Unformatted text preview: in which the piece is played, so different keys can be associated with different characteristics. In this day of tuning to equal temperament, the key in which a piece is played still changes the frequency range of the piece. Therefore, even though the frequency ratios are the same, there will be very small changes in consonance and dissonance because of the variation in the width of the critical bands. EX1. Since the semitone of equal temperament has the ratio of 05946 . 1 2 12 / 1 = , we can calculate other ratios by direct multiplication. For a major third: 260 . 1 ) 05946 . 1 )( 05946 . 1 )( 05946 . 1 )( 05946 . 1 ( = For a minor third: 189 . 1 ) 05946 . 1 )( 05946 . 1 )( 05946 . 1 ( = EX2. We know that twelve equal semitones make up an octave. The ratio of a semitone is 05946 . 1 2 12 / 1 = and the ratio of an octave is 2. Hence if we invest money at the rate of 5.9%, the money will become (1+5.9%) =1.059 times next year. Since 12 / 1 2 059 . 1 ! , the investment approximately doubles in 12 years....
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This document was uploaded on 02/11/2012.
 Fall '09

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