Semitone (music)

In Western music, a semitone or half-tone is the interval or step in pitch between adjacent notes in a particular tuning of the chromatic musical scale called equal temperament. These terms are introduced below.

A variety of scales

Many scales are used in practice. Western classical music typically employs twelve pitches in an octave, the so-called chromatic scale. (The octave is the musical interval between two pitches, one the double of the frequency of the other.) On the other hand, Arabic-Persian music uses 22-24 pitches, commonly accepted to be spaced an interval of a quarter-tone apart.

Tuning

The interval between notes in a scale is determined by the choice of tuning. Some schools of ancient Greek music argued that intervals between notes should be capable of expression as ratios of integers (so-called pure intervals), while others argued for equal spacing. The interval between notes in the chromatic scale is determined by a variety of methods, with the most common method based upon the same interval between all notes in the scale, a method called equal temperament. In this approach, because there are twelve notes in the chromatic scale, the interval of the semitone corresponds to a frequency ratio between any two adjacent pitches of 2^1/12.

Formula

When tuned according to equal temperament, the the separation or interval between two frequencies of the chromatic scale in semitones, ƒ₁ and ƒ₂, is determined as:

$s=12\log _{2}\left({\frac {f_{1}}{f_{2}}}\right)\ .$

Consequently, two frequencies ƒ₁ and ƒ₂ separated by an interval of 1 semitone are in the ratio:

${\frac {f_{1}}{f_{2}}}=2^{1/12}\approx 1.059463094\ ,$

that is, by a ratio given by the 12th root of 2. A complete cycle of notes separated by a semitone is A, (A♯, B♭), B, C, (C♯, D♭), D, (D♯, E♭), E, F, (F♯, G♭), G, (G♯, A♭), A, and so on.