The chromatic scale or twelve-tone 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 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 and there are twelve semitones in an octave. As a result, the notes of an equal-tempered chromatic scale are equally-spaced. The ascending and descending chromatic scale is shown below.
Notation
The chromatic scale has no set enharmonic spelling that is always used. Its spelling is, however, often dependent upon major or minorkey 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. 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 increase ease of comparing inverse intervals and forms.
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 the chromatic scale is tuned as follows, in perfect fifths from G to A centered on D , with sharps higher than their enharmonic flats : where is a diatonic semitone and is a chromatic semitone. The chromatic scale in Pythagorean tuning can be tempered to the 17-EDO tuning.
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 : The fractions and, and, and, and, and many other pairs are interchangeable, as is tempered out. Just intonation tuning can be approximated by 19-EDO tuning.
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 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.
