The method for learning music through mathematics

BarcelonaWhen we talk about Pythagoras, the first thing that probably comes to mind is the theorem that bears his name, one of the discoveries this Greek philosopher and mathematician of the late 6th century BC made during his lifetime. But he made quite a few more. He was also the first to relate music to numbers, which led him to identify mathematical patterns in music. So, it's not so strange that these two fields are linked.

In fact, if we bring this to the present day, the 21st century, this is what Play Nuzic encourages us to do: a new educational methodology that allows students to understand and create music through mathematical thinking. "It occurred to me that the world of science and numbers could be combined with the world of music and the arts, and that they could help each other," says Mauricio Villavecchia, composer, music educator, pianist, and the ideologue and driving force behind Play Nuzic. This tool, originally designed for schools—but now open source and therefore available to everyone at Playnuzic.com—allows young people to learn music using numbers and simple mathematical operations.

Villavecchia asserts that musical knowledge is unnecessary to learn how to work with music, or even to compose musical pieces. The idea she wants to convey through this tool is that music can be understood and experimented with through numbers, a language students already know and use regularly in the classroom, and that they can see how the operations they perform have a musical reflection. "For example, each note has a number, and there's a distance between one note and another. Students can calculate the movement of notes within a melody because melodies arise from a series of mathematical operations. That is, you add or subtract numbers, and the melody rises or falls," Villavecchia explains, describing one of Play's capabilities. On the website, you'll find the available options and can choose the one you want to work with: rhythm, melody, time signature, duration, interval, and composition.

For months now, Villavecchia and her team have been conducting workshops in various schools to demonstrate how this application works and all it can offer, so they can integrate it as another tool within their institutions. "We begin the workshops with physical and perceptual exercises. Then, we have them work on paper to understand how the system works, and subsequently, they work with the application and create compositions that they then share with each other. We want them to work as a team, give their opinions, and reach a consensus on what they've created," explains Villavecchia, who is more analytical. "Ultimately, the application is the tool that allows us to understand the entire system and hear the results obtained right there in the workshop," she says. She also acknowledges that sometimes the first thing they've done with the students has been to find the formula for the reggaeton rhythm.

A complementary methodology

One of the centers where Play Nuzic workshops have been held is the Oriol Martorell Artistic School Institute in Barcelona. The workshops were offered to second-year ESO (secondary school) music and dance students. Although they normally study the subjects together, in this case they did so separately. "The dance students found it very interesting and were able to see the results immediately. The music students, who have a higher level in this area, understood everything right away, because they were essentially talking about the same thing but using different languages. The truth is that learning and understanding music from another perspective was very enriching for them," says Sergi Pasgi. Pascual affirms that this tool allows students to see music in a different, more holistic way, outside of classical musical language. "It's very intuitive, very fast, and direct. Both students and teachers really liked the approach, which they have already used in their regular classes."

Rich, multi-layered, complex, and creative enough to be useful for consolidating abstract mathematical learning. This is how Joan Pedroche, director of the Institute of Audiovisual and Performing Arts Techniques of Barcelona (Itaeb), sees this methodology. He witnessed the initial genesis of this initiative some years ago, when it was just beginning to take shape, which is why he readily agreed when they proposed a workshop to demonstrate its potential at the center he now directs.

"We have a technology-focused high school program, but very much geared towards audiovisual media, and with a student profile that has a strong affinity for music production, the world of electronic music, and all aspects of audiovisual language. Therefore, we offered our students as a testing ground, since they have a faster capacity for understanding." And the experience was very positive. They were able to create music in an innovative way while working with patterns, geometry, and fractions.

The experience isn't limited to simply learning to make music with numerical operations; the tasks students complete also help them become more adept at math. "It activates a part of their mathematical logic that complements what they've been working on in class and what we've always explained to them about fractions, for example, through rhythmic patterns. I think this opportunity offered by the app to consolidate mathematical learning that might be somewhat abstract is fantastic," adds Pedroche. Villavecchia confirms that the reception of Play Nuzic by both students and teachers has been very positive and encourages them to continue. In fact, they are working with the Barcelona Education Consortium to help them connect with schools and start these workshops in primary school. "We started with middle school and the first year of high school, but we see that it can also be very interesting in elementary school. They're younger, but they're also more open. Another element of Play Nuzic is that it's very playful. Numbers might seem very serious, but they're also used in games."