Intervals & Scales
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
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. 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. : \override Score.TimeSignature #‘stencil = ##f \relative c’ \time 5/4 c d e g a c 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. : \override Score.TimeSignature #‘stencil = ##f \relative c \time 5/4 ges aes bes des ees ges
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. 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. : \override Score.TimeSignature #‘stencil = ##f \relative c \time 5/4 a4 c d e g a 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. : \override Score.TimeSignature #‘stencil = ##f \relative c’ \time 5/4 e f a b c e
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).
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 = ––––).
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 (––––). They tuned the Mills gamelan so that the intervals between scale steps are 8:7–7:6–9:8–8:7–7:6 (––––septimal major sixth – = 42:48:56:63:72)
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, and Maurice Ravel used the pentatonic scale extensively in their works. Giacomo Puccini used pentatonic scales in his operas Madama Butterfly and Turandot to imitate east Asian musical styles. Puccini also used whole-tone scales in the former to evoke similar ideas.
Indian ragas#
Indian classical music has hundreds of ragas, of which many are pentatonic. Examples include Raag Abhogi Kanada (C, D, E-flat, F, A), Raag Bhupali (C, D, E, G, A), Raag Bairagi (C, D-flat, F, G, B-flat), Raag Chandrakauns (C, E-flat, F, A-flat, B), Raag Dhani (C, E-flat, F, G, B-flat), Raag Gunakari (C, D-flat, F, G, A-flat), Raag Hamsadhwani (C, D, E, G, B), Raag Hindol (C, E, F#, A, B), Raag Kalavati (C, E, G, A, B-flat), Raag Malkauns (C, E-flat, F, A-flat, B-flat), Raag Megh (C, D, F, G, B-flat), Raag Shuddha Sarang (C, D, F#, G, B), Raag Tilang (C, E, F, G, B), Raag Vibhas (C, D-flat, E, G, A-flat), Raag Vrindavani Sarang (C, D, F, G, B), and others. (For Tamil Music System, See here - Ancient Tamil music#Evolution of panns )
Further Asian pentatonic musical traditions#
The major pentatonic scale is the basic scale of the music of China and the music of Mongolia as well as many Southeast Asian musical traditions such as that of the Karen people as well as the indigenous Assamese ethnic groups. The pentatonic scale predominates most Eastern countries as opposed to Western countries where the heptatonic scale is more commonly used. The fundamental tones (without meri or kari techniques) rendered by the five holes of the Japanese shakuhachi flute play a minor pentatonic scale. The yo scale used in Japanese shomyo Buddhist chants and gagaku imperial court music is an anhemitonic pentatonic scale shown below, which is the fourth mode of the major pentatonic scale. In Javanese gamelan music, the slendro scale has five tones, of which four are emphasized in classical music. Another scale, pelog, has seven tones, and is generally played using one of three five-tone subsets known as pathet, in which certain notes are avoided while others are emphasized.
Somali#
Somali music uses a distinct modal system that is pentatonic, with characteristically long intervals between some notes. As with many other aspects of Somali culture and tradition, tastes in music and lyrics are strongly linked with those in nearby Ethiopia, Eritrea, Djibouti and Sudan.
Insular Celtic#
In Scottish music, the pentatonic scale is very common. Seumas MacNeill suggests that the Great Highland bagpipe scale with its augmented fourth and diminished seventh is “a device to produce as many pentatonic scales as possible from its nine notes” (although these two features are not in the same scale). Roderick Cannon explains these pentatonic scales and their use in more detail, both in Piobaireachd and light music. It also features in Irish traditional music, either purely or almost so. The minor pentatonic is used in Appalachian folk music.
Andean#
In Andean music, the pentatonic scale is used substantially minor, sometimes major, and seldom in scale. In the most ancient genres of Andean music being performed without string instruments (only with winds and percussion), pentatonic melody is often led with parallel fifths and fourths, so formally this music is hexatonic.