Semitone Frequency Table

How each frequency is calculated

Every note in equal temperament sits a fixed ratio away from its neighbours: twelve semitones make an octave, which is a doubling of frequency, so each semitone is a multiple of the twelfth root of two. Once A4 is fixed at a reference pitch, the frequency of any other note follows from how many semitones it sits above or below that A4, positive for notes above and negative for notes below.

Why A4 is not always 440 Hz

440 Hz became the most common international reference pitch during the twentieth century, but it was never universal. Some orchestras tune slightly higher, around 442 to 444 Hz, for a brighter sound. A small community of musicians and instrument builders prefers 432 Hz, a choice more rooted in tradition and personal preference than in acoustics. Baroque ensembles playing on period instruments often tune close to 415 Hz, roughly a semitone below modern concert pitch.

Reading period and wavelength

The period is simply the inverse of the frequency, the time one full cycle of the sound wave takes, useful when working with oscillators or synthesis parameters expressed in milliseconds rather than hertz. The wavelength assumes a speed of sound of 343 m/s, the commonly used value for dry air at around 20°C, and shows how physically long one cycle of the note is as it travels through the air, which is why bass instruments need larger resonating bodies than treble ones.

Finding a note from a frequency

The reverse lookup takes any frequency and reports the closest note in equal temperament along with how far off it is, measured in cents, where 100 cents make one semitone. This is the same measurement instrument tuners use to describe how sharp or flat a string or pipe is relative to its target pitch.