Outwardly, math and music appear to be very different topics. Math seems very calculated and precise with little room for emotion, while music is thought to be impulsive and expressive. However, the individual studies of math and music, in fact, have many similar aspects. This report will show the connections between math and music stating specific examples in the areas of rhythm, tone and frequency, tuning, and composition. By further understanding the correlation between math and music it is possible to gain a deeper appreciation of music and insight into the creative applications of mathematics.
             Rhythm is the foundation of music. It surrounds us always, although we may not notice its presence. The beating of our hearts, our breathing patterns and even the crash of the ocean on the beach are rhythms found around us everyday. Although this may not seem mathematical, the rhythm found in nature is believed to be the origin of early music around the world.
             In music, rhythm is used to measure time. Therefore, the rules used to measure rhythm are the time signature and the measure. The time signature is found at the beginning of musical compositions and is used subsequently throughout the piece to signal a change in rhythm. The time signature resembles a fraction with the numerator representing how many beats in a measure and the denominator indicating which kind of note gets the beat. The time signature, 4/4, is the main time signature and is used for naming the kinds of notes. When this time signature is filled up with one note for a whole measure that note is called a whole note and is held for four beats. If the measure is split in half, you get two half notes each equal to two beats. If the measure is split into four equal parts, you get four notes called quarter notes. Following this pattern, each note is divided in two to get the next smallest note (eighth notes, sixteenth notes, thirty second notes and so on.). ...