“Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry. As Stravinsky once said: “The musician should find in mathematics a study as useful to him as the learning of another language is to a poet. Mathematics swims seductively just below the surface.” – Du Sautoy 2011
There has been some distinction in school subjects between those creative subjects such as music and art, and subjects which are considered more academic, such as maths and science. However, when we look at the relationship between music and mathematics, there are a substantial amount of links between the two.
Counting plays a huge role in music, especially if playing along with a backing track or other musicians in an ensemble. I personally joined the school orchestra in my sixth year of school as a percussionist, and found out these difficulties quickly. However, I believe that this is a prime example of Liping Ma’s “multiple perspectives”. There are large sections of the piece where certain instruments would not play, often written in sheet music as shorthand, such as in the picture right. This would indicate that there are 15 bars rest. If a piece of music has 4 beats in the bar (as indicated by the time signature, see picture left, where the number of beats is the top number), then this would indicate 15×4 beats rest, or 60 beats. A musician has a few option in how to approach this mathematically. They can work out that they are waiting for 60 beats and count these out, however, this becomes difficult if you lose count. The other option is to keep the numbers in their simplest form. I found it easier to count using your fingers, a skill which is often discouraged past early primary mathematics. Counting four beats and then denoting this with one finger, then counting another four beats and denoting this with a second finger was my strategy, which seemed to work well.
Looking back on this with the mathematically thinking I have acquired through this module, I can see many other mathematical qualities in this other than simply counting. The number of beats in the bar denote a base system, as I have discussed in a previous post. As I was counting in fours and then denoting this with a symbol (in this case a finger), I had effectively used a base 4 system in working out the timings, just as farmers denoted a particular amount of sheep with a stone in their pocket or a mark on a post.
There is also an element of pattern and symmetry in music that is often overlooked. There are often repeated patterns or phrases in music, especially in minimalist music, which is made up of repeated phrases built upon one another. An example of this is shown below in the clapping music, where one phrase is repeated with slightly altered timing to create a minimalist piece:
I believe that this would be a good tool to use in a classroom with pupils in order to to reinforce their maths learning. This, I believe, can link with Ma’s principle of “Longitudinal Coherence”, which looks into how ideas and topics are developed. In using music to teach children about pattern and sequence, you show them how these skills can be applied, therefore giving the topic a relevance, which is extremely important for young children. This would be an interesting lesson in to try in future.
Du Sautoy, M. (2011). ‘Listen by numbers: music and maths’ Guardian. Available at: https://www.theguardian.com/music/2011/jun/27/music-mathematics-fibonacci (Accessed: 25 November 2015)