As I discovered on Thursday, maths and music have many links, far more than I had previously considered. Seeing myself as reasonably musical, I had not given much thought to linking music with maths and if I’m honest I didn’t know there was such a thing. As a group we were asked to reflect on some of these links, and the first thing that came to me was reading music. Each note has a value depending on how it looks, and we have to assess what each symbol means just like we do with maths (+, x, -, £ etc ). We must also consider the speed and temp of music, tuning, pitch, scales and arpeggios. All of which hold some mathematical substance. In music theory scale is any set of musical notes ordered by fundamental or pitch. Typically scales are listed from low to high pitch.

Scales

We discussed the different types of scales there are in music, again something I had never thought about before this workshop. There is a monotonic scale, consisting of one note, ditonic, tritonic and tetratomic (2, 3, and 4 notes) which is mainly limited to prehistoric music. The pentatonic scale ( also known as the “black note scale”) is 5 notes per octave, which is lacking semi-tones and common in folk music, and I will go into more detail about this later. The Hexatonic scale is 6 notes per octave (you get the idea now…) and is common in Western folk music. The Heptatonic scale is the most common modern western scale and the Octatonic scale is used in jazz and modern classical music.

“The number of the notes that make up a scale as well as the quality of the intervals between successive notes of the scale help to give the music of a culture area its peculiar sound quality.” Nzewi, Meki, and Odyke Nzewi (2007). This quote emphasises the point that different types of scales can create different sounds and vibes, creating genres such as folk, western and classical.

The Pentatonic Scale

Pentatonic scales are found all over the world and are a key part of many, many musical genres, some of which I hadn’t heard of until researching. This is what grabbed my attention the most about the Pentatonic Scale is that it really is everywhere. What really blew my mind was the youtube video we were shown, which involved Bobby McFerrin (Singer of Don’t Worry Be Happy) demonstrating just how powerful and predictable the Pentatonic Scale truly is. In the video he is stood in front of a crowd of people, and he pretty much uses them as his musical instrument. He demonstrates one note to the crowd which they imitate, he then moves up and down the stage, which requires the crowd to sing higher and lower, moving up and down notes. Eventually the crowd are so good at predicting the notes that he manages to get them to sing a tune, all in the space of around 2 minutes.

What I found fascinating about the pentatonic scale is that it is applied within tonnes of popular songs, it is everywhere in music culture no matter what genre. Below is another video that I have found which really emphasises this. It features someone trying to see how many songs they can play using the C major pentatonic scale (notes C, D, E, G, A).  The guy manages to play all sorts of music, songs by  Jimi Hendrix, Drake, Bill Withers, Britney Spears and even nursery rhymes (Mary had a little lamb).

I think the key point I took from this workshop was that maths can be applied in many musical ways. It also made me consider how different mathematical ideas and concepts intertwine in music. Liping Ma’s fundamental principle of mathematics,  interconnectedness, is really highlighted in this topic as it is so crucial as a teacher to reveal connections among mathematical concepts. And this doesn’t just mean within maths itself, hence the musical link. Liping Ma discusses having a profound understanding of fundamental mathematics as “taking something to the most basic principle you can”, which I agree with but I also feel it is about taking maths and stretching it to make links with other subjects like art, music , computing, and in and around everyday life.

References

• Nzewi, Meki, and Odyke Nzewi (2007), A Contemporary Study of Musical Arts. Pretoria: Centre for Indigenous Instrumental African Music and Dance.