From frequencies to harmony: how mathematics helps us understand music


Mathematics and music seem like two completely different things at first glance, but they actually have a lot in common. Both disciplines use systems to process and communicate information, and both are based on patterns and structures. In this blog, we will take a closer look at how mathematics and music are related and how these two disciplines can reinforce each other. One of the ways in which mathematics and music are related is through the frequencies used. In music, frequencies are used to create tones, and these tones combine to form a melody. These tones can be measured and expressed in hertz (Hz), which indicates the amount of waves per second. For example, tone A above middle C has a frequency of 440 Hz. Mathematics also comes into the picture when talking about harmony in music. Harmony is created when two or more tones are played simultaneously, and the ratio between them is important for the sound that is created. These ratios can be expressed as fractions, and these fractions in turn can be converted into decimal numbers. For example, an octave (which is a ratio of 1:2) can be expressed as 1/2 or 0.5. But mathematics and music are not only linked by frequencies and harmony. The structure of music can also be viewed from a mathematical perspective. For example, many styles of music use rhythms and metric patterns, and these patterns can be expressed in notation. This means that music is a kind of language, where the notes are the letters, and the rhythms and metric patterns are the grammar. There are also several ways in which music and mathematics work together in practice. For example, some composers use mathematical concepts in creating their music. The famous composer Johann Sebastian Bach, for example, was interested in mathematics and used the golden ratio in his music. Mathematics can also play an important role in the music industry. For example, in the recording and production industry, mathematical concepts are used to process and edit audio. This can include using equalizers to amplify or attenuate the sound of certain frequencies, or using compression to affect the dynamic range of a recording. Mathematical concepts are also used in music theory to analyze and understand the structure of music. For example, tonal music theory uses mathematical concepts to describe how tones and chords are connected and how these connections affect the emotional charge of the music. In conclusion, mathematics and music have a lot in common, and they can reinforce each other in different ways. Whether it is using mathematics in creating music, processing audio, or analyzing the structure of music, these two disciplines have much to offer each other. Sources:

"Music and Mathematics" (

"The Mathematics of Music" (

"Math in Music" (

Photo by Dan Cristian Pădureț on Unsplash

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