For Students · Equal Temperament
Equal Temperament for a standing wave
Built for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition. Simulate a standing wave live below — adjust the inputs and watch it respond, right in your browser.
Equal Temperament vs Just IntonationLive
the compromise of tuning
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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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- Is this good for students?
- Yes — this version of "Equal Temperament for a standing wave" is framed for students learning it for a class or exam. See the concept move instead of memorizing formulas — and check your homework intuition.
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- No. It runs in any modern browser, free, with no account required.