Chromatic scale

Chromatic scale
Qualities
Number of pitch classes 12
Chromatic scale drawn as a circle: each note is equidistant from its neighbors, separated by a semitone of the same size

The chromatic scale is a musical scale with twelve pitches, each a semitone above or below another. On a modern piano or other equal-tempered instrument, all the semitones have the same size (100 cents). In other words, the notes of an equal-tempered chromatic scale are equally spaced. An equal-tempered chromatic scale is a nondiatonic scale having no tonic because of the symmetry of its equally spaced notes.[1]

Chromatic scale on C: full octave ascending and descending  Play in equal temperament  or  Play in Pythagorean tuning 

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. Equally spaced pitches are provided only by equal temperament tuning systems, which are widely used in contemporary music.

The term chromatic derives from the Greek word chroma, meaning color. Chromatic notes are traditionally understood as harmonically inessential embellishments, shadings, or inflections of diatonic notes.

Notation

The chromatic scale may be notated in a variety of ways.

Ascending and descending:[1]

The chromatic scale has no set spelling agreed upon by all. Its spelling is, however, often dependent upon major or minor key signatures and whether the scale is ascending or descending. The images above, therefore, are only examples of chromatic scale notations. As an abstract theoretical entity (that is, outside a particular musical context), the chromatic scale is usually notated such that no scale degree is used more than twice in succession (for instance G flat - G natural - G sharp).

Non-Western cultures

Total chromatic

The total chromatic (or aggregate[3]) is the set of all twelve pitch classes. An array is a succession of aggregates.[3] See also: Tone row.

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:

C C♯ D♭ D D♯ E♭ E E♯/F♭ F F♯ G♭ G G♯ A♭ A A♯ B♭ B B♯/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 48/25 2

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.

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

C D♭ C♯ D E♭ D♯ E F F♯ G♭ G A♭ G♯ A B♭ A♯ B C
1 256/243 2187/2048 9/8 32/27 8192/6561 81/64 4/3 1024/729 729/512 3/2 128/81 6561/4096 27/16 16/9 4096/2187 243/128 2

These are 17-EDO Pythagorean tuning approximations.

See also

Sources

  1. 1 2 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.
  3. 1 2 Whittall, Arnold. 2008. The Cambridge Introduction to Serialism, p.271. New York: Cambridge University Press. ISBN 978-0-521-68200-8 (pbk).
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