Maths and music go hand in hand. “Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry.” Marcus du Sautoy (2011).
There are many links between maths and music such as the value of notes, the rhythm, the amount of beats in a bar, the tempo of a piece of music, the pitch, musical intervals even scales and arpeggios are mathematical patterns. Maths is very much a big part of music and to learn a musical instrument you must have a basic understanding of mathematical concepts.
As the great 17th century German mathematician Gottfried Leibniz stated, “music is the sensation of counting without being aware you were counting”.
The “grammar” of music – rhythm and pitch – has mathematical foundations. When we hear two notes an octave apart, we feel we’re hearing the same note which is why they’ve been given the same name. The frequencies of the two notes are in an exact 1:2 ratio.
Just as music is not about reaching the final chord, mathematics is about more than just the end result. It is the journey that excites the mathematician. This is much the same way as we listen to a piece of music: understanding how themes are established, mutated, interwoven and transformed. What people don’t realise about mathematics is that it involves a lot of choice: not about what is true or false, but from deciding what piece of mathematics is worth“listening to”.
Symmetry is not restricted to only the visual arts. Music is usually very symmetrical and predictable. Symmetry is the repetition of sounds in music. Symmetry has been used as a formal constraint by many composers, such as Steve Reich and James Tenney. In classical music, Bach also used concepts of symmetry.
Fibonacci Sequence in Music
The Fibonacci sequence beginning 1 1 2 3 5 8 13 can be seen in music. The following video uses visuals to show how the numbers appear in a musical context.
Du Sautoy, M. (2011). ‘Listen by numbers: music and maths’ Guardian. Available: http://theclassicalsuite.com/2011/06/listen-by-numbers-music-and-maths-via-guardian/ (Accessed: 04 November 2013)
The Guardian. 2017. Listen by numbers: music and maths | Music | The Guardian. [ONLINE] Available at:https://www.theguardian.com/music/2011/jun/27/music-mathematics-fibonacci. [Accessed 15 November 2017].