There’s a link between music, maths and our emotions. How can this be and why do major chords in songs make us happy? This is what I am going to explore in this blog post!

The links between maths and music:

• beats (the value of each note)
• timings
• rhythm
• string numbers
• if you are changing key, you go up or down
• scales: scales follow the same pattern, no matter what note
• tempo: speed of the music (metronome)

Music makes us happy. I don’t know about you but I love listening to music and it makes me feel better no matter what mood I’m in. Kim (2015) states that the Feel Good Index (which is an equation itself) is the “… sum of all positive references in the lyrics, the song’s tempo in beats per minute and its key.” Having a fast tempo in a song makes us want to dance, we want to move and it makes us happy. Apparently this is because “Beats automatically activate motor areas of the brain.” Fernández-Sotos, Fernández-Caballero  and Latorre (2016) also agree that the tempo impacts whether the music makes us happy or sad.

However, sad music can make us happy. Sometimes I’ll be in the mood to listen to sad and slow songs but they make me happy however, this contradicts what is said above? The lyrics are sad, not pleasant. This is because whilst the emotion of sadness is seen as negative, in artistic form, sadness can be felt, sensed or understood differently. Therefore, songs that are in a minor key which are identified as being sad songs do not always cause a negative emotion (Kawakami et al. (2013, pp. 1-2). Personally I think the reason for this is more than just the links to the maths behind the music such as a slower tempo or a minor key. It’s also because we connect with the feeling, the emotion through the song or lyrics and this connection is pleasant to us (Nield, 2016). The emotions are caused as the music brings back previous experiences that can make us happy or sad. (Konečni, 2008, cited in Hunter, Schellenberg, and Schimmack, 2010, p.54).

Additionally, why do certain pop songs in the charts make us feel happy because their tempos are fast, around 116 beats per minutes and have a major third musical key (Kim, 2015)? You might be thinking, what does music have to do with maths? Well, music is made up of “…pleasurable patterns of rhythm, beat, harmony and melody” (Gupta, 2009). If you are still asking what do tempo and beats have to with music well, according to Fernández-Sotos, Fernández-Caballero and Latorre (2016),

Tempo is “…the speed of a composition’s rhythm, and it is measured according to beats per minute.”  

“Beat is the regular pulse of music which may be dictated by the rise or fall of the hand or baton of the conductor, by a metronome, or by the accents in music.”

So, what makes a pop song catchy? Why do we enjoy hearing the next new hit song on the radio and want to sing and dance along? The University of Bristol asked the same questions. They formed a mathematical equation to work out what makes a popular song popular. They created a diagram to compare pop songs patterns. The coloured parts of it represented beats and the connections seen in the diagram were sections of music that join. What they found was that many pop songs had a very similar pattern Seeker (2014).

A drawback to the equation that The University of Bristol developed (which they recognise themselves), is that it will need adapted as what becomes popular changes since, over time the songs that have become popular are ones that are getting louder (University of Bristol, 2017). Why is it that what is popular changes over time?

Why do these pop songs make us feel good? In one of my previous posts (Noble, 2017), I talked about how according to Burkeman (2011) gambling is satisfying as we are addicted to the potential of getting a reward and the satisfaction is due to the chemical dopamine being released (How the Brain Gets Addicted to Gambling, 2017). This same chemical is released when we listen to these pop songs therefore, making us feel satisfied, please, happy and feel good. However, why do we not get bored of these songs? In the video linked below it demonstrates how a lot of the famous pop songs are repetitive, they use the same four chords (random804, 2009).

So, we seem to be  satisfied by the same types of songs. These songs that are popular, are popular because they fit “[I]mplicitly learned patterns…” or their patterns only differ by a slight bit (Wheatley, no date, cited in Hughes, 2013). This slight difference must be what keeps us satisfied as we would be bored if it was the exact same every time.

Critically, maths can be non-existent in music according to Sangster (2017). For example, every pitch has a different frequency but a piano note can’t be tuned to the exact frequency that it mathematically should be or it doesn’t sound right musically. This is where maths cannot be applied to music. This video below demonstrates why it’s impossible to tune the piano notes to the exact mathematical frequency although it demonstrates why this is so using maths (Minutephysics, 2015).

In the future, I would like to apply my knowledge and understanding of how maths underpins music to teach pupils about maths. Pupils could make their own short songs, using their maths skills such as counting, timings, rhythms and beats! This would be a fun activity showing the relevance that maths has in the wider environment and in everyday society.

In conclusion, maths is behind music. Music is composed by using basic concepts in maths such as the speed of the music, timings and counting the beats per minute. In order to count beats, people need to know how to count in a sequence, and how long a minute is. All these basic concepts are put together and built upon to make music over a long period of time. All of which relate to what Ma (2010, p. 104) says are the principles of fundamental mathematics. Furthermore, the type of music that is produced from using and building upon all these basic mathematical concepts can have an affect on peoples emotions, making them either happy or sad and formulas can even be created to determine or predict what songs will be big hits!

List of references:

• Burkeman, O. (2011) ‘Can ‘intermittent variable rewards’ help you become addicted to more positive behaviours?’, The Guardian, 23 April. Available at: https://www.theguardian.com/lifeandstyle/2011/apr/23/this-column-change-life-random-rewards (Accessed: 12 October 2017).
• Fernández-Sotos, A., Fernández-Caballero, A., and Latorre, J.M. (2016) Influence of Tempo and Rhythmic Unit in Musical Emotion Regulation. Available at: https://www.frontiersin.org/articles/10.3389/fncom.2016.00080/full (Accessed: 6 November 2017).
• Gupta, A. (2009) ‘The interesting connection between math and music’. Vancouver Sun, 4 September. Available at: http://www.vancouversun.com/Entertainment/interesting+connection+between+math+music/1473881/story.html (Accessed: 6 November 2017).
• How the Brain Gets Addicted to Gambling (2017). Available at: https://www.scientificamerican.com/article/how-the-brain-gets-addicted-to-gambling/ (Accessed: 12 October 2017).
• Hughes, V. (2013) ‘Why Does Music Feel So Good?’ National Geographic, 4 November. Available at: http://phenomena.nationalgeographic.com/2013/04/11/why-does-music-feel-so-good/ (Accessed: 6 November 2017).
• Hunter, P., Schellenberg, G., and Schimmack, U. (2010) ‘Feelings and Perceptions of Happiness and Sadness Induced by Music: Similarities, Differences, and Mixed Emotions’, Psychology of Aesthetics, Creativity, and the Arts, 4(1), pp. 47-56. Available at: http://www.erin.utoronto.ca/~w3psygs/HunterEtAl2010.pdf (Accessed: 9 November 2017).
• Kawakami, A., Furukawa, K., Katahira, K.,  and Okanoya, K. (2013) ‘Sad music induces pleasant emotion’, Frontiers in Psychology, 4(311), pp. 1-15. Available at: https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&ved=0ahUKEwi6qfPf37HXAhUIAsAKHWK_CR4QFggoMAA&url=https%3A%2F%2Fwww.frontiersin.org%2Farticles%2F10.3389%2Ffpsyg.2013.00311%2Fpdf&usg=AOvVaw2FbY5C0IfcYqmIOVC6HeJ4 (Accessed: 9 November 2017).
• Kim, M. (2015) ‘The secret math behind feel-good music’, The Washington Post, 30 October. Available at: https://www.washingtonpost.com/news/to-your-health/wp/2015/10/30/the-mathematical-formula-behind-feel-good-songs/?utm_term=.fc03365dc08a (Accessed: 6 November 2017).
• Ma, L., (2010) Knowing and teaching elementary mathematics (Anniversary Ed.) New York: Routledge.
• Minutephysics (2015) Why It’s Impossible to Tune a Piano. Available at: https://www.youtube.com/watch?v=1Hqm0dYKUx4 (Accessed: 6 November 2017).
• Nield, D. (2016) Here’s Why Listening to Sad Music Makes You Feel Better. Available at: https://www.sciencealert.com/new-research-reveals-the-pain-and-pleasure-of-listening-to-sad-music (Accessed: 9 November 2017).
• Noble, R. (2017) ‘Win with maths?’, My teacher journey, 17 October. Available at: https://blogs.glowscotland.org.uk/glowblogs/rsneportfolio/2017/10/17/win-with-maths/ (Accessed 6 November 2017).
•  random804 (2009) Axis of Awesome – 4 Four Chord Song (with song titles). Available: https://www.youtube.com/watch?v=5pidokakU4I (Accessed: 6 November 2017).
• Sangster, P. (2017) Discovering Maths: Music and Mathematics. [Lecture to Discovering Mathematics Year 2], ED21006: Discovering Mathematics (year 2) (17/18). University of Dundee. Day and month
• Seeker (2014) The Formula Behind Every Perfect Pop Song. Available at: https://www.youtube.com/watch?v=vswg-xXMAys (Accessed: 6 November 2017).
• University of Bristol (2017) Can science predict a hit song? Available at: http://www.bristol.ac.uk/engineering/departments/engineering-mathematics/research/highlights/scoreahit.html (Accessed: 6 November 2017).