A half step is the interval between two tones, or semi-tones, or a tone and a semi-tone on the chromatic scale. To make this a bit easier, if you look at all the tones in the chromatic scale, a half step is the interval between any two next to each other. It is also the interval between two keys on a piano (black or white keys) and the distance between one fret to the next on a guitar.

More facts about the half step:

All letter notes have a sharp, with the exception of B and E. A sharp(#) is the same note as the next letter's flat(b).
There are 12 half steps in an octave.
Each octave up doubles the sound's frequency, so the ratio of the frequency of one half step to the next is one over the twelfth root of two, or approximately 1:1.05946.
(middle C is approx. 261.62 Hz, the A below it is exactly 220 Hz)

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