Ratios
Listen to musical intervals and see their frequency ratios
Connect what an interval sounds like with its numerical ratio and visual pattern. Compare simple ratios with small tuning differences.
Key idea
A frequency ratio describes an interval independently of its register. Multiplying both frequencies by the same factor preserves the ratio. Simple integer ratios also produce wave patterns that repeat after a shared interval of time.
Try this first
Compare the ratio 2:1 with 3:2. Listen to the octave and fifth, then watch their wave and geometric relationships. Make a small tuning adjustment and notice how a nearly simple ratio behaves differently from the exact relationship.
How to get started
- Pick a ratio or type your own.
- Press play to hear the interval.
- Watch the curves it draws in 2D and 3D.
Explore a little further
Try another experiment
Listen to a 3:2 interval at two different root frequencies. Compare its interval identity with its overall height. Then make a small deviation from 3:2 and observe how the repeating pattern changes.
Good to know
The diagrams and audio share the interval parameters. A stable-looking figure describes the modeled relationship; it does not mean every listener will prefer that tuning in every context.
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