In this MOOC series, we are going to look at how Mathematics and Physical Sciences exist in music, how they explain its inner structure and how they have inspired composers through the years.
The first session will be centred around sound’s inner structure and how it can be expressed using mathematics. We will analyse the sound, zoom in and see how it is built from the inside, along with the mathematical formulas that express the different relations between time, frequency and period.
Our second session will focus on the Fibonacci numbers, a mathematical sequence that has accompanied composers through the centuries and is closely related to the idea of the golden ratio. We will analyse Karlheinz Stockhausen’s “Klavierstück 9” and show how the Fibonacci numbers help structure the entire piece, from a micro- to a macro-structural level. In addition, we will show some examples of other ways to use the Fibonacci sequence to compose music.
In our third session, we will focus on the technique of mathematical sieves and how Iannis Xenakis used them to compose music. We will explain what a sieve is, how it is built and what type of logical operations one can apply to it in order to develop it further and come up with interesting musical material.
Finally, in our forth session we will take a closer look on another mathematical notion that Xenakis applied in his compositions, the random walk. Once again, we will explain what it is, some of its applications outside of music and how it has been applied in a musical context, giving some examples in order to help students integrate it in their own potential work.