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Journey · Music

Why does music sound pleasant?

From vibrating strings to the octave and the ratios of harmony

Steps
4
Total time
1 h 8 min
Simulations
7
Your ear listens not to frequencies but to the ratios between them.

Why is this question interesting?

When you pluck a guitar string, what you hear is the trace left in the air by a string moving back and forth hundreds of times a second. When that trace reaches your ear, it becomes a note. But what makes music music isn't the individual notes; it's how they sit together when they're played at the same time. Some notes sound peaceful side by side, others sound tense. Why?

The journey starts with what sound is: vibration, frequency and amplitude. Then you'll discover why a man and a child singing the same song sound as if they're singing "the same notes": the octave. After seeing the inverse proportion between string length and frequency, you'll arrive at the harmonious ratios the Pythagoreans found with the single-stringed monochord.

In the sound lab you'll set two tones yourself and see how the waves fall into order as the ratio gets simpler. It works with the sound off, too. By the end, you'll be able to explain why a chord sounds pleasant through both physics and culture.

Steps

We suggest going in order; each step builds on the one before. You can try every lesson’s simulation without an account.

  1. Step 115 min

    What is sound? Vibration, frequency and amplitude

    First, sound itself: a string vibrates and the air ripples. Learn to tell frequency and amplitude apart.

    • Sound lab
    • Sorting
    • Mini quiz
  2. Step 215 min

    The octave: why does it sound like "the same note"?

    Double the frequency and the same note sounds higher. See that your ear is sensitive to ratios.

    • Sound lab
    • Number line
    • Mini quiz
  3. Step 320 min

    Inverse proportion

    The shorter the string, the higher the frequency. Get to know the maths of inverse proportion, the key to harmony.

    • Number line
    • Mini quiz
  4. Step 418 min

    Why does harmony sound pleasant? Simple ratios and the monochord

    A perfect fifth is 3:2, a perfect fourth 4:3. Use strings and waves to test why simple ratios sound pleasant.

    • Sound lab
    • Mini quiz

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