Maths and music – how do theserelate? – the first question I asked when going to the lecture. This threw me, but I was very interested to learn why maths and music related to each other.  I do not play a musical instrument myself but I enjoy listening to music. A fantastic quote highlighted by Paola in the lecture is by Macus du Sautoy showing the importance of music and maths:

“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.”

Marcus du Sautoy (2011) – this quote directly highlights the importance of mathematics for musicians as without mathematics there wouldnt be music.

When asked to think about it more deeply it was clear that maths and music were closely related and in my pair we came up with 3 or 4 different reasons. We came up with rhythms, beats in a bar and scales just from thinging more deeply about music and mathematics.  There are also several more which I will list below:

• Note values
• chords
• counting songs
• fingering on music
• time signature
• figured bass
• scales
• mucial intervals
• fibonacci sequence …… (shocked to see this again after it being so important in maths and nature!)

This lecture was very hands on with the use of musical instruments such as the glockenspheil, tamborines, rhythm sticks etc. Each of us were set into pairs and rows and firstly had to follow a very simple… rhythm.  Simple for the people with rhythm I suppose.  Each of the rows then had a different rhythm each and had to play it at the same time… very complicated for me and I found it quite a challenge but it showed that for different beats played together we created the backing to a song.

Music and the Fibonacci sequence 

Fibonacci sequence – 1, 1, 2, 3, 5, 8, 13, 21……

How does this relate to maths, well…

• There are 13 notes in an octave
• A 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.

Each of the numbers mentioned are in the Fibonacci sequence – coincidence or not?

Continued:

• The piano keyboard scale of C to C has 13 keys of which:
• 8 keys are white
• 5 keys are black
• These are split into groups of 3 and 2

Wow… I am truely interested in how this is the case, is it just because thats how it has always been or was music influenced by the golden ratio and Fibonacci.

Pentatonic Scale

I guessed that it was something to do with five which is correct and I will explain further what it is. Bobby McFerrin does this very well.

 

The Pentatonic scale comes from the greek words pente – five and tonic – tone.  It consists of 5 notes within an octave. Lots of songs are made up of pentatonic scales and Howard Goodall shows this in 5 different songs from all over the world:

Its amazing how much maths does relate to music in so many different ways which I have found very interesting to look at.  As I am not a musician I thought I would find the concept difficult to understand but with excellent tuition from Paola it has become a lot more clear.  My mind has been opened up to the reality that maths has a strong relationship with music and there are also many more ideas which I have just touched on which could be expanded even more.

https://www.goldennumber.net/music/ – explanation of Fibonacci and music.

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)

Estrella, E. (2017) What are Pentatonic Scales. Available here: https://www.thoughtco.com/the-pentatonic-scales-2456569 (Accessed: 11 November 2017)

http://www.bbc.co.uk/programmes/p003c1b9

Sangster, P (2017) Discovering Mathematics; Music and Maths. [Lecture to MA2 Education Students] ED21006: Discovering Mathematics. Dundee University: 2 November 2017