37: How do Music and Math Relate: Help Your Homeschooler Learn about Note Ratios, Tempo, Beats Per Minute, Intervals, and Pythagorean Tuning!

Welcome to the Music in Our Homeschool podcast, your ultimate resource for integrating a rich and affordable music education into your homeschooling journey. Hosted by Gena Mayo, a homeschooling mom of 8 and an experienced music teacher, our podcast delves into the profound connections between music and math.

Today, we uncover how musical concepts like rhythm, tempo, scales, and tuning intertwine with fundamental mathematical principles. From understanding fractions through note values like quarter notes and half notes, to exploring ratios and proportionality through tempo changes and scales, we make the seemingly complex relationship between music and math both accessible and enjoyable. We offer practical insights and classical music examples, like Steve Reich’s "Clapping Music" and Beethoven’s Symphony No. 7, to help you demonstrate these connections to your children in a hands-on way.

Our podcast doesn't stop at the basics. We also dive deep into historical perspectives, bringing to light how ancient mathematicians like Pythagoras have influenced modern tuning systems with concepts like Pythagorean tuning and frequency ratios. 

The Music in Our Homeschool podcast has episodes tailored for homeschooling families where you'll gain valuable tools and resources that engage students of all ages, making your homeschool experience more holistic and enriching!

Whether you're new to homeschooling or are looking to add a new dimension to your existing curriculum, this podcast provides a treasure trove of strategies, activities, and lessons that weave together the fabric of music and education. Don't miss an episode — subscribe now and explore our show notes for additional resources. Share the podcast with other homeschooling families to build a community that celebrates the joy of learning through music.

Tune in to cultivate a harmonious blend of music, math, and homeschooling, and keep the music alive in your educational journey!

Head here to find all musical pieces, links, and resources mentioned in this episode:  https://musicinourhomeschool.com/music-and-math

Please follow/subscribe to the podcast and leave a 5-star review and comment if you liked this episode! Find all courses at https://Learn.MusicinOurHomeschool.com ,free music lessons here: https://MusicinOurHomeschool.com/FreeMusicLessons , and lots more links here: https://linktr.ee/genamayo !

Transcript

Music and math relate podcast

[00:00:00] Welcome to another episode of Music in Our Homeschool, where we explore the powerful connections between music and education. I'm your host, Gena Mayo, and today we're going to be talking about how music and math relate. At first glance, music and math may seem like two totally different subjects, but they actually share an incredible amount of common ground. From rhythm and fractions to scales and ratios, music is filled with mathematical concepts that not only help us appreciate music, but also strengthen our understanding of math. Today, we'll discuss these connections, and I'll share some classical music examples that you can use with your children to bring these ideas to life.

Rhythm and fractions. So one of the most straightforward connections between music and math is in rhythm. If your [00:01:00] child has ever clapped along to a song or learned about different note values like quarter notes, half notes, and whole notes, they're already starting 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 kind of rhythm-based counting is fun and an intuitive way to introduce the concept of fractions, which is one of the first big ideas in elementary math. As children progress in their music lessons, they learn how to combine these note values to form increasingly complex rhythms.

For instance, a measure may contain a combination of quarter and eighth notes. And as your child has to think about how to fit these fractions into the whole measure, that's math disguised as play.

To demonstrate rhythm and fractions, you can use "Clapping Music" by Steve Reich. He's a minimalist composer. And while this piece is more [00:02:00] modern than traditional classical music, it uses a very clear pattern of clapping in different rhythmic phrases, which is excellent for helping your children understand fractions of a beat.

Or you could listen to Beethoven's Symphony No. 7, the second movement. In this piece, the rhythmic pulse is very strong and repetitive, and that makes it easy for children to understand how different note lengths come together.

Another way to understand how music and math relate is in tempo and ratios. Tempo is the speed of the music, which is often measured in beats per minute, or BPM. When we talk about tempo changes, we're often dealing with ratios. For example, if a piece of music is played at 60 BPM and the tempo doubles to 120 BPM, we have a two to one ratio. This concept of doubling or "halving" tempo introduces your child to [00:03:00] the idea of proportionality, which is a key concept in mathematics. 

Let me encourage you at this point, if you have a metronome to go ahead and take it out and set it to 60 BPM and then change it to 120 BPM, and you can hear the doubling of the beats per minute. You can also find a. metronome online or through an app if you don't have the physical metronome. 

So I encourage you to talk with your child about tempo relationships within a piece of music. In many classical compositions, different sections of music may have different tempos. And composers use these changes to create contrast and excitement.

These tempo changes are often proportional, making it easy to point out the math at work. A wonderful piece to demonstrate tempo and ratios is Johann Sebastian Bach's Brandenburg Concerto No. 3, which has [00:04:00] clear tempo, markings for each movement. You can compare and contrast the different movements, especially the lively quick Allegro tempo in the first movement and how much faster it feels than the slower movements.

Another example for tempo is Maurice Ravel's Bolero. In this piece, the tempo remains steady, but as the orchestration becomes more complex, you can talk about how maintaining a constant tempo can still create a sense of growth and expansion in the music by what's happening with the instruments. 

All right, now let's move on to another mathematical concept in music, which is scales, intervals, and frequency ratios.

This is where music and math really meet. A scale is a series of notes ordered by pitch, and the distance between two notes is called an interval. [00:05:00] These intervals can be described mathematically through frequency ratios. One of the most well known intervals is the octave. If you play one note on the piano, for example, and the same note an octave higher, counting up eight notes on the keyboard, the frequency of the higher note is exactly double that of the lower note. That gives us a 2 to 1 ratio. 

But the mathematical structure of music goes even further. In the western system, we divide an octave into 12 equally spaced notes, a concept rooted in a complex mathematical relationship. This idea has been explored since ancient times, with the Greek philosopher Pythagoras being one of the first to study how musical intervals relate to simple numerical ratios. His work led to the development of Pythagorean tuning, an early system of tuning instruments based on mathematical [00:06:00] ratios. 

So to explore intervals and scales, try listening to Prelude and Fugue No. 1 in C major from Bach's The Well Tempered Clavier. This piece is written in C major, one of the most straightforward scales. If you played a C major scale on the piano, it would be just the white keys. And you can easily hear the relationship between the different notes. 

Another excellent piece to listen to is Mozart's Eine kleine Nachtmusik, and you can hear the intervals between the notes in that melody.

Finally, let's talk about Pythagoras and tuning systems. 

Speaking of Pythagoras, his exploration of musical tuning brings us to an important historical connection between music and math. Pythagoras discovered that musical intervals, like the octave, or the fifth, or the fourth, can be expressed in simple numerical ratios. This insight formed the foundation for many of the [00:07:00] tuning systems used in Western music. The concept of tuning is a great way to introduce kids to the idea of ratios and proportions because it shows how math can affect something as everyday as the sound of an instrument. 

For example, in Pythagorean tuning, the interval of 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. By using these ratios, musicians can tune their instruments to create harmonious sounds. This is a clear and practical example of math in action. 

However, I will say that most musicians do not use ratios when they're tuning. They simply use either their ear or a tuner.

As you can see, music and math are deeply connected. From rhythm and tempo to scales and tuning, math plays a critical role in shaping the music we hear and enjoy. 

[00:08:00] As a homeschooling parent, you have a unique opportunity to help your child see these connections in a fun and engaging way. Next time you're working on math, consider adding a little music to the mix. Whether you're clapping out rhythms, exploring scales, or comparing tempos, you're helping your child to understand both subjects in a deeper and more integrated way. 

Head over to the blog post that I share in the show notes and description of this episode, and you will find some resources to help you learn more about intervals and rhythms and tempos and the pieces that were spoken about today.

Thank you for tuning into this episode of Music in Our Homeschool. Be sure to subscribe and share this episode with other homeschooling families. And as always, keep the music alive.

Head here to find all musical pieces, links, and resources mentioned in this episode: https://musicinourhomeschool.com/music-and-math