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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 C–D 4 M3 5 / 4 1 . 259 m3 Minor 3rd C–E 5 6 P4 d5 4 / 3 √ 2 1 . 3335 1 . 4125 M3 P4 d5 Major 3rd Perfect 4th Diminished 5th C–E C–F C–G 7 P5 3 / 2 1 . 496 P5 Perfect 5th C–G 8 m6 = P8 − M3 8 / 5 1 . 585 m6 Minor 6th C–A 9 M6 = P8 − m3 5 / 3 1 . 679 M6 Major 6th C–A 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 ....
View Full Document

This note was uploaded on 02/24/2012 for the course MECHANICAL 6.055J taught by Professor Sanjoymahajan during the Spring '08 term at MIT.

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online