How Music and Math Intersect: A Simple Guide to Note Values, Intervals, and Tempo Ratios (E37)

2 Shares

Exploring the Connection Between Music and Math in Homeschool Education

Today, we’re delving into an intriguing topic that combines two seemingly different subjects: music and math. At first glance, these disciplines may appear worlds apart, but they share a significant amount of common ground. From rhythm and fractions to scales and ratios, the mathematical foundations in music can enhance our understanding and appreciation of both subjects.

How Music and Math Intersect: A Simple Guide to Note Values, Intervals, and Tempo Ratios

Rhythm and Fractions

One of the most straightforward connections between music and math is rhythm. If your child has ever clapped along to a song or learned about different note values like quarter notes, half notes, and whole notes, they’ve already started to understand fractions. Think about it: a quarter note is a quarter of a whole note, and a half note is half of a whole note. This rhythm-based counting is a fun and intuitive way to introduce the concept of fractions, one of the foundational ideas in elementary math.

As children progress in their music lessons, they learn to combine these note values into increasingly complex rhythms. For example, a measure may contain a mix of quarter and eighth notes, requiring the child to fit these fractions into the whole measure. This is math disguised as play. Pieces like Steve Reich’s Clapping Music and Beethoven’s Symphony No. 7 second movement are excellent examples to help your children understand fractions of a beat through engaging rhythms.

Tempo and Ratios

Another fascinating intersection between music and math is in the concept of tempo, which is the speed of music measured in beats per minute (BPM). Discussing tempo changes introduces your child to the idea of proportionality, a key concept in mathematics. For example, if a piece of music is played at 60 bpm and then doubles to 120 bpm, it creates a 2:1 ratio.

Using a metronome, you can illustrate this by setting it to 60 bpm and then doubling it to 120 bpm to hear the changes. Classical compositions often incorporate different tempos to create contrast and excitement. For instance, Johann Sebastian Bach’s Brandenburg Concerto No. 3 has clear tempo markings for each movement, making it easy to compare and contrast the tempo relationships. And, you’ll want to listen to Ravel’s Bolero, where the tempo remains steady throughout the entire piece, and it’s the orchestration (different instruments playing) that make us feel it’s growing and changing.

Scales, Intervals, and Frequency Ratios

Looking at scales, intervals, and frequency (pitch) ratios is where music and math truly converge. A scale is a series of notes ordered by pitch, and the distance between two notes is known as an interval. These intervals can be described mathematically through frequency ratios. For instance, the octave is a well-known interval where the frequency of the higher note is exactly double that of the lower note, forming a 2:1 ratio.

The Western system divides an octave into 12 equally spaced notes, rooted in a complex mathematical relationship. Ancient Greek philosopher Pythagoras was one of the first to study how musical intervals relate to simple numerical ratios, leading to Pythagorean tuning.

To explore intervals and scales, you can listen to pieces like Bach’s Prelude and Fugue No. 1 in C Major or Mozart’s Eine Kleine Nachtmusik, which highlight the intervals between notes.

Pythagorean Tuning Systems

Pythagoras’s exploration of musical tuning reveals an important historical connection between music and mathematics. He discovered that musical intervals like the octave, the fifth, and the fourth could be expressed in simple numerical ratios. Pythagorean tuning uses these ratios to create harmonious sounds, offering a clear and practical example of math in action. For instance, the perfect fifth corresponds to a 3:2 ratio, meaning the frequency of the higher note is 1.5 times that of the lower note.

To hear this in action, you can listen to some Gregorian chant music. For a more contemporary example, try “Fantasia on a Theme by Thomas Tallis” by Ralph Vaughan Williams. This piece makes use of the kind of harmonic structures that Pythagoras studied, and you can hear the way the notes blend together through the mathematical relationships of their frequencies.

Conclusion of Math and Music

As a homeschooling parent, you have a unique opportunity to seamlessly integrate music and math into your child’s education. By learning about rhythm, tempo, scales, and intervals, you can make both subjects more engaging.

For more resources to help you learn about these topics, see below:

In the printable set Learn About Music Intervals kids will learn the intervals for basic music theory: perfect unison, major second, major third, perfect fourth, perfect fifth, major sixth, major seventh, and perfect octave.

In the printable set Music and Math kids see note and rest “trees” to visually picture how they subdivide from whole to half to quarter to eighth to sixteenth. Then, there are six worksheets with answers for a total of 14 pages.

Beginning Rhythm Counting with Flashcards contains 14 pages for learning to count rhythms for beginners. Learn quarter note, quarter rest, half note, half rest, eighth note, eighth rest, 2 eighth notes, whole note, whole rest, and dotted half note.

The printable set Beginning Rhythm Counting with Flashcards contains 14 pages for learning to count rhythms for beginners. Learn quarter note, quarter rest, half note, half rest, eighth note, eighth rest, 2 eighth notes, whole note, whole rest, and dotted half note.

See the YouTube Video “How Music and Math Intersect: A Simple Guide to Note Values, Intervals, and Tempo Ratios” here:

Listen to the Podcast Episode “How Music and Math Intersect: A Simple Guide to Note Values, Intervals, and Tempo Ratios”:

Listen here or subscribe and follow The Music in Our Homeschool Podcast through your favorite podcast app, such as Apple Podcasts or Spotify!

Read the Podcast Transcript here.