singing_logs - MIT OpenCourseWare http://ocw.mit.edu 6.055J...

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Unformatted text preview: MIT OpenCourseWare http://ocw.mit.edu 6.055J / 2.038J The Art of Approximation in Science and Engineering Spring 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms . Approximating logarithms using musical intervals KEY Semitones Interval Ratio Exact Value 2 M2 9 / 8 1 . 122 Symbol Interval Notes 3 m3 6 / 5 1 . 1885 M2 Major 2nd CD 4 M3 5 / 4 1 . 259 m3 Minor 3rd CE 5 6 P4 d5 4 / 3 2 1 . 3335 1 . 4125 M3 P4 d5 Major 3rd Perfect 4th Diminished 5th CE CF CG 7 P5 3 / 2 1 . 496 P5 Perfect 5th CG 8 m6 = P8 M3 8 / 5 1 . 585 m6 Minor 6th CA 9 M6 = P8 m3 5 / 3 1 . 679 M6 Major 6th CA 10 P5 + m3 9 / 5 1 . 7783 2 P4 16 / 9 1 . 7783 11 17 / 9 1 . 8836 12 P8 2 1 . 9953 17.4 e 2 . 718 19 P8 + P5 3 2 . 9854 24 2 P8 4 3 . 981 28 2 P8 + M3 5 5 . 012 31 2 P8 + P5 6 5 . 9566 34 3 P8 M2 64 9 7 7 . 080 36 3 P8 8 7 . 943 38 2 (P8 + P5) 9 8 . 913 40 3 P8 + M3 10 10 ....
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singing_logs - MIT OpenCourseWare http://ocw.mit.edu 6.055J...

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