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three apples

Math and Music


By: Mia Daucourt

If you have ever salted a Granny Smith apple, you know that sometimes unexpected things go together. Surprisingly, the salt helps ease some of the sourness and makes the apple sweeter. The finding that math and music achievement are related may be equally surprising, but a recent study by Barroso and colleagues (2019) found that, like salt and Granny Smith apples, math and music are also complementary. Using a sample of 230 incoming freshman undergraduate music majors, they found that math skills are important for music theory achievement. Music theory is the study of the structure of music, and several music theory courses are required for all accredited university music programs. Music theory goes beyond being able to read music with different melodies, key signatures, rhythms, and meters. Instead, just as its name suggests, music theory a way of structuring music in a theoretical framework, which involves learning new terminology, concepts, and constructs. This is where the overlaps between music theory and math class come into play, because even once you know how to recognize and combine numbers, math learning still involves learning new concepts, ideas, and vocabulary. You need to know more than just the basics.

The researchers conducted a dominance analysis, which is a statistical technique for picking the top predictors out of a big combination of potential predictors for an outcome of interest. Predictors are simply assessments that help you accurately anticipate (i.e., predict) an outcome. Dominance analysis uses an algorithm to run through every individual predictor and every possible combination of predictors (yay for machines making things quick and easy!) to choose the best final set of predictors, based on the portion of an outcome those predictors can anticipate. The analysis also accounts for how many separate assessments (or predictors) you are including to make sure you only keep the most important predictors and drop the rest. In this case, there were two outcomes, end-of-the-year grades in Music Theory I and end-of-the-year grades in Music Theory II. Basically, the measures that explain the biggest chunk of the music theory grade pie will be the ones that are chosen by dominance analysis, and the ones that don’t explain a big enough unique sliver of the pie will be dropped. Yum, a Granny Smith apple pie sounds good, but let’s get back to Barroso and colleagues’ study!

There were many different potential assessments included in the dominance analysis in order to try to explain the biggest chunk of the music theory grade pie. Also, the reason they included two music theory grades was so they could determine if different skills mattered for early music theory classes in comparison to later music theory classes. The predictors included assessments of music theory skills and attitudes and math skills and attitudes. There were two music theory measures; one tapped into the students’ background knowledge of music theory and the other measured their ability to apply music theory concepts to new problems. They also measured music theory experience, the level of confidence the students had in their music theory skills, and their anxiety toward music theory. For math, they included standardized math test scores, a measure of statistical numeracy skills, and a measure of spatial skills. They also included measures of math experience with college-level math courses, the students’ confidence in their math skills, and their anxiety toward math. Finally, they also included a measure of reading comprehension, which measures how well a person understands the meaning of what they read, in case reading ability was more important for music theory achievement than math ability.

Overall, the researchers found that ACT math scores, which capture math aptitude, or a person’s potential to solve math problems and do well in math, and how confident students were in their music theory abilities were important predictors their final grades in both Music Theory I and Music Theory II. That means that whether or not you already have any formal music theory experience, your math aptitude and confidence in your music theory ability are going to serve you well in music theory class. In addition to the aptitude-based math skills captured by the ACT math, it turns out that aptitude‐based music theory skills are also important for Music Theory I grades. Then, for Music Theory II, which comes after students already have some music theory experience through their Music Theory I course, the researchers found that the more math courses a student has completed the better the student will score in their final Music Theory II grade.

This study was important for helping explain the most important predictors of the music theory grade pie, and it showed that both aptitude and attitude are important for music majors to excel in music theory classes. It’s not just having the skills, but also having the confidence in your abilities that makes a difference in doing well in music theory classes. Also, just as salt unexpectedly makes a Granny Smith apple sweeter, math unexpectedly helps students excel in their music courses.


Citation: Barroso, C., Ganley, C. M., Hart, S. A., Rogers, N., & Clendinning, J. P. (2019). The relative importance of math‐ and music‐related cognitive and affective factors in predicting undergraduate music theory achievement. Applied Cognitive Psychology, 33, 771-783.