Chromatic scale

File:PianoKeyboard.svg

Chromatic scale: every key of one octave on the piano keyboard

In Western music, a chromatic scale (or twelve-tone scale) is a set of twelve pitches within an octave, where the interval between any two adjacent notes is a semitone.

If the scale is tuned such that the interval between any two adjacent notes may function both as a diatonic and chromatic semitone (as in the modern 12-tone equal temperament), it provides a practical approximation of acoustically pure intervals in every key, and serves as a superset containing subsets like diatonic scales.

Chromatic instruments, such as the piano, are made to produce the chromatic scale. Other instruments capable of continuously variable pitch, such as the trombone and violin, can also produce microtones, or notes between those available on a piano.

Definition

The chromatic scale is a musical scale with twelve pitches, each a semitone, also known as a half-step, above or below its adjacent pitches. As a result, in 12-tone equal temperament (the most common tuning in Western music), the chromatic scale covers all 12 of the available pitches. Thus, there is only one chromatic scale. The ratio of the frequency of one note in the scale to that of the preceding note is given by $\sqrt[12]{2}\approxeq 1.06$.

In equal temperament, all the semitones have the same size (100 cents), and there are twelve semitones in an octave (1200 cents). As a result, the notes of an equal-tempered chromatic scale are equally-spaced.

The ascending and descending chromatic scale is shown below.

<score sound="1"> {

\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
 }

} </score>

File:Pitch class space.svg

Chromatic scale drawn as a circle

File:Chromatic notes diagram.png

The diatonic scale notes (above) and the non-scale chromatic notes (below)

Notation

File:Pitch class space star.svg

The circle of fifths drawn within the chromatic circle as a star dodecagram.

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♯).

Similarly, some notes of the chromatic scale have enharmonic equivalents in solfege. The rising scale is Do, Di, Re, Ri, Mi, Fa, Fi, Sol, Si, La, Li, Ti and the descending is Ti, Te/Ta, La, Le/Lo, Sol, Se, Fa, Mi, Me/Ma, Re, Ra, Do, However, once 0 is given to a note, due to octave equivalence, the chromatic scale may be indicated unambiguously by the numbers 0-11 mod twelve. Thus two perfect fifths are 0-7-2. Tone rows, orderings used in the twelve-tone technique, are often considered this way due to the increased ease of comparing inverse intervals and forms (inversional equivalence).

Pitch-rational tunings

Pythagorean

The most common conception of the chromatic scale before the 13th century was the Pythagorean chromatic scale (). 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 (i.e. 3-limit just intonation) the chromatic scale is tuned as follows, in perfect fifths from G♭ to A♯ centered on D (in bold) (G♭–D♭–A♭–E♭–B♭–F–C–G–D–A–E–B–F♯–C♯–G♯–D♯–A♯), with sharps higher than their enharmonic flats (cents rounded to one decimal):

	C	D♭	C♯	D	E♭	D♯	E	F	G♭	F♯	G	A♭	G♯	A	B♭	A♯	B	C
Pitch ratio	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	243⁄128	2
Cents	0	90.2	113.7	203.9	294.1	317.6	407.8	498	588.3	611.7	702	792.2	815.6	905.9	996.1	1019.6	1109.8	1200

where 256⁄243 is a diatonic semitone (Pythagorean limma) and 2187⁄2048 is a chromatic semitone (Pythagorean apotome).

Just intonation

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 (cents rounded to one decimal):

	C	C♯	D♭	D	D♯	E♭	E	E♯/F♭	F	F♯	G♭	G	G♯	A♭	A	A♯	B♭	B	B♯/C♭	C
Pitch ratio	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	48⁄25	2
Cents	0	70.7	111.7	203.9	274.6	315.6	386.3	427.4	498	568.7	631.3	702	772.6	813.7	884.4	955	1017.6	1088.3	1129.3	1200

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 (the syntonic comma) is tempered out.

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." However, "from the standpoint of tonal music [the chromatic scale] is not an independent scale, but derives from the diatonic scale," making the Western chromatic scale a gamut of fundamental notes from which scales could be constructed as well.

See also

• Atonality
• Chromaticism
• Twelve-tone technique
• 20th century music#Classical
• "All Through the Night" (Cole Porter song)

Further reading

• Hewitt, Michael. 27 January 2013. Musical Scales of the World. The Note Tree. Template:ISBN

External links

• The Chromatic Scale arranged for guitar in several fingerings. (Formatted for easy printing)
• The 12 golden notes of music
• Chromatic Scale – Analysis

Notes of the chromatic scale

C
(B♯)

C♯
D♭

D

D♯
E♭

E
(F♭)

F
(E♯)

F♯
G♭

G

G♯
A♭

A

A♯
B♭

B
(C♭)