How this calculation works
Twelve-tone equal temperament divides an octave into twelve equal frequency ratios. Equal does not mean a fixed number of hertz: each successive semitone multiplies frequency by the same twelfth root of two.
Target Hz = A4 reference × 2^((MIDI index + semitone shift − 69 + cents/100)/12); comparison cents = 1200 log2(measured/target)A worked example
At MIDI sixty-nine, zero transposition and zero cent offset, a 440 Hz reference produces exactly 440 Hz. One octave above produces 880 Hz. A measured 442 Hz is about 7.85 cents above the 440 Hz target. Changing the reference to 442 Hz makes that same measurement agree without changing the MIDI note number.
Good to know
Ideal twelve-tone equal temperament only; no just intonation, instrument compensation, audio analysis or universal octave-label convention. Use a suitable measurement and tuning method for the actual instrument. A numeric target alone does not establish which pitch standard an ensemble intends.
Reference: UNSW — equal temperament and frequency ratios (opens in a new tab) ↗
What this calculation answers
Twelve-tone equal temperament divides an octave into twelve equal frequency ratios. Equal does not mean a fixed number of hertz: each successive semitone multiplies frequency by the same twelfth root of two.
This page uses MIDI note numbering with A4 at sixty-nine and C4 at sixty. The octave label is a stated naming convention because different software can display a different octave name for the same MIDI number.
The Music tempo delay and sample timing calculator converts rhythmic durations, not pitch. A note’s frequency and a beat’s timing are separate quantities even when both involve cycles.
Use the right input conventions
Transpose is an integer semitone shift, while cents provide a smaller fractional-semitone offset. The final transposed MIDI index must stay within the supported zero-to-127 range.
Reference A4 is an input rather than a universal tuning claim. The measured frequency is also supplied by you; the site does not listen to a microphone, detect pitch or infer an instrument’s fundamental automatically.
Interpret the result
A positive cent comparison means the entered measured frequency is above the calculated target. A negative comparison means it is below. The logarithmic comparison works across different octave ranges.
The neighboring-octave table preserves the same tuning reference and cent offset. It shows the doubling/halving relation without implying that real strings, wind instruments or tuned percussion exactly follow ideal equal temperament.
Work through the example
At MIDI sixty-nine, zero transposition and zero cent offset, a 440 Hz reference produces exactly 440 Hz. One octave above produces 880 Hz.
A measured 442 Hz is about 7.85 cents above the 440 Hz target. Changing the reference to 442 Hz makes that same measurement agree without changing the MIDI note number.
Where the model stops
Ideal twelve-tone equal temperament only; no just intonation, instrument compensation, audio analysis or universal octave-label convention.
Use a suitable measurement and tuning method for the actual instrument. A numeric target alone does not establish which pitch standard an ensemble intends.
A few questions, answered
Why do semitones multiply rather than add hertz?
An octave is a frequency ratio of two, so equal-ratio semitone steps must multiply to two over twelve steps.
Does this detect my played note?
No. It calculates an entered target and compares a frequency measurement you provide.