# Semitone (music)

Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
Citable Version  [?]

This editable Main Article is under development and subject to a disclaimer.

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 complete cycle of notes using equal temperament, adjacent 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.

## A variety of scales

Many scales are used in practice.[1] Western classical music typically employs twelve pitches in an octave, the so-called chromatic scale.[2] (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.[3]

## 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.[4] 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 21/12.

## Formula

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

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

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

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

that is, by a ratio given by the 12th root of 2.

## References

1. The chromatic scale is only one of many scales. See, for example, (2003) “Scale degrees”, Don Michael Randel, ed: The Harvard Dictionary of Music, 4rth ed. Harvard University Press, p. 758. ISBN 0674011635.
2. Herbert Zettl (2010). “§16.13 Chromatic scale”, Sight, Sound, Motion: Applied Media Aesthetics. Cengage learning, p. 326. ISBN 0495802964.
3. There is some debate over the structure of Persian music. See, for example, Hormoz Farhat (2004). “Intervals and scales in contemporary Persian music”, The Dastgāh concept in Persian music. Cambridge University Press, p. 7. ISBN 0521542065.
4. David Creese (2010). “Inconsistent definitions”, The Monochord in Ancient Greek Harmonic Science. Cambridge University Press, p. 27. ISBN 0521843243.