A semitone (British English) (also called a half step or a half tone) is the smallest musical interval used in Western music. It is the distance between two notes which are next to one another in pitch.
A whole tone means a distance of two semitones, i.e. the distance between two notes which are separated by one other note in pitch.
This is easy to see with a picture of a keyboard. The distance between two white notes that are side by side may be a whole tone (if there is a black note in between them) or a semitone (if there is no black note between).
To go from a C to a C sharp (or D flat) is a semitone.
To go from a C sharp (or D flat) to a D is a semitone.
To go from a C to a D is a tone.
An octave is divided into twelve semitones. These semitones are exactly equal in size.
Musical intervals are defined by a ratio of frequencies. An octave is a ratio of 2:1, so from 100 Hz to 200 Hz, and from 200 Hz to 400 Hz, are both octaves. A semitone is a ratio of the 12th root of 2 to 1, which is equal to 1.05946:1, so 1000 Hz and 1059.46 Hz are a semitone apart. A musical interval sounds better if the two notes have a small integer ratio. For this reason, it can be approximated by a ratio of 16:15 in just intonation.
- Semitone, half step, half tone, halftone, and half-tone are all variously used. Archived 2007-04-03 at the Wayback Machine
Aaron Copland, Leonard Bernstein, and others use "half tone". 
One source says that step is "chiefly US", Archived 2007-04-03 at the Wayback Machine and that half-tone is "chiefly N. Amer."[permanent dead link]
- Miller, Michael. The Complete Idiot's Guide to Music Theory, 2nd ed. [Indianapolis, IN]: Alpha, 2005. ISBN 1592574378. p. 19.
- Grout, Donald Jay, and Claude V. Palisca. A History of Western Music, 6th ed. New York: Norton, 2001. ISBN 0-393-97527-4.
- Hoppin, Richard H. Medieval Music. New York: W.W. Norton, 1978. ISBN 0-393-09090-6.