1315/1062 680/531 707/531 1483/1062 257/177 797/531 557/354 1747/1062 1807/1062 314/177 1975/1062 1024/531 2/1 1113/1024: 387/371 400/371 1255/1113 1315/1113 1360/1113 202/159 1483/1113 514/371 1594/1113 557/371 1747/1113 1807/1113 628/371 1975/1113 2048/1113 708/371 2/1 1161/1024: 400/387 1255/1161 1315/1161 1360/1161 1414/1161 1483/1161 514/387 1594/1161 557/387 1747/1161 1807/1161 628/387 1975/1161 2048/1161 236/129 742/387 2/1 75/64 : 251/240 263/240 17/15 707/600 1483/1200 257/200 797/600 557/400 1747/1200 1807/1200 157/100 79/48 128/75 177/100 371/200 387/200 2/1 1255/1024: 263/251 272/251 1414/1255 1483/1255 1542/1255 1594/1255 1671/1255 1747/1255 1807/1255 1884/1255 395/251 2048/1255 2124/1255 2226/1255 2322/1255 480/251 2/1 1315/1024: 272/263 1414/1315 1483/1315 1542/1315 1594/1315 1671/1315 1747/1315 1807/1315 1884/1315 395/263 2048/1315 2124/1315 2226/1315 2322/1315 480/263 502/263 2/1 85/64 : 707/680 1483/1360 771/680 797/680 1671/1360 1747/1360 1807/1360 471/340 395/272 128/85 531/340 1113/680 1161/680 30/17 251/136 263/136 2/1 707/512 : 1483/1414 771/707 797/707 1671/1414 1747/1414 1807/1414 942/707 1975/1414 1024/707 1062/707 159/101 1161/707 1200/707 1255/707 1315/707 1360/707 2/1 1483/1024: 1542/1483 1594/1483 1671/1483 1747/1483 1807/1483 1884/1483 1975/1483 2048/1483 2124/1483 2226/1483 2322/1483 2400/1483 2510/1483 2630/1483 2720/1483 2828/1483 2/1 771/512 : 797/771 557/514 1747/1542 1807/1542 314/257 1975/1542 1024/771 354/257 371/257 387/257 400/257 1255/771 1315/771 1360/771 1414/771 1483/771 2/1 797/512 : 1671/1594 1747/1594 1807/1594 942/797 1975/1594 1024/797 1062/797 1113/797 1161/797 1200/797 1255/797 1315/797 1360/797 1414/797 1483/797 1542/797 2/1 1671/1024: 1747/1671 1807/1671 628/557 1975/1671 2048/1671 708/557 742/557 774/557 800/557 2510/1671 2630/1671 2720/1671 2828/1671 2966/1671 1028/557 3188/1671 2/1 1747/1024: 1807/1747 1884/1747 1975/1747 2048/1747 2124/1747 2226/1747 2322/1747 2400/1747 2510/1747 2630/1747 2720/1747 2828/1747 2966/1747 3084/1747 3188/1747 3342/1747 2/1 1807/1024: 1884/1807 1975/1807 2048/1807 2124/1807 2226/1807 2322/1807 2400/1807 2510/1807 2630/1807 2720/1807 2828/1807 2966/1807 3084/1807 3188/1807 3342/1807 3494/1807 2/1 471/256 : 1975/1884 512/471 177/157 371/314 387/314 200/157 1255/942 1315/942 680/471 707/471 1483/942 257/157 797/471 557/314 1747/942 1807/942 2/1 1975/1024: 2048/1975 2124/1975 2226/1975 2322/1975 96/79 502/395 526/395 544/395 2828/1975 2966/1975 3084/1975 3188/1975 3342/1975 3494/1975 3614/1975 3768/1975 2/1 2/1 | 0.0 : 63.1 144.3 217.4 274.6 352.2 433.0 491.3 558.7 641.2 708.7 766.1 847.8 924.8 983.3 1055.5 1137.2 1200.0 63.1 : 81.2 154.3 211.5 289.1 369.9 428.2 495.6 578.1 645.6 703.0 784.7 861.7 920.2 992.4 1074.1 1136.9 1200.0 144.3 : 73.1 130.3 207.9 288.7 347.0 414.4 496.9 564.4 621.8 703.5 780.5 839.0 911.2 992.9 1055.7 1118.8 1200.0 217.4 : 57.2 134.8 215.6 273.9 341.3 423.8 491.3 548.7 630.4 707.4 765.9 838.1 919.8 982.6 1045.7 1126.9 1200.0 274.6 : 77.6 158.4 216.7 284.1 366.6 434.1 491.5 573.2 650.2 708.7 780.9 862.6 925.4 988.5 1069.7 1142.8 1200.0 352.2 : 80.9 139.1 206.5 289.0 356.5 414.0 495.6 572.6 631.1 703.3 785.0 847.8 910.9 992.1 1065.2 1122.4 1200.0 433.0 : 58.3 125.7 208.1 275.7 333.1 414.8 491.8 550.2 622.5 704.1 767.0 830.1 911.3 984.4 1041.6 1119.1 1200.0 491.3 : 67.4 149.9 217.4 274.9 356.5 433.5 492.0 564.2 645.9 708.7 771.8 853.0 926.1 983.3 1060.9 1141.7 1200.0 558.7 : 82.5 150.0 207.4 289.1 366.1 424.6 496.8 578.5 641.3 704.4 785.6 858.7 915.9 993.5 1074.3 1132.6 1200.0 641.2 : 67.5 125.0 206.6 283.6 342.1 414.3 496.0 558.8 621.9 703.1 776.2 833.4 911.0 991.9 1050.1 1117.5 1200.0 708.7 : 57.4 139.1 216.1 274.6 346.8 428.5 491.3 554.4 635.6 708.7 765.9 843.5 924.3 982.6 1050.0 1132.5 1200.0 766.1 : 81.7 158.7 217.1 289.4 371.0 433.9 497.0 578.2 651.3 708.5 786.0 866.9 925.1 992.6 1075.0 1142.6 1200.0 847.8 : 77.0 135.5 207.7 289.4 352.2 415.3 496.5 569.6 626.8 704.4 785.2 843.5 910.9 993.4 1060.9 1118.3 1200.0 924.8 : 58.5 130.7 212.4 275.2 338.3 419.5 492.6 549.8 627.4 708.2 766.5 833.9 916.4 983.9 1041.3 1123.0 1200.0 983.3 : 72.2 153.9 216.7 279.8 361.0 434.1 491.3 568.9 649.8 708.0 775.4 857.9 925.4 982.9 1064.5 1141.5 1200.0 1055.5: 81.7 144.5 207.6 288.8 361.9 419.1 496.7 577.5 635.8 703.2 785.7 853.2 910.6 992.3 1069.3 1127.8 1200.0 1137.2: 62.8 125.9 207.1 280.2 337.4 415.0 495.9 554.1 621.5 704.0 771.5 829.0 910.6 987.6 1046.1 1118.3 1200.0 1200.0 | Locations of 59/54: 2 : 0 - 2 diff. 9.021 2 : 1 - 3 diff. -0.994 2 : 4 - 6 diff. -5.127 2 : 7 - 9 diff. 3.412 2 : 8 - 10 diff. 3.282 2 : 11 - 13 diff. -5.367 2 : 14 - 16 diff. -0.601 2 : 15 - 17 diff. 8.807 Total of 8 = 47.06 % Covered degrees: 15 = 88.24 % More than once : 1 = 5.88 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 36.6114 cents Average absolute difference: 4.5764 cents Highest absolute difference: 9.0212 cents | Locations of 64/59: 2 : 0 - 2 diff. -3.457 2 : 2 - 4 diff. 10.531 2 : 3 - 5 diff. 6.045 2 : 5 - 7 diff. 1.725 2 : 7 - 9 diff. -9.066 2 : 8 - 10 diff. -9.196 2 : 10 - 12 diff. 1.738 2 : 12 - 14 diff. 5.367 2 : 13 - 15 diff. 10.125 2 : 15 - 17 diff. -3.672 Total of 10 = 58.82 % Covered degrees: 13 = 76.47 % More than once : 7 = 41.18 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 60.9222 cents Average absolute difference: 6.0922 cents Highest absolute difference: 10.5314 cents | Locations of 13/12: 2 : 0 - 2 diff. -5.713 2 : 2 - 4 diff. 8.276 2 : 3 - 5 diff. 3.789 2 : 5 - 7 diff. -0.530 2 : 7 - 9 diff. -11.322 2 : 8 - 10 diff. -11.452 2 : 10 - 12 diff. -0.518 2 : 12 - 14 diff. 3.111 2 : 13 - 15 diff. 7.869 2 : 15 - 17 diff. -5.927 Total of 10 = 58.82 % Covered degrees: 13 = 76.47 % More than once : 7 = 41.18 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 58.5080 cents Average absolute difference: 5.8508 cents Highest absolute difference: 11.4521 cents | Locations of 12/11 13/11: 2-4 : 1 - 3 - 5 diff. -3.664, 0.125 2-4 : 4 - 6 - 8 diff. -7.797, 5.112 2-4 : 5 - 7 - 9 diff. 11.534, 0.212 2-4 : 8 - 10 - 12 diff. 0.612, 0.094 2-4 : 11 - 13 - 15 diff. -8.037,-0.167 2-4 : 14 - 16 - 18 diff. -3.270, 9.385 2-4 : 15 - 17 - 19 diff. 6.137, 0.424 Total of 7 = 41.18 % Covered degrees: 17 = 100.00 % More than once : 4 = 23.53 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 56.5715 cents Average absolute difference: 8.0816 cents Highest absolute difference: 12.9095 cents | Locations of 13/12 13/11: 2-4 : 2 - 4 - 6 diff. 8.276, 0.479 2-4 : 5 - 7 - 9 diff. -0.530, 0.212 2-4 : 8 - 10 - 12 diff. -11.452, 0.094 2-4 : 12 - 14 - 16 diff. 3.111,-0.159 2-4 : 15 - 17 - 19 diff. -5.927, 0.424 Total of 5 = 29.41 % Covered degrees: 13 = 76.47 % More than once : 2 = 11.76 % Highest coverage: 2 Interval class patterns: 1 Total absolute difference : 30.6653 cents Average absolute difference: 6.1331 cents Highest absolute difference: 11.5463 cents | 283/250 = 2^-1.5^-3.283 = 1.13200000000 size is 214.648750 cents, 53.841061 savarts/eptamerides, or 109.866646 schismas 9.980743 syntonic commas 9.149559 Pythagorean commas ( 183/20 ) 35168.051168 MIDI tuning units 8792.012792 MIDI pitch bend units 6587.682500 Temperament units 5384.642763 jots 304.085729 iotas 1896.063957 Türk senti 146.713973 hekt 130.577989 Woolhouse units 109.794708 grads 109.470862 612-tone schismas 12.878925 moria 10.978033 diaschismas 9.838068 Sauveur commas 9.480320 53-tone commas 7.872947 septimal commas 7.691580 43-tone merides 7.333832 41-tone supracommas 5.545093 31-tone normal dieses 5.227830 minor dieses 3.430804 major dieses 2.379039 Pythagorean limmas 1.839479 secors 1.132278 1/3-comma mean whole tones 1.111267 1/4-comma mean whole tones 1.099030 1/5-comma mean whole tones 1.091021 1/6-comma mean whole tones 0.178874 octaves, 5.590529 / octave | 31/25 = 5^-2.31 = 1.24000000000 size is 372.408145 cents, 93.412376 savarts/eptamerides, or 190.614824 schismas 17.316243 syntonic commas ( 329/19 ) 15.874168 Pythagorean commas ( 127/8 ) 61015.350433 MIDI tuning units 15253.837608 MIDI pitch bend units 11429.400918 Temperament units 9342.168651 jots 527.578205 iotas 3289.605278 Türk senti 254.543661 hekt 226.548288 Woolhouse units 190.490015 grads 189.928154 612-tone schismas 22.344489 moria 19.046507 diaschismas 17.068707 Sauveur commas 16.448026 53-tone commas 13.659290 septimal commas 13.344625 43-tone merides 12.723945 41-tone supracommas 9.620544 31-tone normal dieses 9.070105 minor dieses 5.952326 major dieses 4.127550 Pythagorean limmas 3.191432 secors 1.964463 1/3-comma mean whole tones 1.928009 1/4-comma mean whole tones 1.906779 1/5-comma mean whole tones 1.892883 1/6-comma mean whole tones 0.310340 octaves, 3.222271 / octave | 0.99999673738 size is -0.005648 cents, -0.001417 savarts/eptamerides, or -0.002891 schismas -0.000263 syntonic commas ( 0 ) -0.000241 Pythagorean commas ( 0 ) -0.925429 MIDI tuning units -0.231357 MIDI pitch bend units -0.173351 Temperament units -0.141694 jots -0.008002 iotas -0.049894 Türk senti -0.003861 hekt -0.003436 Woolhouse units -0.002889 grads -0.002881 612-tone schismas -0.000339 moria -0.000289 diaschismas -0.000259 Sauveur commas -0.000249 53-tone commas -0.000207 septimal commas -0.000202 43-tone merides -0.000193 41-tone supracommas -0.000146 31-tone normal dieses -0.000138 minor dieses -0.000090 major dieses -0.000063 Pythagorean limmas -0.000048 secors -0.000030 1/3-comma mean whole tones -0.000029 1/4-comma mean whole tones -0.000029 1/5-comma mean whole tones -0.000029 1/6-comma mean whole tones 0.000005 octaves, 212450.714200 / octave | 32/25 = 2^5.5^-2 = 1.28000000000 size is 427.372572 cents, 107.199287 savarts/eptamerides, or 218.748029 schismas 19.871981 syntonic commas 18.217067 Pythagorean commas ( 419/23 ) 70020.722241 MIDI tuning units 17505.180560 MIDI pitch bend units 13116.287973 Temperament units 10720.997119 jots 605.444477 iotas 3775.124388 Türk senti 292.112244 hekt 259.984981 Woolhouse units 218.604800 grads 217.960012 612-tone schismas 25.642354 moria 21.857618 diaschismas 19.587910 Sauveur commas 18.875622 53-tone commas 15.675291 septimal commas 15.314184 43-tone merides 14.601896 41-tone supracommas 11.040458 31-tone normal dieses 10.408779 minor dieses 6.830841 major dieses 4.736743 Pythagorean limmas 3.662461 secors 2.254402 1/3-comma mean whole tones 2.212567 1/4-comma mean whole tones 2.188204 1/5-comma mean whole tones 2.172257 1/6-comma mean whole tones 0.356144 octaves, 2.807854 / octave classic diminished fourth | 7/5 = 5^-1.7 = 1.40000000000 size is 582.512193 cents, 146.113475 savarts/eptamerides, or 298.155292 schismas 27.085667 syntonic commas ( 623/23 ) 24.830006 Pythagorean commas 95438.797636 MIDI tuning units 23859.699409 MIDI pitch bend units 17877.604136 Temperament units 14612.803778 jots 825.225606 iotas 5145.524368 Türk senti 398.151297 hekt 354.361584 Woolhouse units 297.960069 grads 297.081218 612-tone schismas 34.950732 moria 29.792105 diaschismas 26.698475 Sauveur commas 25.727622 53-tone commas 21.365545 septimal commas 20.873354 43-tone merides 19.902500 41-tone supracommas 15.048232 31-tone normal dieses 14.187248 minor dieses 9.310490 major dieses 6.456217 Pythagorean limmas 4.991963 secors 3.072768 1/3-comma mean whole tones 3.015747 1/4-comma mean whole tones 2.982539 1/5-comma mean whole tones 2.960804 1/6-comma mean whole tones 0.485427 octaves, 2.060043 / octave septimal or Huygens' tritone, BP fourth | 37647/25000 = 2^-3.3^2.5^-5.47.89 = 1.50588000000 size is 708.728172 cents, 177.772650 savarts/eptamerides, or 362.758167 schismas 32.954461 syntonic commas ( 725/22 ) 30.210054 Pythagorean commas ( 574/19 ) 116118.023632 MIDI tuning units 29029.505908 MIDI pitch bend units 21751.238605 Temperament units 17779.036791 jots 1004.031576 iotas 6260.432182 Türk senti 484.420832 hekt 431.142971 Woolhouse units 362.520643 grads 361.451368 612-tone schismas 42.523690 moria 36.247318 diaschismas 32.483375 Sauveur commas 31.302161 53-tone commas 25.994931 septimal commas 25.396093 43-tone merides 24.214879 41-tone supracommas 18.308811 31-tone normal dieses 17.261273 minor dieses 11.327843 major dieses 7.855120 Pythagorean limmas 6.073598 secors 3.738561 1/3-comma mean whole tones 3.669185 1/4-comma mean whole tones 3.628781 1/5-comma mean whole tones 3.602337 1/6-comma mean whole tones 0.590607 octaves, 1.693174 / octave | 803136/803125 = 2^6.3.5^-5.47.89.257^-1 = 1.00001369650 size is 0.023712 cents, 0.005948 savarts/eptamerides, or 0.012137 schismas 0.001103 syntonic commas ( 0 ) 0.001011 Pythagorean commas ( 0 ) 3.884922 MIDI tuning units 0.971230 MIDI pitch bend units 0.727724 Temperament units 0.594827 jots 0.033592 iotas 0.209453 Türk senti 0.016207 hekt 0.014425 Woolhouse units 0.012129 grads 0.012093 612-tone schismas 0.001423 moria 0.001213 diaschismas 0.001087 Sauveur commas 0.001047 53-tone commas 0.000870 septimal commas 0.000850 43-tone merides 0.000810 41-tone supracommas 0.000613 31-tone normal dieses 0.000578 minor dieses 0.000379 major dieses 0.000263 Pythagorean limmas 0.000203 secors 0.000125 1/3-comma mean whole tones 0.000123 1/4-comma mean whole tones 0.000121 1/5-comma mean whole tones 0.000121 1/6-comma mean whole tones 0.000020 octaves, 50607.967427 / octave | 639999/640000 = 2^-10.3^2.5^-4.17.47.89 = 0.99999843750 size is -0.002705 cents, -0.000679 savarts/eptamerides, or -0.001385 schismas -0.000126 syntonic commas ( 0 ) -0.000115 Pythagorean commas ( 0 ) -0.443196 MIDI tuning units -0.110799 MIDI pitch bend units -0.083020 Temperament units -0.067859 jots -0.003832 iotas -0.023895 Türk senti -0.001849 hekt -0.001646 Woolhouse units -0.001384 grads -0.001380 612-tone schismas -0.000162 moria -0.000138 diaschismas -0.000124 Sauveur commas -0.000119 53-tone commas -0.000099 septimal commas -0.000097 43-tone merides -0.000092 41-tone supracommas -0.000070 31-tone normal dieses -0.000066 minor dieses -0.000043 major dieses -0.000030 Pythagorean limmas -0.000023 secors -0.000014 1/3-comma mean whole tones -0.000014 1/4-comma mean whole tones -0.000014 1/5-comma mean whole tones -0.000014 1/6-comma mean whole tones 0.000002 octaves, 443613.848970 / octave | 1/1 : 531/512 1113/1024 1161/1024 75/64 1255/1024 1315/1024 85/64 707/512 1483/1024 771/512 797/512 1671/1024 1747/1024 1807/1024 471/256 1975/1024 2/1 531/512 : 371/354 129/118 200/177 1255/1062 1315/1062 680/531 707/531 1483/1062 257/177 797/531 557/354 1747/1062 1807/1062 314/177 1975/1062 1024/531 2/1 1113/1024: 387/371 400/371 1255/1113 1315/1113 1360/1113 202/159 1483/1113 514/371 1594/1113 557/371 1747/1113 1807/1113 628/371 1975/1113 2048/1113 708/371 2/1 1161/1024: 400/387 1255/1161 1315/1161 1360/1161 1414/1161 1483/1161 514/387 1594/1161 557/387 1747/1161 1807/1161 628/387 1975/1161 2048/1161 236/129 742/387 2/1 75/64 : 251/240 263/240 17/15 707/600 1483/1200 257/200 797/600 557/400 1747/1200 1807/1200 157/100 79/48 128/75 177/100 371/200 387/200 2/1 1255/1024: 263/251 272/251 1414/1255 1483/1255 1542/1255 1594/1255 1671/1255 1747/1255 1807/1255 1884/1255 395/251 2048/1255 2124/1255 2226/1255 2322/1255 480/251 2/1 1315/1024: 272/263 1414/1315 1483/1315 1542/1315 1594/1315 1671/1315 1747/1315 1807/1315 1884/1315 395/263 2048/1315 2124/1315 2226/1315 2322/1315 480/263 502/263 2/1 85/64 : 707/680 1483/1360 771/680 797/680 1671/1360 1747/1360 1807/1360 471/340 395/272 128/85 531/340 1113/680 1161/680 30/17 251/136 263/136 2/1 707/512 : 1483/1414 771/707 797/707 1671/1414 1747/1414 1807/1414 942/707 1975/1414 1024/707 1062/707 159/101 1161/707 1200/707 1255/707 1315/707 1360/707 2/1 1483/1024: 1542/1483 1594/1483 1671/1483 1747/1483 1807/1483 1884/1483 1975/1483 2048/1483 2124/1483 2226/1483 2322/1483 2400/1483 2510/1483 2630/1483 2720/1483 2828/1483 2/1 771/512 : 797/771 557/514 1747/1542 1807/1542 314/257 1975/1542 1024/771 354/257 371/257 387/257 400/257 1255/771 1315/771 1360/771 1414/771 1483/771 2/1 797/512 : 1671/1594 1747/1594 1807/1594 942/797 1975/1594 1024/797 1062/797 1113/797 1161/797 1200/797 1255/797 1315/797 1360/797 1414/797 1483/797 1542/797 2/1 1671/1024: 1747/1671 1807/1671 628/557 1975/1671 2048/1671 708/557 742/557 774/557 800/557 2510/1671 2630/1671 2720/1671 2828/1671 2966/1671 1028/557 3188/1671 2/1 1747/1024: 1807/1747 1884/1747 1975/1747 2048/1747 2124/1747 2226/1747 2322/1747 2400/1747 2510/1747 2630/1747 2720/1747 2828/1747 2966/1747 3084/1747 3188/1747 3342/1747 2/1 1807/1024: 1884/1807 1975/1807 2048/1807 2124/1807 2226/1807 2322/1807 2400/1807 2510/1807 2630/1807 2720/1807 2828/1807 2966/1807 3084/1807 3188/1807 3342/1807 3494/1807 2/1 471/256 : 1975/1884 512/471 177/157 371/314 387/314 200/157 1255/942 1315/942 680/471 707/471 1483/942 257/157 797/471 557/314 1747/942 1807/942 2/1 1975/1024: 2048/1975 2124/1975 2226/1975 2322/1975 96/79 502/395 526/395 544/395 2828/1975 2966/1975 3084/1975 3188/1975 3342/1975 3494/1975 3614/1975 3768/1975 2/1 2/1 | 0.0 : 63.1 144.3 217.4 274.6 352.2 433.0 491.3 558.7 641.2 708.7 766.1 847.8 924.8 983.3 1055.5 1137.2 1200.0 63.1 : 81.2 154.3 211.5 289.1 369.9 428.2 495.6 578.1 645.6 703.0 784.7 861.7 920.2 992.4 1074.1 1136.9 1200.0 144.3 : 73.1 130.3 207.9 288.7 347.0 414.4 496.9 564.4 621.8 703.5 780.5 839.0 911.2 992.9 1055.7 1118.8 1200.0 217.4 : 57.2 134.8 215.6 273.9 341.3 423.8 491.3 548.7 630.4 707.4 765.9 838.1 919.8 982.6 1045.7 1126.9 1200.0 274.6 : 77.6 158.4 216.7 284.1 366.6 434.1 491.5 573.2 650.2 708.7 780.9 862.6 925.4 988.5 1069.7 1142.8 1200.0 352.2 : 80.9 139.1 206.5 289.0 356.5 414.0 495.6 572.6 631.1 703.3 785.0 847.8 910.9 992.1 1065.2 1122.4 1200.0 433.0 : 58.3 125.7 208.1 275.7 333.1 414.8 491.8 550.2 622.5 704.1 767.0 830.1 911.3 984.4 1041.6 1119.1 1200.0 491.3 : 67.4 149.9 217.4 274.9 356.5 433.5 492.0 564.2 645.9 708.7 771.8 853.0 926.1 983.3 1060.9 1141.7 1200.0 558.7 : 82.5 150.0 207.4 289.1 366.1 424.6 496.8 578.5 641.3 704.4 785.6 858.7 915.9 993.5 1074.3 1132.6 1200.0 641.2 : 67.5 125.0 206.6 283.6 342.1 414.3 496.0 558.8 621.9 703.1 776.2 833.4 911.0 991.9 1050.1 1117.5 1200.0 708.7 : 57.4 139.1 216.1 274.6 346.8 428.5 491.3 554.4 635.6 708.7 765.9 843.5 924.3 982.6 1050.0 1132.5 1200.0 766.1 : 81.7 158.7 217.1 289.4 371.0 433.9 497.0 578.2 651.3 708.5 786.0 866.9 925.1 992.6 1075.0 1142.6 1200.0 847.8 : 77.0 135.5 207.7 289.4 352.2 415.3 496.5 569.6 626.8 704.4 785.2 843.5 910.9 993.4 1060.9 1118.3 1200.0 924.8 : 58.5 130.7 212.4 275.2 338.3 419.5 492.6 549.8 627.4 708.2 766.5 833.9 916.4 983.9 1041.3 1123.0 1200.0 983.3 : 72.2 153.9 216.7 279.8 361.0 434.1 491.3 568.9 649.8 708.0 775.4 857.9 925.4 982.9 1064.5 1141.5 1200.0 1055.5: 81.7 144.5 207.6 288.8 361.9 419.1 496.7 577.5 635.8 703.2 785.7 853.2 910.6 992.3 1069.3 1127.8 1200.0 1137.2: 62.8 125.9 207.1 280.2 337.4 415.0 495.9 554.1 621.5 704.0 771.5 829.0 910.6 987.6 1046.1 1118.3 1200.0 1200.0 | Interval class, Number of incidences, Size: 1: 1 400/387 57.200 cents 1: 1 797/771 57.419 cents 1: 1 272/263 58.253 cents 1: 1 1807/1747 58.460 cents 1: 1 2048/1975 62.836 cents 1: 1 531/512 63.082 cents 1: 1 707/680 67.411 cents 1: 1 1542/1483 67.541 cents 1: 1 1884/1807 72.243 cents 1: 1 387/371 73.097 cents 1: 1 1747/1671 77.001 cents 1: 1 251/240 77.584 cents 1: 1 263/251 80.851 cents 1: 1 371/354 81.204 cents 1: 1 1975/1884 81.664 cents 1: 1 1671/1594 81.672 cents 1: 1 1483/1414 82.484 cents 2: 1 1594/1483 124.960 cents 2: 1 1414/1315 125.663 cents 2: 1 2124/1975 125.917 cents 2: 1 400/371 130.297 cents 2: 1 1884/1747 130.703 cents 2: 1 1255/1161 134.783 cents 2: 1 1807/1671 135.462 cents 2: 1 557/514 139.091 cents 2: 1 272/251 139.103 cents 2: 1 1113/1024 144.285 cents 2: 1 512/471 144.500 cents 2: 1 1483/1360 149.894 cents 2: 1 771/707 150.025 cents 2: 1 1975/1807 153.907 cents 2: 1 129/118 154.301 cents 2: 1 263/240 158.434 cents 2: 1 1747/1594 158.674 cents 3: 1 1414/1255 206.514 cents 3: 1 1671/1483 206.632 cents 3: 1 2226/1975 207.121 cents 3: 1 797/707 207.443 cents 3: 1 177/157 207.582 cents 3: 1 628/557 207.705 cents 3: 1 1255/1113 207.881 cents 3: 1 1483/1315 208.147 cents 3: 1 200/177 211.501 cents 3: 1 1975/1747 212.368 cents 3: 1 1315/1161 215.634 cents 3: 1 1747/1542 216.092 cents 3: 1 17/15 216.687 cents 3: 1 2048/1807 216.743 cents 3: 1 1807/1594 217.134 cents 3: 1 1161/1024 217.383 cents 3: 1 771/680 217.435 cents 4: 1 1360/1161 273.886 cents 4: 1 1807/1542 274.552 cents 4: 1 75/64 274.582 cents classic augmented second 4: 1 797/680 274.854 cents 4: 1 2048/1747 275.203 cents 4: 1 1542/1315 275.688 cents 4: 1 2124/1807 279.825 cents 4: 1 2322/1975 280.218 cents 4: 1 1747/1483 283.633 cents 4: 1 707/600 284.097 cents 4: 1 1315/1113 288.731 cents 4: 1 371/314 288.786 cents 4: 1 1483/1255 288.997 cents 4: 1 1255/1062 289.084 cents 4: 1 1671/1414 289.116 cents 4: 1 1975/1671 289.369 cents 4: 1 942/797 289.377 cents 5: 1 1594/1315 333.107 cents 5: 1 96/79 337.418 cents 5: 1 2124/1747 338.285 cents 5: 1 1414/1161 341.297 cents 5: 1 1807/1483 342.093 cents 5: 1 314/257 346.795 cents 5: 1 1360/1113 346.984 cents 5: 1 1255/1024 352.166 cents 5: 1 2048/1671 352.205 cents 5: 1 1671/1360 356.526 cents 5: 1 1542/1255 356.538 cents 5: 1 2226/1807 361.029 cents 5: 1 387/314 361.883 cents 5: 1 1747/1414 366.117 cents 5: 1 1483/1200 366.581 cents 5: 1 1315/1062 369.935 cents 5: 1 1975/1594 371.041 cents 6: 1 1594/1255 413.957 cents 6: 1 1884/1483 414.336 cents 6: 1 202/159 414.394 cents 6: 1 1671/1315 414.779 cents | 8192/7225 = 2^13.5^-2.17^-2 = 1.13384083045 size is 217.461753 cents, 54.546656 savarts/eptamerides, or 111.306464 schismas 10.111542 syntonic commas ( 91/9 ) 9.269465 Pythagorean commas 35628.933656 MIDI tuning units 8907.233414 MIDI pitch bend units 6674.015049 Temperament units 5455.209299 jots 308.070817 iotas 1920.912154 Türk senti 148.636681 hekt 132.289233 Woolhouse units 111.233584 grads 110.905494 612-tone schismas 13.047705 moria 11.121902 diaschismas 9.966997 Sauveur commas 9.604561 53-tone commas 7.976123 septimal commas 7.792379 43-tone merides 7.429943 41-tone supracommas 5.617762 31-tone normal dieses 5.296342 minor dieses 3.475765 major dieses 2.410216 Pythagorean limmas 1.863585 secors 1.147117 1/3-comma mean whole tones 1.125830 1/4-comma mean whole tones 1.113433 1/5-comma mean whole tones 1.105319 1/6-comma mean whole tones 0.181218 octaves, 5.518212 / octave | 65536/65535 = 2^16.3^-1.5^-1.17^-1.257^-1 = 1.00001525902 size is 0.026417 cents, 0.006626 savarts/eptamerides, or 0.013521 schismas 0.001228 syntonic commas ( 0 ) 0.001126 Pythagorean commas ( 0 ) 4.328118 MIDI tuning units 1.082030 MIDI pitch bend units 0.810743 Temperament units 0.662686 jots 0.037424 iotas 0.233348 Türk senti 0.018056 hekt 0.016070 Woolhouse units 0.013512 grads 0.013473 612-tone schismas 0.001585 moria 0.001351 diaschismas 0.001211 Sauveur commas 0.001167 53-tone commas 0.000969 septimal commas 0.000947 43-tone merides 0.000903 41-tone supracommas 0.000682 31-tone normal dieses 0.000643 minor dieses 0.000422 major dieses 0.000293 Pythagorean limmas 0.000226 secors 0.000139 1/3-comma mean whole tones 0.000137 1/4-comma mean whole tones 0.000135 1/5-comma mean whole tones 0.000134 1/6-comma mean whole tones 0.000022 octaves, 45425.747051 / octave | 8192/7225 = 2^13.5^-2.17^-2 = 1.13384083045 size is 217.461753 cents, 54.546656 savarts/eptamerides, or 111.306464 schismas 10.111542 syntonic commas ( 91/9 ) 9.269465 Pythagorean commas 35628.933656 MIDI tuning units 8907.233414 MIDI pitch bend units 6674.015049 Temperament units 5455.209299 jots 308.070817 iotas 1920.912154 Türk senti 148.636681 hekt 132.289233 Woolhouse units 111.233584 grads 110.905494 612-tone schismas 13.047705 moria 11.121902 diaschismas 9.966997 Sauveur commas 9.604561 53-tone commas 7.976123 septimal commas 7.792379 43-tone merides 7.429943 41-tone supracommas 5.617762 31-tone normal dieses 5.296342 minor dieses 3.475765 major dieses 2.410216 Pythagorean limmas 1.863585 secors 1.147117 1/3-comma mean whole tones 1.125830 1/4-comma mean whole tones 1.113433 1/5-comma mean whole tones 1.105319 1/6-comma mean whole tones 0.181218 octaves, 5.518212 / octave | 8388608/8388225 = 2^23.3^-3.5^-2.17^-2.43^-1 = 1.00004565924 size is 0.079045 cents, 0.019827 savarts/eptamerides, or 0.040459 schismas 0.003675 syntonic commas 0.003369 Pythagorean commas 12.950738 MIDI tuning units 3.237684 MIDI pitch bend units 2.425933 Temperament units 1.982910 jots 0.111980 iotas 0.698231 Türk senti 0.054028 hekt 0.048086 Woolhouse units 0.040432 grads 0.040313 612-tone schismas 0.004743 moria 0.004043 diaschismas 0.003623 Sauveur commas 0.003491 53-tone commas 0.002899 septimal commas 0.002832 43-tone merides 0.002701 41-tone supracommas 0.002042 31-tone normal dieses 0.001925 minor dieses 0.001263 major dieses 0.000876 Pythagorean limmas 0.000677 secors 0.000417 1/3-comma mean whole tones 0.000409 1/4-comma mean whole tones 0.000405 1/5-comma mean whole tones 0.000402 1/6-comma mean whole tones 0.000066 octaves, 15181.219962 / octave | 174760/174741 = 2^3.3^-1.5.7^-1.17.53^-1.157^-1.257 = 1.00010873235 size is 0.188231 cents, 0.047215 savarts/eptamerides, or 0.096345 schismas 0.008752 syntonic commas 0.008023 Pythagorean commas 30.839754 MIDI tuning units 7.709938 MIDI pitch bend units 5.776905 Temperament units 4.721929 jots 0.266660 iotas 1.662706 Türk senti 0.128657 hekt 0.114507 Woolhouse units 0.096282 grads 0.095998 612-tone schismas 0.011294 moria 0.009627 diaschismas 0.008627 Sauveur commas 0.008314 53-tone commas 0.006904 septimal commas 0.006745 43-tone merides 0.006431 41-tone supracommas 0.004863 31-tone normal dieses 0.004584 minor dieses 0.003009 major dieses 0.002086 Pythagorean limmas 0.001613 secors 0.000993 1/3-comma mean whole tones 0.000974 1/4-comma mean whole tones 0.000964 1/5-comma mean whole tones 0.000957 1/6-comma mean whole tones 0.000157 octaves, 6375.148224 / octave | 139808/139807 = 2^5.17.251^-1.257.557^-1 = 1.00000715272 size is 0.012383 cents, 0.003106 savarts/eptamerides, or 0.006338 schismas 0.000576 syntonic commas ( 0 ) 0.000528 Pythagorean commas ( 0 ) 2.028828 MIDI tuning units 0.507207 MIDI pitch bend units 0.380040 Temperament units 0.310637 jots 0.017543 iotas 0.109383 Türk senti 0.008464 hekt 0.007533 Woolhouse units 0.006334 grads 0.006315 612-tone schismas 0.000743 moria 0.000633 diaschismas 0.000568 Sauveur commas 0.000547 53-tone commas 0.000454 septimal commas 0.000444 43-tone merides 0.000423 41-tone supracommas 0.000320 31-tone normal dieses 0.000302 minor dieses 0.000198 major dieses 0.000137 Pythagorean limmas 0.000106 secors 0.000065 1/3-comma mean whole tones 0.000064 1/4-comma mean whole tones 0.000063 1/5-comma mean whole tones 0.000063 1/6-comma mean whole tones 0.000010 octaves, 96907.174446 / octave | Number of notes : 17 -- Interval properties -- Smallest one step interval : 400/387, 57.1997 cents Average step (divided formal octave) : 70.588 cents Average / Smallest step : 1.234066 Largest one step interval : 1483/1414, 82.4838 cents Largest / Average step : 1.168520 Largest / Smallest step : 1.442031 Linear approximation average step : 70.6123 cents Number of one step interval sizes : 17 Median interval of one step : 1884/1807, 72.2430 cents Scale is strictly proper Interval pattern: ABCDEFGHIJKLMNOPQ Best fifths form a closed circle Scale is sum-free (all different intervals) Scale is a Constant Structure, by a margin of 42.476 cents Number of different intervals : 272 = 17.00000 / class Smallest interval difference : 464400/464399, 0.0037 cents Number of recognisable fifths : 17, average 705.882 cents Rothenberg stability : 1.000000 = 1 Lumma stability : 0.701755 Rothenberg efficiency : 0.117647 redundancy : 0.882353 Efficiency x scale size : 2.000000 Limited transpositions with margin 19.9198 cents : 3 7 10 14 Formal octave complements present : 1 = 5.8824% -- Rational properties -- Prime limit : 1747 Odd number limit : 1975 (O: 1975 U: 1975) Fundamental : 1/1024,-10.000 octaves, 0.255 Hz. Guide tone : too high to compute Mersenne's string divisions : too high to compute Vogel's harmonic complexity : 360.00000 Wille's k value : 987 Sum of van Prooijen's expressibility : 46.35836, average 2.72696 Sum of Tenney's harmonic distance : 90.60977, average 5.32999 Sum of Mann's harmonic distance : 14307.5, average 841.61765 Number of different primes : 20 Prime exponents' range and average: 2: -10 .. 1 -8.52941 3: 0 .. 3 0.58824 5: 0 .. 2 0.41176 7: 0 .. 1 0.11765 13: 0 .. 1 0.05882 17: 0 .. 1 0.05882 43: 0 .. 1 0.05882 53: 0 .. 1 0.05882 59: 0 .. 1 0.05882 79: 0 .. 1 0.05882 101: 0 .. 1 0.05882 139: 0 .. 1 0.05882 157: 0 .. 1 0.05882 251: 0 .. 1 0.05882 257: 0 .. 1 0.05882 263: 0 .. 1 0.05882 557: 0 .. 1 0.05882 797: 0 .. 1 0.05882 1483: 0 .. 1 0.05882 1747: 0 .. 1 0.05882 Average exponent except of 2 : 2.05882 Average absolute exponent except of 2: 35 / 17 = 2.05882 -- Statistical properties -- Standard deviation of one step : 9.3680 cents Skew of one step intervals : 0.0000 cents Average distance from equal tempered : 5.3825 cents, 0.076252 steps Standard deviation from equal tempered : 6.0728 cents, 0.086031 steps Maximum distance from equal tempered : 10.3475 cents, 0.146589 steps Geometric average of pitches 0..n : 599.943 cents Arithmetic average of pitches 0..n : 8885/6144, 638.6323 cents Harmonic average of pitches 0..n : 561.253 cents Geometric average of pitches 1..n-1 : 599.935 cents Arithmetic average of pitches 1..n-1 : 23583/16384, 630.5516 cents Harmonic average of pitches 1..n-1 : 569.319 cents Geometric average of pitches 1..n : 635.233 cents Arithmetic average of pitches 1..n : 25631/17408, 669.7672 cents Harmonic average of pitches 1..n : 600.700 cents | 6400/6399 = 2^8.3^-4.5^2.79^-1 = 1.00015627442 size is 0.270526 cents, 0.067857 savarts/eptamerides, or 0.138467 schismas 0.012579 syntonic commas 0.011531 Pythagorean commas 44.323054 MIDI tuning units 11.080764 MIDI pitch bend units 8.302599 Temperament units 6.786382 jots 0.383246 iotas 2.389650 Türk senti 0.184907 hekt 0.164570 Woolhouse units 0.138377 grads 0.137968 612-tone schismas 0.016232 moria 0.013836 diaschismas 0.012399 Sauveur commas 0.011948 53-tone commas 0.009922 septimal commas 0.009694 43-tone merides 0.009243 41-tone supracommas 0.006989 31-tone normal dieses 0.006589 minor dieses 0.004324 major dieses 0.002998 Pythagorean limmas 0.002318 secors 0.001427 1/3-comma mean whole tones 0.001401 1/4-comma mean whole tones 0.001385 1/5-comma mean whole tones 0.001375 1/6-comma mean whole tones 0.000225 octaves, 4435.795373 / octave