Pentatonic scale

A pentatonic scale is a musical scale with five notes per octave, in contrast to heptatonic scales, which have seven notes per octave (such as the major scale and minor scale). Pentatonic scales were developed independently by many ancient civilizations and are still used in various musical styles to this day. As Leonard Bernstein put it: "The universality of this scale is so well known that I'm sure you could give me examples of it, from all corners of the earth, as from Scotland, or from China, or from Africa, and from American Indian cultures, from East Indian cultures, from Central and South America, Australia, Finland ... now, that is a true musico-linguistic universal." There are two types of pentatonic scales: those with semitones (hemitonic) and those without (anhemitonic).

Types

Hemitonic and anhemitonic

Musicology commonly classifies pentatonic scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones and anhemitonic scales do not contain semitones. (For example, in Japanese music the anhemitonic yo scale is contrasted with the hemitonic in scale.) Hemitonic pentatonic scales are also called "ditonic scales", because the largest interval in them is the ditone (e.g., in the scale C–E–F–G–B–C, the interval found between C–E and G–B). (This should not be confused with the identical term also used by musicologists to describe a scale including only two notes.)

Major pentatonic scale Anhemitonic pentatonic scales can be constructed in many ways. The major pentatonic scale may be thought of as a gapped or incomplete major scale, using scale tones 1, 2, 3, 5, and 6 of the major scale. One construction takes five consecutive pitches from the circle of fifths; starting on C, these are C, G, D, A, and E. Rearranging the pitches to fit into one octave creates the major pentatonic scale: C, D, E, G, A.

Another construction works backward: It omits two pitches from a diatonic scale. If one were to begin with a C major scale, for example, one might omit the fourth and the seventh scale degrees, F and B. The remaining notes then make up the major pentatonic scale: C, D, E, G, and A. Omitting the third and seventh degrees of the C major scale obtains the notes for another transpositionally equivalent anhemitonic pentatonic scale: F, G, A, C, D. Omitting the first and fourth degrees of the C major scale gives a third anhemitonic pentatonic scale: G, A, B, D, E. The black keys on a piano keyboard comprise a G-flat (or equivalently, F-sharp) major pentatonic scale: G-flat, A-flat, B-flat, D-flat, and E-flat, which is exploited in Chopin's black key étude.

Minor pentatonic scale Although various hemitonic pentatonic scales might be called minor, the term is most commonly applied to the relative minor pentatonic derived from the major pentatonic, using scale tones 1, ♭3, 4, 5, and ♭7 of the natural minor scale. (It may also be considered a gapped blues scale.) The C minor pentatonic scale, the relative minor of the E-flat pentatonic scale, is C, E-flat, F, G, B-flat. The A minor pentatonic, the relative minor of C pentatonic, comprises the same tones as the C major pentatonic, starting on A, giving A, C, D, E, G. This minor pentatonic contains all three tones of an A minor triad.

The standard tuning of a guitar uses the notes of an E minor pentatonic scale: E–A–D–G–B–E, contributing to its frequency in popular music. Stevie Wonder employed the minor pentatonic for the funky clavinet riff on the track "Superstition" (1972).

Japanese scale

The Japanese mode is based on the Phrygian mode, but uses scale tones 1, 2, 4, 5, and 6 instead of scale tones 1, 3, 4, 5, and 7.

Modes of the pentatonic scale

The pentatonic scale (containing notes C, D, E, G, and A) has five modes, which are derived by treating a different note as the tonic:

Ricker assigned the major pentatonic scale mode I while Gilchrist assigned it mode III.

Relationship to diatonic modes Each mode of the pentatonic scale (containing notes C, D, E, G, and A) can be thought of as the five scale degrees shared by three different diatonic modes with the two remaining scale degrees removed:

Intervals from tonic

Each mode of the pentatonic scale (containing notes C, D, E, G, and A) features different intervals of notes from the tonic according to the table below. Note the omission of the semitones above (m2) and below (M7) the tonic as well as the tritone (TT).

Tuning

Pythagorean tuning

Ben Johnston gives the following Pythagorean tuning for the minor pentatonic scale:

Naturals in that table are not the alphabetic series A to G without sharps and flats: Naturals are reciprocals of terms in the Harmonic series (mathematics), which are in practice multiples of a fundamental frequency. This may be derived by proceeding with the principle that historically gives the Pythagorean diatonic and chromatic scales, stacking perfect fifths with 3:2 frequency proportions (C–G–D–A–E). Considering the anhemitonic scale as a subset of a just diatonic scale, it is tuned thus: 20:24:27:30:36 (A–C–D–E–G = 5⁄6–1⁄1–9⁄8–5⁄4–3⁄2).

Just intonation

(A minor seventh can be 7:4, 16:9, or 9:5; a major sixth can be 27:16 or 5:3. Both were chosen to minimize ratio parts.)

Other Assigning precise frequency proportions to the pentatonic scales of most cultures is problematic as tuning may be variable.

For example, the slendro anhemitonic scale and its modes of Java and Bali are said to approach, very roughly, an equally-tempered five-note scale, but their tunings vary dramatically from gamelan to gamelan. Composer Lou Harrison has been one of the most recent proponents and developers of new pentatonic scales based on historical models. Harrison and William Colvig tuned the slendro scale of the gamelan Si Betty to overtones 16:19:21:24:28 (1⁄1–19⁄16–21⁄16–3⁄2–7⁄4). They tuned the Mills gamelan so that the intervals between scale steps are 8:7–7:6–9:8–8:7–7:6 (1⁄1–8⁄7–4⁄3–3⁄2–12⁄7–2⁄1 = 42:48:56:63:72)

Use of pentatonic scales

Overview Pentatonic scales occur in many musical traditions:

Example details

In classical music Examples of its use include:

Beethoven, Quartet in F major, Op. 135, finale: Chopin's Etude in G-flat major, Op. 10, No. 5, the "Black Key" etude, in the major pentatonic. Western Impressionistic composers such as French composer Claude Debussy and Maurice Ravel used the pentatonic scale extensively in their works.

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