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.
|Number of pitch classes||12|
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.
The chromatic scale may be notated in a variety of ways.
Ascending and descending:
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).
- 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."
- The Indian solfège, i.e. sargam, makes up the twelve notes of the chromatic scale with respective sharps and flats.
Tonal Chromatic ScaleEdit
In "The Tonal Chromatic Scale as a Model for Functional Chromaticism" (Music Perception, 4:1, Fall 1986), James Marra proposes a "Tonal Chromatic Scale" (TCS) as a pitch-notational representation of major-minor tonal chromaticism. In order to maintain tonal modality, this representation comes in two forms, one each for the major and minor modes.
Four axioms constrain its structure:
1) No Symmetry Rule (NS): Symmetrical pitch class universes are never tonal. (The 12-tone chromatic, whole tone, octatonic scales, and the Dorian mode are not major-minor tonal structures.) The major and minor diatonic scales are tonal and are not symmetrical. This restriction insures structural consistency between modalities, and chromatic and diatonic tonal relations. Although modality is obscured stylistically in highly chromatic music, the tonality remains bi-modal.
2) No Alteration Rule (NA): Tones of the tonic triad are not subject to chromatic alteration, except for the mediant scale degree, which always functions as a “stable” scale degree within the parallel minor mode. (This is modeled formally in the Neo-Riemannian "parallel" transform.) A “stable” tone is phenomenologically defined as the tone “expected” by a competent listener of tonal music to follow a tonally chromatic or diatonic “unstable” tone.
3) No Enharmonic Rule (NE): Diatonic tones cannot be chromatically transformed such that the altered tones are pitch-class (pc) equivalent with another diatonic pc. For example, pc 11+1 = pc 0 and pc 4+1 = pc 5, which respectively would generate in C major: B -> B# (C) and E -> E#(F) respectively. This rule maintains the desired unique structural status of members of the tonic triad. It also insures that a lowered subdominant is only possible in the minor mode. (In C, F - Fb [E])
4) Tonal Resolution Rule (TR): A chromatic tone is functional in a tonality with tonic triad T iff it “resolves to” (or is “followed by”) a member of T. This rule provides the contextual phenomenology required to support empirical testing.
The NE and TR rules model preserve the surjective functions required to insure that stable tones of the tonic triad (the range of the mapping functions) are mapped to potentially multiple unstable diatonic or chromatic. For example, the stable tone E of the C major tonic triad maps to both the diatonic tone F and the chromatic tone D#. (A PC3 functioning within c minor, would consider that pitch class a "stable" Eb. The employment of surjective mapping allows the tonal chromatic scale to represent both diatonic and chromatic tonal relations, while also providing a mapping constraint on enharmonic tonal relations.
The notational representations of the two forms of the TCS are:
Major Mode: C-Db-D-D#-E-F-F#-G-Ab-A-B-(C)
11 tones only. Bb/A# are not tonally-functional within the prevailing tonality. The set is not symmetrical.
Minor Mode: C-Db-D-Eb-Fb-F-F#-G-Ab-A-Bb-B-C
Although this 12-tone collection is symmetrical, it is not a fundamental functional scale. Rather, is comprised of the ascending (C-Db-D-Eb-Fb-F-F#-G-A-B-C) and descending (C-Db-D-Eb-Fb-F-F#-G-Ab-Bb-C) melodic minor scales, with chromatic tones. Neither of these scales are symmetrical.
These three TCSs preserve modal uniqueness through the cardinality of their fundamental chromatic collections.
A passage from Brahms Alte Liebe (Op. 72/1 - “Low Voice” f minor version) illuminates the explanatory value of the TCS. In mm. 25-26, the harmony comprised of Gb-C#-E-Bb (from the lower voice upward) progresses to a first inversion tonic triad in d minor (F-A-D). Unless a lowered chromatic subdominant scale degree is included in the tonal structuring of minor keys, which is not the case in many alternative chromatic theories, this former chord remains functionally unexplained with respect to the incoming key of d minor. This failure often leads to an incorrect identification of a leading tone harmony as a “dominant seventh” in the key of Cb; a tonality not expressed in the passage. The TCS simply interprets the former harmony as an unambiguously functional “leading tone” harmony in d minor, however with a lowered fifth. The tones C#-E-Gb-Bb (vii - second inversion) resolve respectively to D-D(F)-F-A (i - first inversion).
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:
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:
These are 17-EDO Pythagorean tuning approximations.
- Benward & Saker (2003). Music: In Theory and Practice, Vol. I, p.47. Seventh Edition. ISBN 978-0-07-294262-0.
- Needham, Joseph (1962/2004). Science and Civilization in China, Vol. IV: Physics and Physical Technology, p.170-171. ISBN 978-0-521-05802-5.
- 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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