Scale

(Fr. gamme; Ger. Tonleiter; It. gamma).

A sequence of notes in ascending or descending order of pitch. As a musicological concept, a scale is a sequence long enough to define unambiguously a mode, tonality, or some special linear construction, and that begins and ends (where appropriate) on the fundamental note of the tonality or mode; a scale, therefore, is usually thought of as having the compass of one or more octaves. The following discussion is limited to the scales of European musical theory.

Seven-note scales lying within the octave, which are also known as ‘heptachords’, contain one representative of each letter name (A–B–C–D–E–F–G), any of which may be inflected by an accidental. A scale is Diatonic if the sequence of notes is based on a particular species of octave consisting of five tones (t) and two semitones (s). The white notes of the piano perhaps offer the simplest illustration of diatonic scales; see Table 1. The scales on D, E, F and G as given are the most common of the four authentic church modes (see Mode). The Locrian or Hyperaeolian scale, given on B in Table 1, is almost never used, since the unstable interval of a tritone occurs between the two most important degrees, the first and fifth. The remaining scales are those of the major and minor mode without any key signature.

Transposition, the raising or lowering of every note by the same interval, affects the name of a diatonic scale only insofar as it changes its starting note. For instance, if the notes in Table 1 were transposed a semitone up, they would yield scales in D major (D–E–F–G–A–B–C–D), E Dorian (E–F–G–A–B–C–D–E), F Phrygian and so on.

There are three ways of conceiving the minor scale in tonal theory. The natural minor (ex.1) consists simply of the ascending or descending sequence of tones and semitones given under the scale from A to A in Table 1. The melodic minor (ex.2) has raised sixth and seventh degrees ascending, but is the same as the natural minor descending. This scale can be abstracted from the characteristic movement of minor key melodies where the raised seventh acts as a leading note in the ascending direction (the sixth is raised to avoid an augmented interval between the sixth and seventh degrees). The harmonic minor scale has a raised seventh in both directions, but the sixth is left unaltered. In this way it becomes the product of the three primary harmonic functions, being generated from the triads of the tonic, subdominant, and dominant (with raised third), as illustrated in ex.3.

The chromatic scale proceeds entirely by semitones. It can be spelt either in such a way that every note makes a diatonic interval with the starting note (minor 2nd, major 2nd, minor 3rd etc.), as in ex.4a, or so that a minimum number of accidentals is used, as in ex.4b. A ‘gapped scale’ contains intervals of a minor 3rd or more, and is so called because it appears to be incomplete in comparison with heptatonic scales; the most widely used example is the Pentatonic scale. In the Whole-tone scale, which consists of only six notes, one letter name is missing; however, this scale is not truly gapped, because if enharmonic re-spelling is allowed there is no interval which cannot be written as a 2nd (C–D–E–F–G–A–C contains the diminished 3rd A–C, but C–D–E–F–G–B–C replaces this with the major 2nd B–C). The whole-tone scale can only be transposed by a semitone once without reproducing the original set of notes; it is therefore a Mode of limited transposition. Another such mode is the Octatonic scale, which includes eight notes in a pattern of alternating semitones and tones; at least one letter name is duplicated (e.g. C–D–E–E–F–G–A–B–C).

A scale which, when its letter names are arranged in alphabetical order, contains at least one descending interval, is termed ‘re-entrant’ (e.g. A–B–C–D–E–F–G).

WILLIAM DRABKIN/R