Music, both vocal and instrumental is richly mathematical. Music is made up of beats- pulses in which time is marked. Connection of music to mathematics comes in three different ways; the set theory, abstract algebra and real and complex analysis. In set theory, operations such as inversion and transposition are applied to achieve deep structures in the music. Transposition and inversion preserve intervals between tones in a set. Abstract algebra has been used to analyze music. The pitch classes form an abelian group with 12 elements. Algebra has also been used to emphasize transformation between musical objects. Real and complex analysis have been applied by use of the theory of the Riemann zeta function. Mathematics can explain many phenomena in music. It explains how strings vibrate at certain frequencies, and sound waves are used to describe these mathematical frequencies . Technology used to make recordings on a compact disc purely rely on mathematics.
Robert Schneider is a rock star mathematician. He created a micro-tonal scale in which “the sequence of prime numbers created melodic patterns arising from the algebraic structure of the scale”. His song Al-Jabar mixed color theory with abstract algebra ( Vaughn, 2006 ). Mathematics played a huge role in his music. Musical pieces are divided into bars. Each bar is divided into equal portions called beats. He used fractions in his music to indicate lengths of notes. Each note has different shape to indicate its beat length. He used Pythagoras and frequency to make different sounds with different weights and vibrations. The pitch of a vibrating string is proportional to and can be controlled by its length. Notes of certain frequencies sound best with multiple frequencies of that note ( Garland and Kahn, 2009) .
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No musical notes fits together better than those which are exactly one octave apart. Pairs of notes like Middle C and High C often arise in music. Going up one octave is always the same as doubling the frequency. Notes one octave apart are always bound together by this basic mechanism. Notes an octave apart do fit together so well. If you play Middle C and High C together, there is no discordance. However, it may sound hollow. Other notes are brought in to bring more combinations like chords and make the sound interesting. Adding a third note- E gets the really pleasant sound. The notes form a C major chord when played together (Arvind, 2009).
Changing the song’s keys raises or lowers the all the notes by the same amount. This might make the song more convenient to play on a particular musical instrument or more comfortable for vocalists to accompany. It should be done properly so that the key change has no effect on the way the song sounds ( Garland and Kahn, 2009) .
References
Vaughn, K., (2006). "Music and mathematics: Modest support for the oft-claimed relationship. US: penguin.
Garland, T., and Kahn, C., (2009). Math and Music: Harmonious Connections. New York: Dale Seymour Publications
Arvind, G., (2009). The Interesting Connection between Math and Music. Retrieved on 27 th March from www.vancouversun.com/touch/interesting+connection+between+math+music/1473881/story.html
