Tuning and cents

Convert a positive frequency ratio, two frequencies or a signed interval in cents. Ratios accept a/b or decimals; commas and points are accepted. cents=1200·log₂(f₂/f₁), ratio=2^(cents/1200). Positive cents raise pitch, negative cents lower it. The nearest equal-tempered interval is a multiple of 100ct; a tie goes to the higher interval. The inverse negates cents and inverts the ratio.

The comparison uses one conventional 5-limit just-intonation ratio set against 12-tone equal temperament. Other just ratios are possible; this is not a universal tuning for every key. The table gives all 12 chromatic intervals from the entered reference frequency, including the unison. Select an interval to see both target frequencies and its cent difference.

Listen plays the reference and target together as a short sine-tone pair, helping reveal the difference between a pure and equal-tempered interval. Playback is available only for 20–20000 Hz and below the browser’s Nyquist limit. Changing reference, interval, tab or page stops sound. This is a calculated comparison, not a microphone tuner.

Very small ratios use scientific notation. Ratios beyond the representable JavaScript number range are marked explicitly; their finite cent interval can still be computed. Extremely large cent values cannot resolve a nearest semitone.

Inputs update directly; Enter updates immediately. The comparison toolbar groups reference, interval and listening controls. Expand All intervals for the complete table; on narrow screens it scrolls locally without hiding frequency columns. Only raw inputs and the selected tab are kept locally, including invalid drafts. Results are recalculated; audio and expanded tables are not stored. No sound starts on loading. Beats plays the two target frequencies together for up to four seconds. Their absolute difference in Hz is the number of loudness pulses per second. Equal frequencies produce no beats.