Frequency to Note

The Inverse Formula

Given a frequency f, which MIDI note is it closest to?

Inverting the formula f = 440 × 2^((n−69)/12):

n = 69 + 12 × log₂(f / 440)

Round to the nearest integer to get the closest MIDI note.

Logarithm Review

log₂(x) = Math.log2(x) in JavaScript.

Cents

The fractional part tells you how far off the frequency is from the nearest note, measured in cents (1/100th of a semitone):

cents = (exact_n − nearest_n) × 100

• ±50 cents = halfway between notes (maximally out of tune)
• 0 cents = perfectly in tune

Examples

Your Task

Implement freqToNote(f) that returns the nearest MIDI note number for frequency f.

Run your code to hear the note detected from 440 Hz.