Semitone

A semitone 
(British English) (also called a half step or a half toneSemitone, half step, half tone, halftone, and half-tone are all variously used. 
Aaron Copland, Leonard Bernstein, and others use "half tone".

One source says that step is "chiefly US",  and that half-tone is "chiefly N. Amer.") is the smallest musical interval used in Western music.Miller, Michael. The Complete Idiot's Guide to Music Theory, 2nd ed. [Indianapolis, IN]: Alpha, 2005. . p. 19. 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. 
Related pages
Scale (music)
Interval (music)
Circle of fifths 
Chromaticism

References

Further reading
Grout, Donald Jay, and Claude V. Palisca. A History of Western Music, 6th ed. New York: Norton, 2001.  .
Hoppin, Richard H. Medieval Music. New York: W.W. Norton, 1978. .

Category:Music theory