Decoding the Sounds: A Journey Through Musical Intervals

Chris Caton-Greasley

5 days ago4 min read

Updated: 2 days ago

Index

Introduction
Ancient Discoveries: Pythagoras and the Perfect Sounds (with Ratios!)
- Examples Perfect 4th & 5th
Building on the Basics: Major and Minor (and More Ratios!)
- Examples Major and Minor Third
Expanding the Family: Major and Minor Scales
What About the 2nd and 7th? (And Their Ratios!)
- Examples Major and Minor Seconds
The Augmented and Diminished: Adding Spice (and Even More Ratios!)
Putting It All Together
Worksheets
- Major and Minor Intervals
Further Exploration

Introduction

Ever wondered why some musical sounds feel happy, sad, or just right? It's all about intervals – the distance between two notes. These tiny gaps of sound have a fascinating history, stretching back centuries! And believe it or not, there's some cool math behind it all!

Let's start with the basics. Imagine the musical alphabet: A, B, C, D, E, F, G. When we play two of these notes together, we create an interval. But not all intervals are created equal! Some sound harmonious, while others clash. Why?

Ancient Discoveries: Pythagoras and the Perfect Sounds (with Ratios!)

Way back in ancient Greece, the philosopher and mathematician Pythagoras discovered something amazing about music. He found that simple ratios between the lengths of vibrating strings created beautiful, harmonious sounds. These special intervals, like the perfect fifth and perfect fourth, became the foundation of Western music.

Here's the mind-blowing part: A perfect fifth, like the interval between C and G, is created by a string length ratio of 3:2. That means if one string is 3 units long, the other string that produces the perfect fifth will be 2 units long. A perfect fourth (like C to F) has a ratio of 4:3. These simple whole number ratios are what Pythagoras considered consonant in sound.

Think of the first two notes of Twinkle, Twinkle, Little Star – that's a perfect fifth! The perfect fourth can be heard at the beginning of the hymn Amazing Grace

Examples Perfect Fourths & Fifths

Building on the Basics: Major and Minor (and More Ratios!)

Centuries later, during the Renaissance, music started to get more complex. Composers wanted to express a wider range of emotions. That's where major and minor intervals came in. Gioseffo Zarlino, an important music theorist from the 16th century, helped solidify the understanding of major thirds and minor thirds.

A major third (like C to E) has a ratio of 5:4, while a minor third (C to Eb) has a ratio of 6:5. Notice how these ratios are a little more complex than the perfect intervals. These more complex ratios are what give major and minor intervals their distinctive color. Major intervals generally sound bright and happy, while minor intervals tend to sound darker and more melancholic. Think of the difference between a major and a minor chord – it's all about the third!

Examples Major and Minor Thirds

Expanding the Family: Major and Minor Scales

Heinrich Glarean, another influential theorist, added even more to our understanding of scales and modes. He formally described the major scale (also known as the Ionian mode) and the minor scale (Aeolian mode). These scales, built from specific patterns of major and minor intervals, became the basis for much of the music we hear today. They are, in essence, a carefully chosen sequence of these specific ratios!

What About the 2nd and 7th? (And Their Ratios!)

You're right to ask about the 2nd and 7th! These intervals are also crucial. The major second (like C to D) has a ratio of 9:8, while the major seventh (C to B) has a ratio of 15:8. The minor second and minor seventh have slightly different ratios, creating their characteristic sound.

Examples Major and Minor Seconds

The Augmented and Diminished: Adding Spice (and Even More Ratios!)

Sometimes, composers want to create tension or surprise. That's where augmented and diminished intervals come in. These are created by slightly widening or narrowing a perfect or major interval, respectively. This changes the ratio slightly, creating a dissonant sound. They add a bit of "spice" to the music, making it more interesting. Calculating the exact ratios for augmented and diminished intervals can get a bit more complex, often involving irrational numbers, but the principle remains the same: a slight change in the ratio creates a noticeable change in the sound.

Putting It All Together

The next time you listen to music, pay attention to the intervals. They're the secret ingredients – and the math behind them is pretty cool too! From the ancient Greeks to modern musicians, the exploration of intervals has shaped the music we love. It’s a fascinating journey through sound, history, and emotion!

Worksheets

Major and Minor Intervals Worksheet

Further Exploration

Look up the Circle of Fifths and how it relates to intervals and ratios.
Explore online resources that demonstrate the ratios of intervals using vibrating strings or other visual aids.
Try playing around with intervals on an instrument or using online music tools to hear the differences in their ratios.