Count on Music for Math Fun By Catherine Schmidt-Jones
This is just one of the excellent articles in Homeschool.com’s newest e-magazine.
Many people consider music to be too fun and interesting to count as “serious” learning, while at the same time considering math to be a necessary but uninteresting subject. Actually, music and math are closely related in many ways, and lessons that combine the two are not only fun and interesting; they also help to strengthen and deepen understanding of both subjects. The activities and lessons suggested below range from elementary-level arithmetic and basic musical concepts to advanced math and music studies suitable for teens.
Think you don’t know enough to lead a music lesson? The suggestions are explained and designed so that you don’t need to be an expert. In fact, music is a great subject to learn about together as a family, and while “playing math” with your kids, you may discover that you’d like to learn more about music yourself!
I Got Rhythm
A wide variety of real-world examples helps to build understanding of basic math concepts such as multiplication, division, and fractions. Fractions, Multiples, Beats, and Measures in particular engages auditory and kinesthetic learners. Introduce it alongside math manipulatives and visual examples, or use it alone to help beginning musicians develop a feeling for rhythm and meter.
Conducting Activities and Musical Meter Activities also help beginning musicians to internalize that divided-into-equal-parts concept that is so crucial both to music and to fractions, or they can simply be used as fun counting activities and general introductions to what musicians do.
Get Ready, Get Set . . .
Sets are a fundamental math concept; keys and scales are fundamental music concepts. Put them together and you can use intersections of sets to demonstrate that keys and scales are sets of notes, and to explore how closely any two keys are related to each other. Keys and Scales are Sets provides hands-on practice with set theory, as well as an introduction to the musical concepts of keys and scales. To focus on math understanding, use this activity along with other visual and hands-on demonstrations of sets. To focus on music-theory understanding, extend it to explore the scales, keys and pieces that your young musician is working on.
The Powers of Music
How high or low is a sound? Engineers and scientists talk about frequencies, while musicians talk about pitch. The relationship between pitch and frequency is not a simple, linear correspondence, so translating between the two requires some math! This is a subject that will fascinate teens who are interested in science or engineering, and can be of practical use for anyone interested in music or audio recording.
To understand the relationship between frequency and pitch, math concepts such as ratios, powers and roots are needed. Musical Interval, Frequency, and Ratio explains the basic relationship between frequency and pitch, and provides some examples and practice of the math concepts. There are also websites that will “play” any frequency that you request, which can be a great resource for “hands-on” explorations and demonstrations.
Another real-world exploration involves equal temperament, which is the tuning system that determines the exact pitches for pianos and many other instruments. In equal temperament, the difference in pitch between one note and the next-higher note is always the same. But the difference in frequency changes, getting bigger as the notes get higher. It takes an understanding of powers and roots to calculate the correct frequencies of equal-temperament notes. Those interested specifically in exploring equal temperament and other tuning systems can learn about the math involved in Powers, Roots, and Equal Temperament.
Count on Music Theory
If you happen to have a budding musician in the household, consider adding music theory to the curriculum. It opens a pathway to enjoyable skills, such as improvising, composing, and arranging music. In addition, music theory is based on the patterns that repeat across all keys, and it often uses numbers to keep track of the notes and chords within those patterns. So using music theory to practice those enjoyable skills also means using numbers and patterns to engage in creativity!
You may have to request it, but music theory can be included in music lessons, youth music programs, or music camps. Signing up for a course focused on music theory, through a local junior college or an online curriculum, may be an option for you. There are also open and free music-theory courses and texts online, such as Understanding Basic Music Theory.
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