It seems that there is virtually no escaping maths. In a recent lecture with Anna Robb we
explored the idea of maths in music. Although I have played violin and piano for a large part of my life, I have never really appreciated the large amount of mathematics found in music.

When I first began playing violin I was taught about time signatures and the values of different

Learning note values and equivalent values is important in music.

notes. For example a crotchet is one beat, a minum two and a quaver is half. To understand this basic concept I must’ve had an understanding of fundamental mathematics as I could understand the value of each note and how to count to that value. Even being able to associate notes to which finger to put down on the fingerboard required some aspect of maths I was unaware of at the time. I knew that on each string the higher the note required to play meant the higher number of finger to use. (e.g. playing a G on the D string uses the 3rd finger which is a note higher than F which uses the 2nd finger) It all seems more complex trying to explain in words.

Different music also required different speeds. The speed was dictated at the top of each piece of music by stating a note (mainly crotchet) and a number which represented how many beats were to be played per minute. ( crotchet = 128 bpm, or quaver = 140 bpm, the higher the number generally the quicker the pace of the music. This can also be put into a metronome which produces a sound at the speed requested allowing you to play music to the correct speed whilst keeping to the beat.

Time signatures also dictate how many beats are in a bar and the value of the beat. More maths! 4/4 is the most basic and most used timesignature in music and consists of 4 crotchet beats per bar. This tells the musician that there are four beats in the bar and also that when to play the downbeat. 3/4 is commonly used in Waltz as it is a simple 1,2,3 1,2,3, 1,2,3. In music exams you are also required to identify how many beats in a bar are in certain pieces of music played by the examiner, this means you must have a basic knowledge of maths as you need to know the value of the beat and count.

Patterns and repetition are also apparent in nearly all music. A composer often repeats the same pattern, or creates a pattern to invert, mirror or play at a different pitch. Patterns are often recurring. We have already discovered the mathematics behind forming patterns so patterns in music is another example of maths. Music can take different form, ABA, ABCD, ABACAD. Each letter has a different theme or pattern. In ABA, the A is the repeated pattern.

Today’s lecture also showed me that there is a concept in maths, firstly which I had never heard of, but secondly that I would have never associated with music. This is the Fibonacci sequence. The Fibonacci sequence is a series of numbers where a number is found by adding up the two numbers before it.(Hom, 2014) Starting with 0 and 1, the sequence goes 0, 1, 1, 2, 3, 5, 8, 13, 21, 34 (the rule for this can be expressed as x_n = x_n–1 + x_n-2 ). It is interesting to note that in music a chord is made up of the root (1st note of a scale), the 3rd and the 5th. These are all Fibonacci numbers, infact Fibonacci numbers are apparent in

An example of Debussy’s work where is a clear pattern of Fibonacci numbers.

the octave and multiple scales too! In a previous post I discussed the use of the Golden Ratio in Art. I have now discovered that the Golden Ratio is also closely linked to music and is infact used when designing instruments like the violin. (Something I will be investigating when I am reunited with my own violin). The Fibonacci sequence is used in many melodies and harmonies as the pattern of notes is most pleasing to the ear and can be heard in many of Claude Debussy’s compositions (Shah, 2010). Although when listening to music it may be hard to pinpoint exactly where the sequence is present, when reading the music itself this becomes slightly clearer. (I have uploaded a picture of an extract from Debussy’s work where the notes, 1,2,3,5,8, and 13 form the main melody).

Music in maths is something I found very interesting as even though music is something I play or listen to everyday I don’t tend to associate with maths. It reinforces the idea that maths is crucial to our understanding of multiple aspects of our lives. Music provided me with so many different opportunities and experiences, my favourite being touring Italy with Perth Youth Orchestra.  I can’t imagine a life without music and it seems absurd to me that if I didn’t have a basic knowledge of fundamental mathematics I wouldn’t have been able to progress this far in music.

http://www.perth-youth-orchestra.org.uk/lord-of-the-dance/ – Link to one of my favourite performances from my time at PYO (skip to 3:48)

References:

Elaine J. Hom, 2014, What is the Fibonacci Sequence? Available at: http://bit.ly/2dtNlVm (accessed on 9th November 2016)