F0 Frequency in Hz

F0 sits in the sub-bass, below the lowest note of almost every acoustic instrument. Every number on this page is calculated from one formula rather than copied from a table, so the values here agree exactly with the full note frequency chart and with what the chromatic tuner reads back from your microphone.

How is the frequency of F0 calculated?

Twelve tone equal temperament divides the octave into twelve equal ratios. Each semitone multiplies the frequency by the twelfth root of two, about 1.059463, so twelve semitones multiply it by exactly two and you land one octave higher. Fix one note as the anchor and the rest follow. The anchor is A4, and the modern standard puts it at 440 Hz, which is what ISO 16 specifies as the standard tuning frequency.

Written as a formula, the frequency of MIDI note m is 440 x 2^((m - 69) / 12), because A4 is MIDI note 69. For F0 that is 440 x 2^((17 - 69) / 12) = 440 x 2^(-4.3333) = 21.83 Hz. That is 52 semitones below the reference.

What is F0 at other tuning references?

A4 at 440 Hz is the standard, not a law. Historical pitch was lower, and plenty of modern ensembles tune a little higher because a raised pitch is often described as sounding brighter in a large hall. Rebasing the same formula gives these values for F0.

Changing the reference multiplies every note by the same ratio, so intervals stay identical and only the absolute pitch moves.

What is F0 in every octave?

Moving up an octave doubles the frequency and moving down halves it, which is the one relationship in tuning that needs no calculator. Here is F across the full chart range.

What are the harmonics of F0?

A real instrument playing F0 does not produce 21.83 Hz alone. It produces a fundamental plus a series of whole-number multiples, and the balance between them is what makes a violin sound different from a flute on the same note. The harmonics land close to familiar notes but not exactly on them, because the harmonic series is built on simple ratios while equal temperament is not.

The seventh harmonic is the famous outlier: it lands roughly 31 cents flat of the nearest equal-tempered note, which is why it sounds bluesy rather than in tune.

How do I tune to F0?

Play the note and watch the cents readout rather than the hertz readout, because cents are proportional and hertz are not. A tuner rounds to the nearest note, so anything from 21.21 Hz to 22.47 Hz is read as F0: that is the band fifty cents either side. Most players aim to land inside five cents, which for F0 is roughly 21.76 Hz to 21.89 Hz.

Use the tone generator to play 21.83 Hz as a reference and match it by ear, or open the chromatic tuner and let your microphone do the measuring. Its neighbours are E0 at 20.60 Hz below and F#0 at 23.12 Hz above, one semitone in each direction.

What intervals are built on F0?

Ratios are the equal-tempered values. Pure just intonation would put the perfect fifth at exactly 1.5 and the major third at 1.25, which is why equal temperament thirds sound slightly wide.

What is the wavelength of F0?

Sound travels at roughly 343 m/s in dry air at 20 degrees Celsius, so a 21.83 Hz wave is about 15.715 m long, or 1571.5 cm. That matters for room acoustics: a wavelength that fits neatly between two parallel walls builds a standing wave, and it is also why a pipe or string producing F0 has the physical length it does. The speed of sound changes with temperature, so treat the figure as a good approximation rather than a constant.

Frequently asked questions

Other notes in octave 0

Music tools that use this frequency