Connection Between Math and Music

Students can learn much more efficiently when the curriculum material becomes relevant to their interests and their daily activities.  When students can make connections between different subjects, their learning becomes more meaningful and long lasting.  For all of those musically intelligent learners in your math classes, here I will outline some of the numerous connections between music and mathematics.

In my experience with school music, a high number of music students excel in the areas of math and science.  I have since sought out information on the topic and have found that several studies show a connection between music education and the development of mathematical skills.  In each the three studies listed below, the authors found significant correlations between years of musical training and children’s spatial-temporal processing.  Spatial-temporal processing is responsible for the development of logic and mathematical skills.  In these studies children who were musically trained from a young age showed increased development in the brain areas that correlate to spatial-temporal reasoning than those who did not receive musical training. For more information on these studies, see the following citations:

•           Hyde, K., Lerch, J., Norton, A., Forgeard, M., Winner, E., Evans, Al, et al. (2009). Musical training shapes structural brain development. The Journal of Neuroscience, 29 (10), 3019-3025.
•           Rauscher, F., and Zupan, M. (2000). Classroom keyboard instruction improves kindergarten children’s spatial-temporal performance: a field experiment. Early Childhood Research Quarterly, 15 (2), 215-228.
•           Schmithorst, V., and Holland, S. (2004). The effect of musical training on the neural correlates of math processing: a functional magnetic resonance imaging study in humans. Neuroscience Letters, 354 (3), 193-196.

Mathematical relationships are also fundamental to music itself.  Every piece of music is made of notes and melodic lines that are dictated by the intervals between each note; the mathematical distances between each pitch.  Different notes are distinguished by the differences between their frequencies.  The musical scale is made up of eight notes, which are related by the ratio between their frequencies.  For example, a G and a D are a musical distance of a “perfect fifth” apart, which vibrate at frequencies at a ratio of 3:2.

Musical rhythm also demonstrates a mathematical relationship.  Notes and chords in a song make up different beats which each denote fractions in time.  Musical notation shows these different rhythms, and each symbol represents a note as a different fraction of time within the piece as a whole.   Music is also ridden with patterns and repetition that can be decoded and analyzed.  Musical chords are notated using numbers and roman numerals, and all songs can be described according to a specific functional form.  Musical form is determined according to the patterns of repetition between chords, cadences, and musical sections.

In modern classical music, 12-tone composition has become quite popular, which is a completely mathematical mode of composition.  In 12-tone music, the composer creates a pattern of notes using each of the 12 tones used in Western music.  This “tone row” (pattern of 12 tones) gets repeated over and over for the entirety of the piece, which creates a very mechanical sounding work of art.  For an example of a 12-tone composition, follow this link: http://www.youtube.com/watch?v=xrjg3jzP2uI

I have outlined several connections between music and mathematics.  I think that math can be found in all areas of life, and should be pointed out to students to make their education relevant.  Can you think of connections between mathematics and other school subjects?