# data[].attributes.attachment_link.title
Music and math: The genius of Beethoven - Natalya St. Clair

# data[].attributes.body
The intervals between notes that sound good in a melody also form the basis of Harmony -- the playing of multiple notes at the same time. A chord played on the piano or strummed on a guitar consists of three or more notes played simultaneously or in quick succession, so they overlap with each other. Chords that sound harmonious to most ears contain the same integer intervals that are often considered melodious.

# data[].attributes.body
Firstly let's talk about rhythm. When you're tapping your toes to a catchy beat, you're basically working with a periodic function -- in other words, a wave. Even music without a drumbeat has a rhythm -- it determines where you place the notes (and even the silences!).

Next we can talk about melody. A musical note is made up of waves. These waves are produced by vibrations of a string (like in guitars, pianos and harps) of a membrane (like drums) or of a column of air (like flutes, saxophones and trumpets). High frequency vibrations are not heard as discrete rhythms, but instead as more continuous sounds that have a particular pitch and timbre. For reasons that are still being studied by mathematicians, musicians and scientists, the particular notes that sound pleasurable when played in a sequence as a melody often have particular mathematical relationships.

The "gap" between two musical notes is called an interval. An important number is the ratio of the frequency between two notes. Cultures all around the world like to hear sequences of notes involving small integer ratios among the frequencies of the notes. One such popular interval is the perfect fifth which is the interval between C and G (or 'Do' and 'So', or 'Sa' and 'Pa' in Indian classical music). The ratio between the two frequencies is 2:3. If you were building a harp, you could use these ratios to determine the lengths of the strings.

# data[].attributes.body
Music and math have a very close relationship that stretches back thousands of years, to the very origins of music and civilization. In fact, it's unfortunate that we don't teach these connections to kids in school, because that might make them see mathematics in a new light.

Music involves creating patterns of sound. Mathematics can be described as the study of patterns. So you can study everything in music -- melody, harmony, rhythm, timbre -- from several different mathematical perspectives, including geometry, number theory, trigonometry, differential calculus, combinatorics and signal processing. Also, the electrical and electronic tools used to make modern music are based on a mathematical understanding of how music works.