Fun with Math & Music

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Learning Objects (6)

Direct Access Links:

Doodle Music (Vihart)
Twelve Tones (Vihart)
Sound Braid (Vihart)
Shepard Tones in Film-Making (Shutterstock)
Music & Math: The Genius of Beethoven (TED)
The Golden Ratio and Fibonacci Sequence in Music (Sound Field)


Whether it’s doodling with music or 12-tone theories with Vihart videos, or musing about the Fibonacci Sequence in classical music, playing around with the intersection of math and music can be fun!

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Doodle Music

A visual and musical expression of mathematical symmetry groups. The transformations done to the video are equivalent to the transformations done to the notes.

Twelve Tones

Composer Arnold Schoenberg developed a 12-tone technique of music composition.  Read an overview about the basics of twelve-tone music theory here. Listen to what BBC suggests are five of the best twelve-tone works here.  Then click on the Twelve Tones link above to learn about Vihart’s twelve-tone experimentation and try to create your own composition!

Sound Braid

Creating a sound braid using math. Use this to create your own music!


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Shepard Tones in Film-Making

A Shepard tone is a sound consisting of a superposition of sine waves (mathematical curve) separated by octaves. When played with the bass pitch moving upward or downward it creates an auditory illusion of a tone that continually ascends or descends in pitch, yet which ultimately gets no higher or lower.

The Shepard Tone creates the illusion of continuously swelling sound, which can  build tension or suspense or descending sound creating a sense of falling. A continuous Shepard Tone is a Shepard-Risset Glissando.


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Music & Math: The Genius of Beethoven

How is it that Beethoven, who is celebrated as one of the most significant composers of all time, wrote many of his most beloved songs while going deaf? The answer lies in the math behind his music. Natalya St. Clair employs the “Moonlight Sonata” to illustrate the way Beethoven was able to convey emotion and creativity using the certainty of mathematics.

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The Golden Ratio and Fibonacci Sequence in Music 

Since the beginning of time Phi—also known as the golden ratio—has inspired the world around us. Have you ever noticed how some pieces of music just seem to make sense? From the notes and chords to the phrasing and dynamics, they can all feel like they were meant to go together. Many people believe this is not a coincidence but the golden ratio in action. Hosts Nahre and LA explore this phenomenon and create their own composition inspired by the golden ratio.


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Ontology Tags Arts & Entertainment: (1) Authorship & Composition – Learning through Math (2) Mirror of Society – (a) Music as Form of Communication (b) Philosophical Reflection

Search Terms Media Produced – (1) Digital Content – Audio Content (2) Artistic Composition –  Musical Score | Challenging Problems: Humans in the World – Historical Times & Periods |Intended Learning Outcomes: (1) Creativity – (a) Brainstorm (b) Design or Create (2) Critical Thinking – (a) Draw Analytic Conclusions (b) Model with Math (c) Reflect Critically on Learning | Success Skills & Depth of Knowledge: (1) Cognitive Demand – (a) Analyzing (b) Creating (2) Learning Styles & Intelligences – (a) Logical or Mathematical (b) Musical or Rhythmic |CTEs & Disciplines: (1) Arts & Entertainment (2) Authorship & Composition (3) Film-making Studies (4) Music Studies (5) Nonverbal Communication (6) Basic Math