# Maths and Music in Harmony

“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)

Believe it or not maths and music are very closely linked with one another. Which at first I wasn’t sure that there was a connection but after a lecture about this, I could see that this connection was more apparent than I had thought.

Here are some connections:

• Note values/rhythms
• Beats in a bar
• Tuning/Pitch
• Chords
• Counting songs
• Fingering on music
• Time signature
• Figured bass
• Scales
• Musical Intervals
• Fibonacci sequence

In the lecture about maths and music, the group were divided into 4 smaller groups. We were all given a bar to look at and clap out the beat. Every group was given a different line which they had to clap a different beat. This worked well as we were all able to clap in sync with one another. The bars that were given all added up to 8 and it was important that we were able to do this in order for this to sound good. This links with Ma’s Basic ideas as counting to 8 is very basic.

This activity would work well in a classroom setting as it may help children with their counting but also with their rhythm in music.

The Fibonacci Sequence and Music

“It is well known that the Fibonacci sequence of numbers and the associated “golden ratio” are manifested in nature and in certain works of art. It is less well known that these numbers also underlie certain musical intervals and compositions.” Gend (quoted in Vesic, 2014, p.72)

• 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.
• 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

All of these numbers appear in Fibonacci’s sequence. The Fibonacci sequence is seen everywhere around us and now, it is evident that it can also be heard in music. When it is seen in everyday life, it can be appealing to the eye but also now we can hear that it is appealing in the way that it sounds.

The picture here shows a piano piece which is based on the Fibonacci sequence.  The structure of the piece is based on groupings of bars into Fibonacci numbers, which gives the sense of growth of the whole work. The use of only Fibonacci notes works well for harmonious writing. It seems that the Fibonacci sequence works well in music and can sound very appealing to us without even knowing that the numbers are occurring.

Here is an example of the Fibonacci sequence in music. It is very relaxing and even I would listen to this while studying (mainly to keep me calm and distract me from becoming stressed.)

Patterns in Maths and Music

Maths and music are usually seen as two different subjects with no connections, However, it is important that children that children learn that there is a link which can be extremely important.

“Musical pieces are read much like you would read math symbols.  The symbols represent some bit of information about the piece.  Musical pieces are divided into sections called measures or bars.” Music, math, and patterns (no date)

The link between maths and music is patterns! We often look for patterns in maths which links to Ma’s idea of Basic ideas. Patterns in maths is often what children will initially look for which can be seen as a basic idea. This is similar in music as children will hear a pattern in music in repeating choruses and bars. In music, patterns can be recognised in notes. There may be a repeating high or low note throughout a piece of music.

Therefore, I believe that music and maths have a close relationship and children should be made aware of this.

• Gerben Schwab (2012) Fibonacci sequence in music. Available at: https://www.youtube.com/watch?v=2pbEarwdusc (Accessed: 21 November 2016).
• Maths in music: The secret mathematicians (2014) Available at: https://podcasts.ox.ac.uk/maths-music-secret-mathematicians (Accessed: 21 November 2016).
• Music, math, and patterns (no date) Available at: http://mathcentral.uregina.ca/beyond/articles/Music/music1.html (Accessed: 21 November 2016).