Scale (music)

Ascending and descending chromatic scale  Play 
Pattern of intervals in the C-major scale  Play 

In music theory, a scale is any set of musical notes ordered by fundamental frequency or pitch. A scale ordered by increasing pitch is an ascending scale, and a scale ordered by decreasing pitch is a descending scale. Some scales contain different pitches when ascending than when descending, for example, the melodic minor scale.

Often, especially in the context of the common practice period, most or all of the melody and harmony of a musical work is built using the notes of a single scale, which can be conveniently represented on a staff with a standard key signature.[1]

Due to the principle of octave equivalence, scales are generally considered to span a single octave, with higher or lower octaves simply repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance (or interval) between two successive notes of the scale.[2] However, there is no need for scale steps to be equal within any scale and, particularly as demonstrated by microtonal music, there is no limit to how many notes can be injected within any given musical interval.

A measure of the width of each scale step provides a method to classify scales. For instance, in a chromatic scale each scale step represents a semitone interval, while a major scale is defined by the interval pattern T–T–S–T–T–T–S, where T stands for whole tone (an interval spanning two semitones), and S stands for semitone. Based on their interval patterns, scales are put into categories including diatonic, chromatic, major, minor, and others.

A specific scale is defined by its characteristic interval pattern and by a special note, known as its first degree (or tonic). The tonic of a scale is the note selected as the beginning of the octave, and therefore as the beginning of the adopted interval pattern. Typically, the name of the scale specifies both its tonic and its interval pattern. For example, C major indicates a major scale with a C tonic.

Background

Scales, steps, and intervals

Diatonic scale in the chromatic circle

Scales are typically listed from low to high pitch. Most scales are octave-repeating, meaning their pattern of notes is the same in every octave (the Bohlen–Pierce scale is one exception). An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing (or decreasing) pitch class. For instance, the increasing C major scale is C–D–E–F–G–A–B–[C], with the bracket indicating that the last note is an octave higher than the first note, and the decreasing C major scale is C–B–A–G–F–E–D–[C], with the bracket indicating an octave lower than the first note in the scale.

The distance between two successive notes in a scale is called a scale step.

The notes of a scale are numbered by their steps from the root of the scale. For example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to each other: C and E create an interval of a third (in this case a major third); D and F also create a third (in this case a minor third).

Pitch

A single scale can be manifested at many different pitch levels. For example, a C major scale can be started at C4 (middle C; see scientific pitch notation) and ascending an octave to C5; or it could be started at C6, ascending an octave to C7. As long as all the notes can be played, the octave they take on can be altered.

Types of scale

Scales may be described according to the intervals they contain:

or by the number of different pitch classes they contain:

"The number of the notes that make up a scale as well as the quality of the intervals between successive notes of the scale help to give the music of a culture area its peculiar sound quality."[3] "The pitch distances or intervals among the notes of a scale tell us more about the sound of the music than does the mere number of tones."[4]

Harmonic content

The notes of a scale form intervals with each of the other notes of the chord in combination. A 5-note scale has 10 of these harmonic intervals, a 6-note scale has 15, a 7-note scale has 21, an 8-note scale has 28.[5] Though the scale is not a chord, and might never be heard more than one note at a time, still the absence, presence, and placement of certain key intervals plays a large part in the sound of the scale, the natural movement of melody within the scale, and the selection of chords taken naturally from the scale.[6]

A musical scale that contains tritones is called tritonic (though the expression is also used for any scale with just three notes per octave, whether or not it includes a tritone), and one without tritones is atritonic. A scale or chord that contains semitones is called hemitonic, and without semitones is anhemitonic. The significance of these categories lies in their bases of semitones and tritones being the severest of dissonances, which is often desirable to avoid. Most scales used across the planet are anhemitonic.

Scales in composition

The lydian mode  Play , middle, functions as an intermediary between the whole tone scale  Play , top, and the major scale  Play , bottom.

Scales can be abstracted from performance or composition. They are also often used precompositionally to guide or limit a composition. Explicit instruction in scales has been part of compositional training for many centuries. One or more scales may be used in a composition, such as in Claude Debussy's L'Isle Joyeuse.[7] To the right, the first scale is a whole tone scale, while the second and third scales are diatonic scales. All three are used in the opening pages of Debussy's piece.

Western music

Scales in traditional Western music generally consist of seven notes and repeat at the octave. Notes in the commonly used scales (see just below) are separated by whole and half step intervals of tones and semitones. The harmonic minor scale includes a three-semitone step; the anhemitonic pentatonic includes two of those and no semitones.

Western music in the Medieval and Renaissance periods (1100–1600) tends to use the white-note diatonic scale C–D–E–F–G–A–B. Accidentals are rare, and somewhat unsystematically used, often to avoid the tritone.

Music of the common practice periods (1600–1900) uses three types of scale:

These scales are used in all of their transpositions. The music of this period introduces modulation, which involves systematic changes from one scale to another. Modulation occurs in relatively conventionalized ways. For example, major-mode pieces typically begin in a "tonic" diatonic scale and modulate to the "dominant" scale a fifth above.

In the 19th century (to a certain extent), but more in the 20th century, additional types of scales were explored:

A large variety of other scales exists, some of the more common being:

Scales such as the pentatonic scale may be considered gapped relative to the diatonic scale. An auxiliary scale is a scale other than the primary or original scale. See: modulation (music) and Auxiliary diminished scale.

Note names

In many musical circumstances, a specific note of the scale is chosen as the tonic—the central and most stable note of the scale, also known as the root note. In Western tonal music, simple songs or pieces typically start and end on the tonic note. Relative to a choice of a certain tonic, the notes of a scale are often labeled with numbers recording how many scale steps above the tonic they are. For example, the notes of the C major scale (C, D, E, F, G, A, B) can be labeled {1, 2, 3, 4, 5, 6, 7}, reflecting the choice of C as tonic. The expression scale degree refers to these numerical labels. Such labeling requires the choice of a "first" note; hence scale-degree labels are not intrinsic to the scale itself, but rather to its modes. For example, if we choose A as tonic, then we can label the notes of the C major scale using A = 1, B = 2, C = 3, and so on. When we do so, we create a new scale called the A minor scale. See the musical note article for how the notes are customarily named in different countries.

The scale degrees of a heptatonic (7-note) scale can also be named using the terms tonic, supertonic, mediant, subdominant, dominant, submediant, subtonic. If the subtonic is a semitone away from the tonic, then it is usually called the leading-tone (or leading-note); otherwise the leading-tone refers to the raised subtonic. Also commonly used is the (movable do) solfège naming convention in which each scale degree is denoted by a syllable. In the major scale, the solfège syllables are: do, re, mi, fa, so (or sol), la, ti (or si), do (or ut).

In naming the notes of a scale, it is customary that each scale degree be assigned its own letter name: for example, the A major scale is written A–B–C♯–D–E–F♯–G♯ rather than A–B–D♭–D–E–E–G♯. However, it is impossible to do this in scales that contain more than seven notes, at least in the English-language nomenclature system.

Scales may also be identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale. It is assumed that the scale is tuned using 12-tone equal temperament (so that, for instance, C♯ is the same as D♭), and that the tonic is in the leftmost position. For example, the binary number 101011010101, equivalent to the decimal number 2773, would represent any major scale (such as C–D–E–F–G–A–B). This system includes scales from 100000000000 (2048) to 111111111111 (4095), providing a total of 2048 possible species, but only 352 unique scales containing from 1 to 12 notes.[8]

A more mathematically flexible schema for binary representation, espoused by theorist Ian Ring in his study of musical scales,[9] has bits representing ascending tones, with the smaller bits representing lower pitches and higher bits representing higher pitches. This causes the bits to appear reversed compared with Duncan's system. Under this schema, a major scale is 101010110101 = (2741), a single root tone is 1, and a chromatic scale is still 111111111111 (4095). All the tone possibilities that begin with a root tone, and are thus scale-like, are odd-numbered.

Scales may also be shown as semitones from the tonic. For instance, 0 2 4 5 7 9 11 denotes any major scale such as C–D–E–F–G–A–B, in which the first degree is, obviously, 0 semitones from the tonic (and therefore coincides with it), the second is 2 semitones from the tonic, the third is 4 semitones from the tonic, and so on. Again, this implies that the notes are drawn from a chromatic scale tuned with 12-tone equal temperament. For some fretted string instruments, such as the guitar and the bass guitar, scales can be notated in tabulature, an approach which indicates the fret number and string upon which each scale degree is played.

Transposition and modulation

Composers transform musical patterns by moving every note in the pattern by a constant number of scale steps: thus, in the C major scale, the pattern C–D–E might be shifted up, or transposed, a single scale step to become D–E–F. This process is called "scalar transposition" or "shifting to a new key" and can often be found in musical sequences and patterns. Since the steps of a scale can have various sizes, this process introduces subtle melodic and harmonic variation into the music. In Western tonal music, the simplest and most common type of modulation (or changing keys) is to shift from one major key to another key built on the first key's fifth (or dominant) scale degree. In the key of C major, this would involve moving to the key of G major (which uses an F#). Composers also often modulate to other related keys. In some Romantic music era pieces and contemporary music, composers modulate to "remote keys" that are not related to or close to the tonic. An example of a remote modulation would be taking a song that begins in C major and modulating (changing keys) to F# major. This variation from transposition and modulation is what gives scalar music much of its complexity.

Jazz and blues

Through the introduction of blue notes, jazz and blues employ scale intervals smaller than a semitone. The blue note is an interval that is technically neither major nor minor but "in the middle", giving it a characteristic flavour. A regular piano cannot play blue notes, but with electric guitar, saxophone, trombone and trumpet, performers can "bend" notes a fraction of a tone sharp or flat to create blue notes For instance, in the key of E, the blue note would be either a note between G and G♯ or a note moving between both. In blues. a pentatonic scale is often used. In jazz many different modes and scales are used, often within the same piece of music. Chromatic scales are common, especially in modern jazz.

Non-Western scales

Equally tempered

In Western music, scale notes are often separated by equally tempered tones or semitones, creating 12 notes per octave. A scale uses a subset of these 12. There are other traditional tempered scale systems dividing the octave to equal intevals in other numbers than 12. Examples are 53 in the Middle East, and 72 in southern India.

Other

Many other musical traditions use scales that include other intervals. These scales originate within the derivation of the harmonic series. Musical intervals are complementary values of the harmonic overtones series.[10] Many musical scales in the world are based on this system, except most of the musical scales from Indonesia and the Indochina Peninsulae, which are based on inharmonic resonance of the dominant metalophone and xylophone instruments.

Intra-scale intervals

There are also scales that use a different number of pitches. A common scale in Eastern music is the pentatonic scale, consisting of five notes spanning an octave.

Some scales span part of an octave; Several such short scales are typically combined to form a scale spanning a full octave or more, and usually called with a third name of its own. The Middle Eastern music has around a dozen such short scales that are combined to form hundreds of full-octave spanning scales. Among these middle eastern scales Hejaz scale has one interval spanning 14 commas (of the middle eastern type found 53 in an octave) roughly similar to 3 semitones (of the western type found 12 in an octave), while Saba scale, another of these middle eastern scales, has 3 consecutive tones within 14 commas, i.e. separated by roughly one western semitone either side of the middle tone.

Gamelan music uses a small variety of scales including Pélog and Sléndro, none including equally tempered nor harmonic intervals. Indian classical music uses a moveable seven-note scale. Indian Rāgas often use intervals smaller than a semitone.[11] Arabic music maqamat may use quarter tone intervals.[12] In both rāgas and maqamat, the distance between a note and an inflection (e.g., śruti) of that same note may be less than a semitone.

Microtonal scales

The term microtonal music usually refers to music with roots in traditional Western music that uses non-standard scales or scale intervals. In the late 19th century, Mexican composer Julián Carrillo created microtonal scales that he called Sonido 13. The composer Harry Partch made custom musical instruments to play compositions based on 43-note scale system, and the American jazz vibraphonist Emil Richards experimented with such scales in his Microtonal Blues Band in the 1970s. Easley Blackwood wrote compositions in all equal-tempered scales from 13 to 24 notes. Erv Wilson introduced concepts such as Combination Product Sets (Hexany), Moments of Symmetry and golden horagrams, used by many modern composers. Microtonal scales are also used in traditional Indian Raga music, which uses a variety of modes not only as modes or scales, but also as defining elements of the song, or raga.

See also

References

  1. ↑ Benward, Bruce and Saker, Marilyn Nadine (2003). Music: In Theory and Practice, seventh edition: vol. 1, p.25. Boston: McGraw-Hill. ISBN 978-0-07-294262-0.
  2. ↑ Hewitt, Michael (2013). Musical Scales of the World, pp. 2–3. The Note Tree. ISBN 978-0-9575470-0-1.
  3. ↑ Nzewi, Meki, and Odyke Nzewi (2007), A Contemporary Study of Musical Arts. Pretoria: Centre for Indigenous Instrumental African Music and Dance. ISBN 978-1-920051-62-4.
  4. ↑ Nettl, Bruno, and Helen Myers (1976). Folk Music in the United States, p.39. ISBN 978-0-8143-1557-6.
  5. ↑ Hanson, Howard. (1960) Harmonic Materials of Modern Music, pp.7ff. New York: Appleton-Century-Crofts. LOC 58-8138.
  6. ↑ Hanson, Howard. (1960) Harmonic Materials of Modern Music, pp.7ff. New York: Appleton-Century-Crofts. LOC 58-8138.
  7. ↑ Tymoczko, Dmitri (2004). "Scale Networks and Debussy" (PDF). Journal of Music Theory. 48 (2): 219–294. ISSN 0022-2909. doi:10.1215/00222909-48-2-219. Retrieved 18 July 2017.. Citation on 254–264.
  8. ↑ Duncan, Andrew (1991). "Combinatorial Music Theory". Journal of the Audio Engineering Society. 39 (6): 427–448. ISSN 0004-7554. Archived from the original on 7 January 2008. Retrieved 18 July 2017.
  9. ↑ Ring, Ian. "A Study of Scales". Ian Ring. Retrieved 18 July 2017.
  10. ↑ Explanation of the origin of musical scales clarified by a string division method by Yuri Landman on furious.com
  11. ↑ Burns, Edwaard M. 1998. "Intervals, Scales, and Tuning.", p.247. In The Psychology of Music, second edition, edited by Diana Deutsch, 215–64. New York: Academic Press. ISBN 0-12-213564-4.
  12. ↑ Zonis [Mahler], Ella. 1973. Classical Persian Music: An Introduction. Cambridge, MA: Harvard University Press.

Further reading

  • Barbieri, Patrizio (2008). Enharmonic Instruments and Music, 1470–1900. Latina, Italy: Il Levante Libreria Editrice. ISBN 978-88-95203-14-0. 
  • Yamaguchi, Masaya (2006). The Complete Thesaurus of Musical Scales (revised ed.). New York: Masaya Music Services. ISBN 978-0-9676353-0-9. 

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