Equal temperament divides an octave into 12 equal steps, so every frequency in the table comes from one formula: the frequency of MIDI note m is A4 multiplied by 2 to the power of (m - 69) / 12. A4 is MIDI note 69, an octave is a doubling, and a semitone is the twelfth root of 2, about 1.0595.
Both directions
Note to hertz takes a note name and octave and gives the frequency. Hertz to note takes a measured frequency and returns the nearest note plus the distance to it in cents, which is the reading a tuner shows.
A cents value near zero means the frequency lands on the note. Near 50 it sits halfway between two notes, and the label flips to the other one past that point.
The tuning reference
A4 sets everything else. 440 Hz has been the international standard since 1955, though orchestras in continental Europe often play at 442 or 443, and historically informed ensembles use 415 for baroque repertoire.
Changing the reference moves every note by the same ratio, so intervals hold. That also means a sample recorded at A4 = 442 needs 7.85 cents of correction, not a different note.
MIDI numbers
MIDI note numbers run from 0 to 127, C-1 to G9. They are integers, so they carry no tuning information at all: the same note number sounds at a different frequency depending on what the instrument’s reference is set to.
Period and wavelength
Period is 1000 divided by the frequency, in milliseconds. It is the number to reach for when setting a delay or a filter time in relation to a pitch: a single cycle of A2 at 110 Hz is 9.09 ms.
Wavelength is the speed of sound divided by the frequency. A 50 Hz tone is 6.9 m long, which is longer than most rooms, and that is why the lowest octave of a mix behaves so differently in a small space than the rest of it. Half a wavelength across a room dimension is where the first mode sits.
Example: reading a bass part
An open low E on a bass guitar is 41.20 Hz, MIDI note 28, E1. Its second harmonic is 82.41 Hz, which is where the note usually reads as pitched, and the fundamental is mostly felt. A high-pass at 30 Hz leaves both alone. A high-pass at 60 Hz sits above the fundamental of every note below B1, which is most of the bass part.