Semitone (music): Difference between revisions
imported>John R. Brews (typos) |
imported>John R. Brews (headers; shuffling of material, formula) |
||
| Line 1: | Line 1: | ||
{{subpages}} | {{subpages}} | ||
{{TOC|right}} | |||
In Western music, a '''semitone''' or '''half-tone''' is the interval or step in [[Pitch (music)|pitch]] between adjacent [[Note (music)|notes]] in a particular [[Tuning (music)|tuning]] of the ''chromatic'' [[Scale (music)| 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''.<ref name=chromatic/> (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.<ref name=Persian/> | |||
==Tuning== | |||
The interval between notes in a scale is determined by the choice of [[Tuning (music)|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.<ref name=Greek/> 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<sup>1/12</sup>. | |||
==Formula== | |||
When tuned according to ''equal temperament'', the the separation or interval between two frequencies of the chromatic scale in ''semitones'', ƒ<sub>1</sub> and ƒ<sub>2</sub>, is determined as: | |||
:<math> s = 12 \log _2 \left( \frac {f_1}{f_2} \right) \ . </math> | |||
Consequently, two frequencies ƒ<sub>1</sub> and ƒ<sub>2</sub> separated by an interval of 1 semitone are in the ratio: | |||
:<math>\frac{f_1}{f_2}=2^{1/12} \approx 1.059463094 \ , </math> | |||
that is, by a ratio given by the 12th root of 2. | |||
==References== | ==References== | ||
Revision as of 11:45, 14 July 2012
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.[1] (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.[2]
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.[3] 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 the separation or interval between two frequencies of the chromatic scale in semitones, ƒ1 and ƒ2, is determined as:
Consequently, two frequencies ƒ1 and ƒ2 separated by an interval of 1 semitone are in the ratio:
that is, by a ratio given by the 12th root of 2.
References
- ↑ Herbert Zettl (2010). “§16.13 Chromatic scale”, Sight, Sound, Motion: Applied Media Aesthetics. Cengage learning, p. 326. ISBN 0495802964.
- ↑ 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.
- ↑ David Creese (2010). “Inconsistent definitions”, The Monochord in Ancient Greek Harmonic Science. Cambridge University Press, p. 27. ISBN 0521843243.