Post-tonal music theory
Encyclopedia
Post-tonal music theory is the set of theories
put forward to describe music
written outside of, or 'after', the tonal system
of the common practice period
.
's music, especially Tristan und Isolde
(the Tristan chord
, for example). Arnold Schoenberg
and his pupil Anton Webern
proposed a theory on the emancipation of the dissonance
to help analyse the general trend and, in particular, their own atonal
music. Composers such as Charles Ives
, Dane Rudhyar
, and even Duke Ellington
and Lou Harrison
, connected the emancipation of the dissonance with the emancipation of society and humanity.
The basic idea is that as time progresses, the ear becomes acclimatised to more and more complex sounds. This happens not just for individuals but also for societies as they start to write more complex music. Consonance and dissonance
become indistinct from each other: dissonances slowly become heard as consonances. Jim Samson explained it this way: "As the ear becomes acclimatized to a sonority within a particular context, the sonority will gradually become 'emancipated' from that context and seek a new one. The emancipation of the dominant-quality dissonances has followed this pattern, with the dominant seventh developing in status from a contrapuntal note in the sixteenth century to a quasi-consonant harmonic note in the early nineteenth. By the later nineteenth century the higher numbered dominant-quality dissonances had also achieved harmonic status, with resolution delayed or omitted completely. The greater autonomy of the dominant-quality dissonance contributed significantly to the weakening of traditional tonal function within a purely diatonic context."
is the "Tonic" chord. Other notes and chords are subservient to the Tonic and in a strict hierarchy: the "Dominant" note/chord is second in importance, others are lower down still. One example of this style of analysis is called Schenkerian analysis
. However, this form of analysis cannot be applied to Atonal music since the very point is to make all the notes and chords equal: there is no hierarchy. Instead, notes/chords can be described in terms of their properties and relationships at any particular moment: whether one note is higher than another, whether one chord has more notes than another, whether one chord is more widely spaced than another, and so on. One can also compare and contrast different strings of notes as transposition
s (change in pitch) or inversion
s (change in note order) of each other. These terms are also used compare chords. These methods of analysis have been used for centuries but became more important as music began to lose its tonal basis. One also needs to consider other aspects, such as how two or more simultaneous melodies relate to each other (counterpoint
) and the same tools are used for this.
In the later 20th century, analysts started to adapt these tools to the yet more complex music being written. Musical set theory
was first elaborated for tonal music but was quickly applied to atonal music since it simply provides concepts for categorizing musical objects (notes, chords, melodies and so on) and describing their relationship, without defining any particular note or chord as "primary". The later Transformational theory
uses a similar approach but concentrates on the relationships themselves. There are also theories which attempt to relate pitch and rhythm.
. In this system, certain notes are chosen then written in an order eg E-F♯-C-B♭-G-F. (Usually there is no repetition, but this is not always observed.) These notes are then used as the basis for a composition by playing them in the original order, in reverse order (Retrograde), in "upside down" order (Inversion ie upward intervals now go down, and vice versa), or both (Retrograde Inversion or "Reversion" [Stravinsky's term]), and then transposed up or down. Chords can also be formed out of the "Series" and these can be treated to similar techniques. Schoenberg used these methods in what has become known as Twelve-tone technique
. In this, all unique twelve notes of the musical scale are played once and once only in a specified order. The serial techniques described above are then applied. Later composers, such as Jean Barraqué
and Pierre Boulez
, sought to unify pitch and rhythm by organising the elements into sets of twelve, which resulted in what became known as Total Serialism. See also Formula composition
which describes techniques used by Karlheinz Stockhausen
.
Aside from Serialism, other forms of compositional technique arose such as those based on chords utilizing fourths rather than the more traditional thirds (see Quartal and quintal harmony
and Synthetic chord
), those based on other mathematical processes (see Schillinger System
and those based on specific scales (or "modes
": see Hexatonic scale
, Heptatonic scale
, Octatonic scale
and Synthetic scale
). Olivier Messiaen
in his work The Technique of my Musical Language developed what he called Modes of limited transposition
which displayed a special type of symmetry and which he used in numerous compositions.
s have been used in music of the 20th and 21st centuries. These are the notes smaller than a semitone
. A full theory governing these has yet to be developed but the articles relating to these contain some of the most recent thoughts. (See 15 equal temperament
, 19 equal temperament
, 24 equal temperament, 34 equal temperament
and 72 equal temperament
.)
Inversion:
When viewing the following musical examples, it may help to imagine a mirror being placed between the various versions:
Music theory
Music theory is the study of how music works. It examines the language and notation of music. It seeks to identify patterns and structures in composers' techniques across or within genres, styles, or historical periods...
put forward to describe music
Music
Music is an art form whose medium is sound and silence. Its common elements are pitch , rhythm , dynamics, and the sonic qualities of timbre and texture...
written outside of, or 'after', the tonal system
Tonality
Tonality is a system of music in which specific hierarchical pitch relationships are based on a key "center", or tonic. The term tonalité originated with Alexandre-Étienne Choron and was borrowed by François-Joseph Fétis in 1840...
of the common practice period
Common practice period
The common practice period, in the history of Western art music , spanning the Baroque, Classical, and Romantic periods, lasted from c. 1600 to c. 1900.-General characteristics:...
.
Overview
In the latter part of the 19th century, composers began to move away from the tonal system. This is typified in Richard WagnerRichard Wagner
Wilhelm Richard Wagner was a German composer, conductor, theatre director, philosopher, music theorist, poet, essayist and writer primarily known for his operas...
's music, especially Tristan und Isolde
Tristan und Isolde
Tristan und Isolde is an opera, or music drama, in three acts by Richard Wagner to a German libretto by the composer, based largely on the romance by Gottfried von Straßburg. It was composed between 1857 and 1859 and premiered in Munich on 10 June 1865 with Hans von Bülow conducting...
(the Tristan chord
Tristan chord
The Tristan chord is a chord made up of the notes F, B, D and G. More generally, it can be any chord that consists of these same intervals: augmented fourth, augmented sixth, and augmented ninth above a root...
, for example). Arnold Schoenberg
Arnold Schoenberg
Arnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
and his pupil Anton Webern
Anton Webern
Anton Webern was an Austrian composer and conductor. He was a member of the Second Viennese School. As a student and significant follower of Arnold Schoenberg, he became one of the best-known exponents of the twelve-tone technique; in addition, his innovations regarding schematic organization of...
proposed a theory on the emancipation of the dissonance
Emancipation of the dissonance
The emancipation of the dissonance was a concept or goal put forth by composer Arnold Schoenberg and others, including his pupil Anton Webern. The phrase first appears in Schoenberg's 1926 essay "Opinion or Insight?". It may be described as a metanarrative to justify atonality...
to help analyse the general trend and, in particular, their own atonal
Atonality
Atonality in its broadest sense describes music that lacks a tonal center, or key. Atonality in this sense usually describes compositions written from about 1908 to the present day where a hierarchy of pitches focusing on a single, central tone is not used, and the notes of the chromatic scale...
music. Composers such as Charles Ives
Charles Ives
Charles Edward Ives was an American modernist composer. He is one of the first American composers of international renown, though Ives' music was largely ignored during his life, and many of his works went unperformed for many years. Over time, Ives came to be regarded as an "American Original"...
, Dane Rudhyar
Dane Rudhyar
Dane Rudhyar , born Daniel Chennevière, was an author, modernist composer and humanistic astrologer. He was the pioneer of modern transpersonal astrology.-Biography:...
, and even Duke Ellington
Duke Ellington
Edward Kennedy "Duke" Ellington was an American composer, pianist, and big band leader. Ellington wrote over 1,000 compositions...
and Lou Harrison
Lou Harrison
Lou Silver Harrison was an American composer. He was a student of Henry Cowell, Arnold Schoenberg, and K. P. H. Notoprojo Lou Silver Harrison (May 14, 1917 – February 2, 2003) was an American composer. He was a student of Henry Cowell, Arnold Schoenberg, and K. P. H. Notoprojo Lou Silver Harrison...
, connected the emancipation of the dissonance with the emancipation of society and humanity.
The basic idea is that as time progresses, the ear becomes acclimatised to more and more complex sounds. This happens not just for individuals but also for societies as they start to write more complex music. Consonance and dissonance
Consonance and dissonance
In music, a consonance is a harmony, chord, or interval considered stable, as opposed to a dissonance , which is considered to be unstable...
become indistinct from each other: dissonances slowly become heard as consonances. Jim Samson explained it this way: "As the ear becomes acclimatized to a sonority within a particular context, the sonority will gradually become 'emancipated' from that context and seek a new one. The emancipation of the dominant-quality dissonances has followed this pattern, with the dominant seventh developing in status from a contrapuntal note in the sixteenth century to a quasi-consonant harmonic note in the early nineteenth. By the later nineteenth century the higher numbered dominant-quality dissonances had also achieved harmonic status, with resolution delayed or omitted completely. The greater autonomy of the dominant-quality dissonance contributed significantly to the weakening of traditional tonal function within a purely diatonic context."
Theory
Music written within the tonal system is generally analysed by defining a certain note as the primary or "Tonic" note and the derived triadTriad (music)
In music and music theory, a triad is a three-note chord that can be stacked in thirds. Its members, when actually stacked in thirds, from lowest pitched tone to highest, are called:* the Root...
is the "Tonic" chord. Other notes and chords are subservient to the Tonic and in a strict hierarchy: the "Dominant" note/chord is second in importance, others are lower down still. One example of this style of analysis is called Schenkerian analysis
Schenkerian analysis
Schenkerian analysis is a method of musical analysis of tonal music based on the theories of Heinrich Schenker. The goal of a Schenkerian analysis is to interpret the underlying structure of a tonal work. The theory's basic tenets can be viewed as a way of defining tonality in music...
. However, this form of analysis cannot be applied to Atonal music since the very point is to make all the notes and chords equal: there is no hierarchy. Instead, notes/chords can be described in terms of their properties and relationships at any particular moment: whether one note is higher than another, whether one chord has more notes than another, whether one chord is more widely spaced than another, and so on. One can also compare and contrast different strings of notes as transposition
Transposition (music)
In music transposition refers to the process, or operation, of moving a collection of notes up or down in pitch by a constant interval.For example, one might transpose an entire piece of music into another key...
s (change in pitch) or inversion
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...
s (change in note order) of each other. These terms are also used compare chords. These methods of analysis have been used for centuries but became more important as music began to lose its tonal basis. One also needs to consider other aspects, such as how two or more simultaneous melodies relate to each other (counterpoint
Counterpoint
In music, counterpoint is the relationship between two or more voices that are independent in contour and rhythm and are harmonically interdependent . It has been most commonly identified in classical music, developing strongly during the Renaissance and in much of the common practice period,...
) and the same tools are used for this.
In the later 20th century, analysts started to adapt these tools to the yet more complex music being written. Musical set theory
Set theory (music)
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Many of the notions were first elaborated by Howard Hanson in connection with tonal music, and then mostly developed in connection with atonal music by theorists such as Allen Forte , drawing...
was first elaborated for tonal music but was quickly applied to atonal music since it simply provides concepts for categorizing musical objects (notes, chords, melodies and so on) and describing their relationship, without defining any particular note or chord as "primary". The later Transformational theory
Transformational theory
Transformational theory is a branch of music theory developed by David Lewin in the 1980s, and formally introduced in his most influential work, Generalized Musical Intervals and Transformations...
uses a similar approach but concentrates on the relationships themselves. There are also theories which attempt to relate pitch and rhythm.
Application
Compositional applications of these theories are numerous, but in the present context of "Post-tonal" music the most important is SerialismSerialism
In music, serialism is a method or technique of composition that uses a series of values to manipulate different musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though his contemporaries were also working to establish serialism as one example of...
. In this system, certain notes are chosen then written in an order eg E-F♯-C-B♭-G-F. (Usually there is no repetition, but this is not always observed.) These notes are then used as the basis for a composition by playing them in the original order, in reverse order (Retrograde), in "upside down" order (Inversion ie upward intervals now go down, and vice versa), or both (Retrograde Inversion or "Reversion" [Stravinsky's term]), and then transposed up or down. Chords can also be formed out of the "Series" and these can be treated to similar techniques. Schoenberg used these methods in what has become known as Twelve-tone technique
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
. In this, all unique twelve notes of the musical scale are played once and once only in a specified order. The serial techniques described above are then applied. Later composers, such as Jean Barraqué
Jean Barraqué
Jean-Henri-Alphonse Barraqué was a French composer and writer on music who developed an individual form of serialism which is displayed in a small output of highly complex but passionate works.-Life:...
and Pierre Boulez
Pierre Boulez
Pierre Boulez is a French composer of contemporary classical music, a pianist, and a conductor.-Early years:Boulez was born in Montbrison, Loire, France. As a child he began piano lessons and demonstrated aptitude in both music and mathematics...
, sought to unify pitch and rhythm by organising the elements into sets of twelve, which resulted in what became known as Total Serialism. See also Formula composition
Formula composition
Formula composition is a serially-derived technique encountered principally in the music of Karlheinz Stockhausen, involving the projection, expansion, and Ausmultiplikation of either a single melody-formula, or a two- or three-voice contrapuntal construction .In contrast to serial music, where the...
which describes techniques used by Karlheinz Stockhausen
Karlheinz Stockhausen
Karlheinz Stockhausen was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. Another critic calls him "one of the great visionaries of 20th-century music"...
.
Aside from Serialism, other forms of compositional technique arose such as those based on chords utilizing fourths rather than the more traditional thirds (see Quartal and quintal harmony
Quartal and quintal harmony
In music, quartal harmony is the building of harmonic structures with a distinct preference for the intervals of the perfect fourth, the augmented fourth and the diminished fourth. Quintal harmony is harmonic structure preferring the perfect fifth, the augmented fifth and the diminished fifth...
and Synthetic chord
Synthetic chord
In music the mystic chord or Prometheus chord is a complex six-note chord, scale, or pitch collection, which loosely serves as the harmonic and melodic basis for some of the later pieces by Russian composer Alexander Scriabin...
), those based on other mathematical processes (see Schillinger System
Schillinger System
The Schillinger System of Musical Composition, named after Joseph Schillinger, is a method of musical composition based on mathematical processes...
and those based on specific scales (or "modes
Musical mode
In the theory of Western music since the ninth century, mode generally refers to a type of scale. This usage, still the most common in recent years, reflects a tradition dating to the middle ages, itself inspired by the theory of ancient Greek music.The word encompasses several additional...
": see Hexatonic scale
Hexatonic scale
In music and music theory, a hexatonic scale is a scale with six pitches or notes per octave. Famous examples include the whole tone scale, C D E F G A C; the augmented scale, C D E G A B C; the Prometheus scale, C D E F A B C; and what some jazz theorists call the "blues scale", C E F F G B...
, Heptatonic scale
Heptatonic scale
A heptatonic scale is a musical scale with seven pitches per octave. Among the most famous of these are the major scale, C D E F G A B C; the melodic minor scale, C D E F G A B C ascending, C B A G F E D C descending; the harmonic minor scale, C D E F G A B C; and a scale variously known as the...
, Octatonic scale
Octatonic scale
An octatonic scale is any eight-note musical scale. Among the most famous of these is a scale in which the notes ascend in alternating intervals of a whole step and a half step, creating a symmetric scale...
and Synthetic scale
Synthetic scale
In music, a synthetic scale is a scale which has been derived from a traditional diatonic major scale through the alteration of one degree by a semitone in either direction. Composer Ferruccio Busoni originally explored these scales in his A New Esthetic of Music and their number and variety were...
). Olivier Messiaen
Olivier Messiaen
Olivier Messiaen was a French composer, organist and ornithologist, one of the major composers of the 20th century. His music is rhythmically complex ; harmonically and melodically it is based on modes of limited transposition, which he abstracted from his early compositions and improvisations...
in his work The Technique of my Musical Language developed what he called Modes of limited transposition
Modes of limited transposition
Modes of limited transposition are musical modes or scales that fulfill specific criteria relating to their symmetry and the repetition of their interval groups...
which displayed a special type of symmetry and which he used in numerous compositions.
Further developments
Microtones and especially Quarter toneQuarter tone
A quarter tone , is a pitch halfway between the usual notes of a chromatic scale, an interval about half as wide as a semitone, which is half a whole tone....
s have been used in music of the 20th and 21st centuries. These are the notes smaller than a semitone
Semitone
A semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
. A full theory governing these has yet to be developed but the articles relating to these contain some of the most recent thoughts. (See 15 equal temperament
15 equal temperament
In music, 15 equal temperament, called 15-TET, 15-EDO, or 15-ET, is the tempered scale derived by dividing the octave into 15 equal steps . Each step represents a frequency ratio of 21/15, or 80 cents...
, 19 equal temperament
19 equal temperament
In music, 19 equal temperament, called 19-TET, 19-EDO, or 19-ET, is the tempered scale derived by dividing the octave into 19 equal steps . Each step represents a frequency ratio of 21/19, or 63.16 cents...
, 24 equal temperament, 34 equal temperament
34 equal temperament
In musical theory, 34 equal temperament, also referred to as 34-tet, 34-edo or 34-et, is the tempered tuning derived by dividing the octave into 34 equal-sized steps...
and 72 equal temperament
72 equal temperament
In music, 72 equal temperament, called twelfth-tone, 72-tet, 72-edo, or 72-et, is the tempered scale derived by dividing the octave into twelfth-tones, or in other words 72 equal steps...
.)
Examples
Transposition:- The notes A-B-C-D can be transposed downwards to A♭-B♭-C♭-D♭ (the ♭, called a flat, lowers the pitch by one semitoneSemitoneA semitone, also called a half step or a half tone, is the smallest musical interval commonly used in Western tonal music, and it is considered the most dissonant when sounded harmonically....
) or upwards to D-E-F-G (the note D is a perfect fourthPerfect fourthIn classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
higher than the note A, E the same amount higher than B and so on).
- The chord C-E-G can be transposed upwards to C♯-E♯-G♯ (the ♯, called a sharp, raises the pitch by one semitone).
Inversion:
- The notes D-F-E-B can be reversed to B-E-F-D - This form of inversion is called Retrograde.
- The upward intervals can become downward intervals and vice versa - This is the form that is properly called Inversion.
- These two can be combined and the result can be transposed: these are inclusive rather than exclusive processes.
When viewing the following musical examples, it may help to imagine a mirror being placed between the various versions:
- The chord C-E-G can be inverted to E-G-C or G-C-E - This is called the Inversion of a chord.
- Two lines ("partPart (music)1) A part is a strand or melody of music played by an individual instrument or voice within a larger work. Parts may be referred to as an outer part or an inner part . Part-writing is the composition of parts in consideration of harmony and counterpoint...
s") of music can be "inverted" so that the original lower one is made to sound above the original higher one - this is Inversion of counterpoint and can be applied to any number of parts.
Further reading
- Messiaen, Olivier. 1956. The Technique of my Musical Language (English Language version). Alphonse Leduc.