For K-12 Students · Equal Temperament
Equal Temperament for a guitar string
Built for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework. Simulate a guitar string live below — adjust the inputs and watch it respond, right in your browser.
Equal Temperament vs Just IntonationLive
the compromise of tuning
Controls
Presets
Just intonation tunes intervals to pure whole-number frequency ratios, which sound perfectly consonant but only in one key. Equal temperament divides the octave into 12 identical steps so every key works, at the cost of every interval except the octave being slightly out of tune. The bars show that compromise in cents.
Data Inspector
Equal-temp fifth392.0 Hz
Just fifth (3:2)392.4 Hz
Fifth error−2 cents
Major 3rd error+14 cents
Governing equation
Reading this result: The equal-tempered fifth sits at 392.0 Hz versus the pure 3:2 fifth at 392.4 Hz — only about 2 cents flat, which the ear forgives; the major third, however, runs a far more audible 14 cents sharp, the price of making every key playable.
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Frequently asked questions
- Is this good for k-12 students?
- Yes — this version of "Equal Temperament for a guitar string" is framed for k-12 students learning it in middle or high school. Watch the idea come alive with plain-language steps and everyday examples — perfect for projects and homework.
- Do I need to install anything?
- No. It runs in any modern browser, free, with no account required.