Yet One More Amusing, if Desperate, Attempt To Get People Interested in Mathematics (from a Mathematics Newsletter):

"Of all the academic subjects, math is most closely connected with music. Music is all based on fractions and patterns," says Michele Adams, a middle grades mathematics teacher, music teacher, and piano player from The Woodlands, Tex. "Where fractions are concerned, music focuses on divisions of time for the rhythm and space for dealing with intervals such as octaves or fifths." Adams points to the Gregorian chants. "They are based on strict rules of mathematics," she notes. Adams points out some mathematical concepts underpinning music:

Counting: It's fundamental to playing music. One must count beats per measure and count how long to hold notes.
Patterns: Music is full of patterns--patterns of notes, chords, and key changes. Musicians learn to recognize these quickly. Patterns, and being able to invert them (known as counterpoint), help musicians form harmonies.

Geometry: Music students use geometric shapes to help them remember the correct finger positions for notes or chords (more than one note played simultaneously)--for instance, guitar players' fingers often form triangular shapes on the neck of the guitar.
Ratios and proportions/ equivalent fractions: Reading music requires an understanding of ratios and proportions. For instance, a whole note needs to be played for twice as long as a half note, four times as long as a quarter note, and so forth. In addition, since the amount of time allotted to one beat in a given time signature is a mathematical constant, the durations of all the notes in that piece are all relative to one another and are played on the basis of that constant. Finally, different frameworks of time with which musicians work are based on an understanding of fractions and multiples--for example, understanding the rhythmic difference between 3/4 and 4/4 time signatures.

Sequences: Music and mathematics are also related through sequences, particularly intervals. Teacher Eli Maor expounded on this relationship further in the September 1979 Mathematics Teacher: "Although a mathematical interval corresponds to the difference between two numbers, a musical interval corresponds to the ratio of the frequencies of the tones." He goes on to say, "Here, then, is a single principle that underlines all musicomathematical relations: Arithmetic progressions in music correspond to geometric progressions in mathematics; that is, the relation between the two is logarithmic."