Every input in this module I realise how much math is laced through nearly everything we do. I did not realise how much math interlinked with so many other curricular areas.
“The astronomer Galileo Galilei observed in 1623 that the entire universe ‘is written in the language of mathematics’, and indeed it is remarkable the extent to which science and society are governed by mathematical ideas” (Rosenthal, 2005). This shows how mathematics has been known to run through several different areas for hundreds of years.
Music has always been hugely important to be. I have always sung or been sung too. When you are learning to read music and play an instrument math is not something that you think you are doing anything with. But in fact you are! Apart from the obvious mathematic part of music like how long notes are held for; how many beats are in a bar or how to pitch a piece of music or a song. There are many ways in which maths runs through music in ways you would never realise.
Patterns are an important and huge part of maths as I have already spoken about (see Maths is Pretty!). They are a huge area in which math can be used in the real world. However, math and music can also be linked through patterns. Many different musical pieces are made up of different patterns of notes. These do not tend to be called patterns though as musicians tend to call them motifs, melodies or sometimes rhythmic patterns. Pieces of music consist of these patterns.
Maths also comes into music when you look at octaves. An octave consists of eight notes. Notes are an octave apart when they are the same named note but played in a different frequency. A note played an octave higher is played at double the frequency while a note played an octave lower is half the frequency than the middle note. For example, High C and Middle C are an octave apart but when played together they sound great. This is the same for all notes. Several famous songs play notes together that are an octave apart – the initial “I’m singing” of “Singing in the Rain”; the first two notes of “Somewhere over the rainbow”; and the first two notes of the third line of “Happy Birthday”. (Rosenthal, 2005) This is a perfect example of how these pairs of notes go together.
The Pentatonic scale is made up of five notes. If you are playing a piano these five notes are your black keys. Every piece of music will have these five notes in it somewhere. It is suggested that we are genetically programmed with these five notes just as we are language (Goodall, 2008). These five notes are innate within us. Several famous songs use the pentatonic scale including, “Mull of Kintyre”, “Auld Lang Syne”, “Swing Low” and lots of rock songs use the pentatonic scale in their guitar riffs including “Whole Lotta Love” by Led Zeppella. If you are using the oentatonic scale to write a song you are not just stuck with these five notes but they can be used to develop from.
Bobby McFerrin demonstrates how this scale is genetically within humans.
He does not tell the audience what is the next note to play but they are able to sing the next note in the scale.
The Pentatonic scale is the perfect notes to give children as they will always sound good together no matter what order they are played in. Is that how these five notes become programmed into us? By music teachers who want children to create a nice sounding piece of music, who knows!
Fibonacci Sequence
The Fibonacci sequence (mentioned in a previous post, Maths and Art) can be seen throughout musical sequences as well. Including all notes in an octave there are thirteen. In a scale there are eight notes, the fifth and the third notes make up the basic foundation for the chords. On a piano keyboard scale there are thirteen keys, eight white and five black, these notes are then split into groups of two and three. All of these numbers are from the Fibonacci sequence.
The Golden Ratio and Phi can be seen in music instruments as well. Violins are designed using the golden ratio.
References
K. (2012) Bobby McFerrin demonstrates the power of the Pentatonic scale. Available at: https://www.youtube.com/watch?v=_Irii5pt2qE (Accessed: 13 November 2016).
Rosenthal, J. (2005) The magical mathematics of music. Available at: https://plus.maths.org/content/magical-mathematics-music (Accessed: 13 November 2016).
ScoobyTrue (2008) Howard Goodall on Pentatonic music. Available at: https://www.youtube.com/watch?v=jpvfSOP2slk (Accessed: 13 November 2016).
(No Date) Available at: http://www.goldennumber.net/music/ (Accessed: 13 November 2016).
