# Maths in Music

I have never played an instrument in my life or classed myself as musically talented. My brother plays the bagpipes and it amazes me how he can look at the notes and knows what it means. My musical abilities go as far as playing the recorder in primary school. So, when I found out we had a musical input, I was a bit apprehensive with what to expect.

We started off by listing some things that we think link maths and music. We came up with:

• Rhythm
• Scale
• Chords
• Tuning

It was quite difficult to think of the relations between maths and music without having a musical background, as I did not know but about music anyway. Du Sautoy (2011) said “rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry.”

The next thing we looked at was the Fibonacci sequence within music. Having previously looked at the Fibonacci sequence within art, it was interesting to see it appear in music as well.  I have written about the Fibonacci sequence in my last blog post so I won’t go into too much detail in this blog. There are 13 notes in an octave, scale is composed of 8 notes, the 5th and 3rd notes of the scale form the basic ‘root’ chord and are based on whole tone which is 2 steps from the root tone, that is the 1st note of the scale (Meisner, 2014).  This links to the Fibonacci sequence (0,1,1,2,3,5,8,13…). A piano keyboard scale goes from C to C with 13 keys, 8 white and 5, also split into groups of 3 and 2.  This 13th note as the octave is essential to computing the frequencies of the other notes (Meisner, 2012).

Here is the piano scale.

We then had a shot playing the instrument ourselves, which at first, I found a bit difficult, but after a few tries, I began to get the hang of. Getting the opportunity to play the instrument allowed me to experience it for myself and improve my understanding of notes and rhythm, which allowed me make connections between maths and music.

Finally, we looked at tuning an instrument. If a guitar is tuned perfectly, the notes that are strummed out are in perfect Fibonacci sequence. This is, however, not the same with a piano. If a piano was tuned in Fibonacci sequence, it would not sound right to the ear. Instead, it has to be tuned with a man made adaption on this sequence. This video does a great job of explaining why a piano cannot be tuned using the Fibonacci sequence.

It was not until taking the discovering maths module that I realised how many different areas maths connects to. This reinforces the ideas of Ma’s (2010) ideas of longitudinal coherence and multiple perspectives. I will take what I have learnt form this module into my practice as a teacher, showing the pupils how maths interconnects with other subjects, whilst creating some cross curricular lessons involving maths, music and art. I thoroughly enjoyed this input as it was practical and I liked getting to have a shot of it for myself.

References

Du Sautoy, M. (2011). Listen by numbers: music and maths. [Article]. Available at: https://www.theguardian.com/music/2011/jun/27/music-mathematics-fibonacci [Accessed 27th November 2017]

Meisner, G. (2014) Music and the Fibonacci Sequence and Phi. [Online]. Available at: https://www.goldennumber.net/music/ [Accessed 27th November 2017]

Minutephysics (2015) Why It’s Impossible to Tune a Piano[Online].  YouTube. Available at: https://www.youtube.com/watch?v=1Hqm0dYKUx4 [Accessed 27th November 2017]

Tindal, C. (2017). Maths in Art and The Fibonacci Sequence. [Blog].  Available at: https://blogs.glowscotland.org.uk/glowblogs/cbteportfolio/2017/11/24/maths-in-art-and-the-fibonacci-sequence/ [Accessed 27th November 2017]