The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely,

pitch class In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...

es) used in tonal music, with notes separated by the interval of a

semitone A semitone, also called a minor second, half step, or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically. It is defined as the interval between ...

. Chromatic instruments, such as the

piano A piano is a keyboard instrument that produces sound when its keys are depressed, activating an Action (music), action mechanism where hammers strike String (music), strings. Modern pianos have a row of 88 black and white keys, tuned to a c ...

, are made to produce the chromatic scale, while other instruments capable of continuously variable pitch, such as the

trombone The trombone (, Italian, French: ''trombone'') is a musical instrument in the Brass instrument, brass family. As with all brass instruments, sound is produced when the player's lips vibrate inside a mouthpiece, causing the Standing wave, air c ...

and

violin The violin, sometimes referred to as a fiddle, is a wooden chordophone, and is the smallest, and thus highest-pitched instrument (soprano) in regular use in the violin family. Smaller violin-type instruments exist, including the violino picc ...

, can also produce microtones, or notes between those available on a piano. Most music uses subsets of the chromatic scale such as

diatonic scale In music theory a diatonic scale is a heptatonic scale, heptatonic (seven-note) scale that includes five whole steps (whole tones) and two half steps (semitones) in each octave, in which the two half steps are separated from each other by eith ...

s. While the chromatic scale is fundamental in western

music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the "Elements of music, ...

, it is seldom directly used in its entirety in

musical composition Musical composition can refer to an Originality, original piece or work of music, either Human voice, vocal or Musical instrument, instrumental, the musical form, structure of a musical piece or to the process of creating or writing a new pie ...

s or

improvisation Improvisation, often shortened to improv, is the activity of making or doing something not planned beforehand, using whatever can be found. The origin of the word itself is in the Latin "improvisus", which literally means un-foreseen. Improvis ...

Definition

The chromatic scale is a

musical scale In music theory, a scale is "any consecutive series of notes that form a progression between one note and its octave", typically by order of pitch or fundamental frequency. The word "scale" originates from the Latin ''scala'', which literal ...

with twelve pitches, each a

, also known as a half-step, above or below its adjacent pitches. As a result, in

12-tone equal temperament 12 equal temperament (12-ET) is the musical system that divides the octave into 12 parts, all of which are Equal temperament, equally tempered (equally spaced) on a logarithmic scale, with a ratio equal to the Twelfth root of two, 12th root of 2 ...

(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 Frequency is the number of occurrences of a repeating event per unit of time. Frequency is an important parameter used in science and engineering to specify the rate of oscillatory and vibratory phenomena, such as mechanical vibrations, audio ...

of one note in the scale to that of the preceding note is given by

\approxeq 1.06

. In equal temperament, all the semitones have the same

size Size in general is the Magnitude (mathematics), magnitude or dimensions of a thing. More specifically, ''geometrical size'' (or ''spatial size'') can refer to three geometrical measures: length, area, or volume. Length can be generalized ...

(100 cents), and there are twelve semitones in an

octave In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referr ...

(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. : Pitch class space

Notation

The chromatic scale has no set

enharmonic spelling In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently. Similarly, written intervals, chords, or key signatures are considered enharmonic if they represent identical pitches that a ...

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 In music theory, the scale degree is the position of a particular note on a scale relative to the tonic—the first and main note of the scale from which each octave is assumed to begin. Degrees are useful for indicating the size of intervals ...

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 In music, an octave (: eighth) or perfect octave (sometimes called the diapason) is an interval between two notes, one having twice the frequency of vibration of the other. The octave relationship is a natural phenomenon that has been referre ...

, the chromatic scale may be indicated unambiguously by the numbers 0-11 mod twelve. Thus two perfect fifths are 0-7-2.

Tone row In music, a tone row or note row ( or '), also series or set, is a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometime ...

s, orderings used in the

twelve-tone technique The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition. The technique is a means of ensuring that all 12 notes of the chromatic scale ...

, 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 In music, just intonation or pure intonation is a musical tuning, tuning system in which the space between notes' frequency, frequencies (called interval (music), intervals) is a natural number, whole number ratio, ratio. Intervals spaced in thi ...

) 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 In music, two written notes have enharmonic equivalence if they produce the same pitch but are notated differently. Similarly, written intervals, chords, or key signatures are considered enharmonic if they represent identical pitches that ar ...

flats (cents rounded to one decimal): : where is a diatonic semitone ( Pythagorean limma) and is a chromatic semitone ( Pythagorean apotome). The chromatic scale in Pythagorean tuning can be tempered to the 17-EDO tuning (P5 = 10 steps = 705.88 cents).

Just intonation

In 5-limit

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): : The fractions and , and , and , and , and many other pairs are interchangeable, as (the

syntonic comma In music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first i ...

) is tempered out. Just intonation tuning can be approximated by 19-EDO tuning (P5 = 11 steps = 694.74 cents).

Non-Western cultures

The ancient Chinese chromatic scale is called '' Shí-èr-lǜ''. However, "it should not be imagined that this

gamut In color reproduction and colorimetry, a gamut, or color gamut , is a convex set containing the colors that can be accurately represented, i.e. reproduced by an output device (e.g. printer or display) or measured by an input device (e.g. cam ...

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." Needham, Joseph (1962/2004). ''Science and Civilization in China, Vol. IV: Physics and Physical Technology'', pp. 170–171. . However, "from the standpoint of tonal music he chromatic scale!--"it"--> 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.

Notes

Sources

External links

The Chromatic Scale arranged for guitar in several fingerings. (Formatted for easy printing)

Chromatic Scale – Analysis
{{Twelve-tone technique Chromaticism Musical scales Post-tonal music theory Musical symmetry Hemitonic scales Tritonic scales