Chromatic scale

The chromatic scale is a musical scale with twelve pitches, each a semitone above or below its adjacent pitches. As a result, in 12-tone equal temperament (the most common temperament in Western music), the chromatic scale covers all 12 of the available pitches. Thus, there is only one chromatic scale.

Moreover, in equal temperament, all the semitones have the same size (100 cents). As a result, the notes of an equal-tempered chromatic scale are equally-spaced. This makes the chromatic scale a nondiatonic scale with no tonic because of the symmetry of its equally-spaced notes.[1]

The ascending and descending chromatic scale is shown below.

{ \override Score.TimeSignature #'stencil = ##f \relative c' { \clef treble \time 12/4 c4^\markup { Ascending } cis d dis e f fis g gis a ais b c^\markup { Descending } b bes a aes g ges f e es d des c } }

The term chromatic derives from the Greek word chroma, meaning color.

Notation

Chromatic scale drawn as a circle

The chromatic scale has no set enharmonic spelling that is always used. Its spelling is, however, often dependent upon major or minor key signatures and whether the scale is ascending or descending. In general, the chromatic scale is usually notated with sharp signs when ascending and flat signs when descending. It is also notated so that no scale degree is used more than twice in succession (for instance, G♭ – G♮ – G♯).

Other tunings

The most common conception of the chromatic scale before the 13th century was the Pythagorean chromatic scale ( Play ). Due to a different tuning technique, the twelve semitones in this scale have two slightly different sizes. Thus, the scale is not perfectly symmetric. Many other tuning systems, developed in the ensuing centuries, share a similar asymmetry.

In Pythagorean tuning (3-limit just intonation) the chromatic scale is tuned as follows, with sharps higher than their enharmonic flats:

CD♭C♯DE♭D♯EFG♭F♯GA♭G♯AB♭A♯BC
1​256⁄243​2187⁄2048​9⁄8​32⁄27​19683⁄16384​81⁄64​4⁄3​1024⁄729​729⁄512​3⁄2​128⁄81​6561⁄4096​27⁄16​16⁄9​59049⁄32768​243⁄1282

These are 17-EDO Pythagorean tuning approximations.

In 5-limit just intonation the chromatic scale, Ptolemy's intense chromatic scale, is as follows, with flats higher than their enharmonic sharps, and new notes between E/F and B/C:

CC♯D♭DD♯E♭EE♯/F♭FF♯G♭GG♯A♭AA♯B♭BB♯/C♭C
1​25⁄24​16⁄15​9⁄8​75⁄64​6⁄5​5⁄4​32⁄25​4⁄3​25⁄18​36⁄25​3⁄2​25⁄16​8⁄5​5⁄3​125⁄72​9⁄5​15⁄8​48⁄252

The fractions ​9⁄8 and ​10⁄9, ​6⁄5 and ​32⁄27, ​5⁄4 and ​81⁄64, ​4⁄3 and ​27⁄20, and many other pairs are interchangeable, as ​81⁄80 (syntonic comma) is tempered out. These are 19-EDO just intonation approximations.

Non-Western cultures

The ancient Chinese chromatic scale is called Shí-èr-lǜ. However, "it should not be imagined that this gamut ever functioned as a scale, and it is erroneous to refer to the 'Chinese chromatic scale', as some Western writers have done. The series of twelve notes known as the twelve lü were simply a series of fundamental notes from which scales could be constructed."[2]

The Indian solfège, i.e. sargam, makes up the twelve notes of the chromatic scale with respective sharps and flats.

See also

Sources

  1. ↑ Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.47. Seventh Edition. ISBN 978-0-07-294262-0.
  2. ↑ Needham, Joseph (1962/2004). Science and Civilization in China, Vol. IV: Physics and Physical Technology, p.170-171. ISBN 978-0-521-05802-5.

Further reading

  • Hewitt, Michael. 2013. Musical Scales of the World. The Note Tree. ISBN 978-0957547001
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