When I learnt that we were going to be doing an input on Maths and Music, I was confused, to me these two subjects have nothing in common with each other. I was fascinated to see what we were going to be focusing on.
I love music but have never had any luck with playing any instruments. My music knowledge is nowhere as good as my fathers’, but I can still appreciate most genres of music. Music is a subject I never really took that much from within School and during my MA1 placement I didn’t witness any music lessons. Thus, I feel I didn’t receive the most exciting music education. So, before this input I was slightly worried I wouldn’t know of any musical terms which may have been quite obvious.
To begin with, we were shown a quote by Marcus du Sautoy (2011) which stated, “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.” After reading this quote, I somewhat understood that Mathematics could have different functions; I could recognise how different harmonies could be associated with “numerical relationships” because when playing music every individual has to count to make sure they are in time with the music playing. From this, I was slightly more open-minded and didn’t think it was such an abnormal concept. (Sangster, P, 2018)
Within the input, we were asked to write down as many different links between Maths and Music that we could think of; (my mind went black) so I only could think of the number of beats within a piece of music. I knew myself, that there was going to be many more links which were not as obvious as my suggestions; however, I didn’t realise how many links there could be. I did recognise the musical terms, I just simply would have never linked Maths to these musical terms. That’s when it dawned on me just how much value the subject of Maths had within Music.
Some of the links we were shown:
• Note values/rhythms
• Beats in a bar
• Counting songs
• Fingering on music
• Time signature
• Figured bass
• Musical Intervals
• Fibonacci sequence
When looking at these links, some are reasonably recognisable or obvious. Although I wanted to learn more about the Fibonacci sequence.
I soon discovered that the Fibonacci sequence “is one of the most famous formulas in mathematics” (Live Science, 2018) which was originally found by Leonardo Pisano Bigollo, who was famously known as Fibonacci. It is a sequence of numbers where each number within the sequence is the sum of the two numbers which come before it. The sequence goes as 0,1,1,2,3,5,8,13,21,34 and this sequence is continuous; the “mathematical equation describing it is Xn+2= Xn+1 + Xn”. For example, if we take the number 21, it is in the sequence that the two preceding numbers equal 21 (8+13). (Live Science, 2018)
When looking at a keyboard the numbers in the Fibonacci sequence can be seen. For example, there are thirteen keys along a keyboard “in the span of a full octave which consists of eight white keys and five back keys that are arranged in groups of two and three along the keyboard”. (PQ, 2016) Fibonacci numbers can also be seen in “the notes that make up musical scales” (PQ, 2016), for instance, the Pentatonic scaled consists of five notes, the Diatonic scales is made up of eight notes and the Chromatic scale has thirteen notes. It appears that the foundation of chords are made up from the 1st, 3rd, and 5th notes in any scale; and all three of these numbers are Fibonacci numbers. (PQ, 2016) This video below demonstrates the Fibonacci sequence in a musical context.
Throughout my research of Maths in Music, I discovered Pythagoras who was historically known as a mathematician and a musician. I already knew that Pythagoras was best known for “his Pythagorean Theorem, which states that in any right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides (A2 + B2 = C2).” (History of Music Theory, undated)
However, I wasn’t aware that he ever had a connection to music. He held the idea that “everything in the universe” was connected to maths and numbers. He felt the same way about music, he viewed music as “the unifying principle of Harmonia, which he regarded as a divine principle that brings order to chaos and discord.” (History of Music Theory, undated) Pythagoras also believed that music could remove stress and he also arranged specific songs “to be played at the end of the day to relieve day to day stress levels”. In addition, he thought that there were particular genres of music which suited to the time of day and to the seasons throughout the year. (History of Music Theory, undated)
Overall, before this input and before any of my research I was so oblivious to the different functions that Maths has in relation to Music. There has been a connection between Maths and Music for at least 2000 years, and I am only learning of it now. That says something doesn’t it? I believe that there is not enough emphasis on Mathematics within Music in Education. I have learnt so much about this concept and think it is useful to know the different links between the two subjects. Every child should be shown the different applications which mathematics has to everyday real-life situations. For example, they should recognise that Maths is not a boring adding sums activity but that “it can be a challenging, exciting and fascinating subject” (Saloni, 2010).
Teachers should try to encourage children to understand how Mathematics is used in a greater context, for example, by bringing music “into mathematical teaching” (Saloni, 2010), they can show how exciting and versatile Maths can be. For example, teachers could implement Pythagoras’ theory of music within the classroom to remove any stress and create a peaceful atmosphere. This could therefore make Mathematics more relevant, entertaining and joyful for children; and also remove the negative attitudes towards Maths from an early age and instead encourage them to indulge within the musically mathematical world and enjoy the many different opportunities and activities that it brings.
History of Music Theory. (undated). Pythagoras: Music, Geometry and Mathematics | History of Music Theory. [online] Available at: http://www.historyofmusictheory.com/?page_id=20 [Accessed 4 Nov. 2018].
Live Science. (2018). What Is the Fibonacci Sequence?. [online] Available at: https://www.livescience.com/37470-fibonacci-sequence.html [Accessed 4 Nov. 2018].
PQ, R. (2016). Music and the Fibonacci Sequence. [online] Dubspot Blog. Available at: http://blog.dubspot.com/fibonacci-sequence-in-music/ [Accessed 4 Nov. 2018].
Saloni, S. (2010). An Exploration of the Relationship between Mathematics and Music. [ebook] University of Manchester. Available at: http://eprints.ma.man.ac.uk/1548/1/covered/MIMS_ep2010_103.pdf [Accessed 4 Nov. 2018].
Sangster, P. (2018). ‘Discovering Maths: Music and Mathematics’. [Powerpoint presentation]. ED21006: Discovering Mathematics. Available at: https://my.dundee.ac.uk/webapps/blackboard/content/listContent.jsp?course_id=_58988_1&content_id=_5173832_1&mode=reset [Accessed 4 Nov. 2018].
Schwab, G. (2012). Fibonacci sequence in music.
Available at: https://www.youtube.com/watch?v=2pbEarwdusc&feature=youtu.be [Accessed 4 Nov. 2018].
Du Sautoy, M. (2011). ‘Listen by numbers: music and maths’ Guardian. Available at: http://theclassicalsuite.com/2011/06/listen-by-numbers-music-and-maths-via-guardian/ [Accessed 4 Nov. 2018].