Twelve-tone technique is a method of musical
compositionMusical composition can refer to an original piece of music, the structure of a musical piece, or the process of creating a new piece of music. People who practice composition are called composers.- Musical compositions :...
devised by
Arnold SchoenbergArnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
. The technique is a means of ensuring that all 12 notes of the
chromatic scaleThe chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
are sounded as often as one another in a piece of music while preventing the emphasis of any through the use of
tone rowIn music, a tone row or note row , also series and set, refers to a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.-History and usage:Tone rows are the basis of...
s, an ordering of the 12 pitches. All 12 notes are thus given more or less equal importance, and the music avoids being in a
keyIn music theory, the term key is used in many different and sometimes contradictory ways. A common use is to speak of music as being "in" a specific key, such as in the key of C major or in the key of F-sharp. Sometimes the terms "major" or "minor" are appended, as in the key of A minor or in the...
. The technique was influential on composers in the mid-twentieth century.
Schoenberg himself described the system as a "Method of Composing with Twelve Tones Which are Related Only with One Another". However, the common English usage is to describe the method as a form of
serialismIn 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...
.
Josef Matthias HauerJosef Mattias Hauer was an Austrian composer and music theorist. He is most famous for developing, independent of and a year or two before Arnold Schoenberg, a method for composing with all 12 notes of the chromatic scale.Hauer "detested all art that expressed ideas, programmes or feelings,"...
also developed a similar system using unordered
hexachordIn music, a hexachord is a collection of six pitch classes including six-note segments of a scale or tone row. The term was adopted in the Middle Ages and adapted in the twentieth-century in Milton Babbitt's serial theory.-Middle Ages:...
s, or
tropes, at the same time and in the same country as Schoenberg but with no connection to Schoenberg's twelve-tone technique. Other composers have created systematic use of the chromatic scale, but Schoenberg's method is considered to be historically and aesthetically most significant.
History of use
Invented by Austrian composer
Arnold SchoenbergArnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
in 1921 and first described privately to his associates in 1923, the method was used during the next twenty years almost exclusively by the composers of the
Second Viennese SchoolThe Second Viennese School is the group of composers that comprised Arnold Schoenberg and his pupils and close associates in early 20th century Vienna, where he lived and taught, sporadically, between 1903 and 1925...
–
Alban BergAlban Maria Johannes Berg was an Austrian composer. He was a member of the Second Viennese School with Arnold Schoenberg and Anton Webern, and produced compositions that combined Mahlerian Romanticism with a personal adaptation of Schoenberg's twelve-tone technique.-Early life:Berg was born in...
,
Anton WebernAnton 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...
,
Hanns EislerHanns Eisler was an Austrian composer.-Family background:Eisler was born in Leipzig where his Jewish father, Rudolf Eisler, was a professor of philosophy...
and Schoenberg himself.
The twelve tone technique was preceded by "freely"
atonalAtonality 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...
pieces of 1908–23 which, though "free", often have as an "integrative element...a minute intervallic cell" which in addition to expansion may be transformed as with a tone row, and in which individual notes may "function as pivotal elements, to permit overlapping statements of a basic cell or the linking of two or more basic cells". The twelve-tone technique was also preceded by "nondodecaphonic serial composition" used independently in the works of
Alexander ScriabinAlexander Nikolayevich Scriabin was a Russian composer and pianist who initially developed a lyrical and idiosyncratic tonal language inspired by the music of Frédéric Chopin. Quite independent of the innovations of Arnold Schoenberg, Scriabin developed an increasingly atonal musical system,...
,
Igor StravinskyIgor Fyodorovich Stravinsky ; 6 April 1971) was a Russian, later naturalized French, and then naturalized American composer, pianist, and conductor....
,
Béla BartókBéla Viktor János Bartók was a Hungarian composer and pianist. He is considered one of the most important composers of the 20th century and is regarded, along with Liszt, as Hungary's greatest composer...
,
Carl RugglesCharles "Carl" Sprague Ruggles was an American composer of the American Five group. He wrote finely crafted pieces using "dissonant counterpoint", a term coined by Charles Seeger to describe Ruggles' music...
, and others. Oliver Neighbour argues that Bartók was "the first composer to use a group of twelve notes consciously for a structural purpose," in 1908 with the third of his fourteen bagatelles. "Essentially, Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of 'modern' musical practice, the
ostinatoIn music, an ostinato is a motif or phrase, which is persistently repeated in the same musical voice. An ostinato is always a succession of equal sounds, wherein each note always has the same weight or stress. The repeating idea may be a rhythmic pattern, part of a tune, or a complete melody in...
". Additionally, the strict distinction between the two, emphasized by authors including Perle, is overemphasized:
The distinction often made between Hauer and the Schoenberg school—that the former's music is based on unordered hexachords while the latter's is based on an ordered series—is false: while he did write pieces that could be thought of as "trope pieces", much of Hauer's twelve-tone music employs an ordered series.
The "strict ordering" of the Second Viennese school, on the other hand, "was inevitably tempered by practical considerations: they worked on the basis of an interaction between ordered and unordered pitch collections."
Rudolph RetiRudolph Reti , was a musical analyst, composer and pianist. He was the older brother of the great chess master Richard Réti ....
, an early proponent, says: "To replace one structural force (tonality) by another (increased thematic oneness) is indeed the fundamental idea behind the twelve-tone technique," arguing it arose out of Schoenberg's frustrations with free atonality, providing a "positive premise" for atonality. In Hauer's breakthrough piece
Nomos, Op. 19 (1919) he used twelve-tone sections to mark out large formal divisions, such as with the opening five statements of the same twelve-tone series, stated in groups of five notes making twelve five-note phrases.
Schoenberg's idea in developing the technique was for it to "replace those structural differentiations provided formerly by
tonalTonality 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...
harmoniesIn music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
". As such, twelve-tone music is usually
atonalAtonality 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...
, and treats each of the 12
semitoneA 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....
s of the
chromatic scaleThe chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
with equal importance, as opposed to earlier classical music which had treated some notes as more important than others (particularly the
tonicIn music, the tonic is the first scale degree of the diatonic scale and the tonal center or final resolution tone. The triad formed on the tonic note, the tonic chord, is thus the most significant chord...
and the dominant note).
The technique became widely used by the fifties, taken up by composers such as
Milton BabbittMilton Byron Babbitt was an American composer, music theorist, and teacher. He is particularly noted for his serial and electronic music.-Biography:...
,
Luciano BerioLuciano Berio, Cavaliere di Gran Croce OMRI was an Italian composer. He is noted for his experimental work and also for his pioneering work in electronic music.-Biography:Berio was born at Oneglia Luciano Berio, Cavaliere di Gran Croce OMRI (October 24, 1925 – May 27, 2003) was an Italian...
,
Pierre BoulezPierre 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...
,
Luigi DallapiccolaLuigi Dallapiccola was an Italian composer known for his lyrical twelve-tone compositions.-Biography:Dallapiccola was born at Pisino d'Istria , to Italian parents....
,
Ernst KrenekErnst Krenek was an Austrian of Czech origin and, from 1945, American composer. He explored atonality and other modern styles and wrote a number of books, including Music Here and Now , a study of Johannes Ockeghem , and Horizons Circled: Reflections on my Music...
,
Riccardo MalipieroRiccardo Malipiero was an Italian composer, pianist, and music educator. He was awarded the gold medal by the city of Milan in 1977 and by the city of Varese in 1984....
, and, after Schoenberg's death,
Igor StravinskyIgor Fyodorovich Stravinsky ; 6 April 1971) was a Russian, later naturalized French, and then naturalized American composer, pianist, and conductor....
. Some of these composers extended the technique to control aspects other than the pitches of notes (such as duration, method of attack and so on), thus producing serial music. Some even subjected all elements of music to the serial process.
Charles WuorinenCharles Peter Wuorinen is a prolific Pulitzer Prize-winning American composer born and living in New York City. His catalog of more than 250 compositions includes works for orchestra, opera, chamber music, as well as solo instrumental and vocal works...
claimed in a 1962 interview that while, "most of the Europeans say that they have 'gone beyond' and 'exhausted' the twelve-tone system," in America, "the twelve-tone system has been carefully studied and generalized into an edifice more impressive than any hitherto known."
In 1971 legendary jazz pianist
Bill EvansWilliam John Evans, known as Bill Evans was an American jazz pianist. His use of impressionist harmony, inventive interpretation of traditional jazz repertoire, and trademark rhythmically independent, "singing" melodic lines influenced a generation of pianists including: Chick Corea, Herbie...
– who played on the landmark modal jazz album
Kind Of BlueKind of Blue is a studio album by American jazz musician Miles Davis, released August 17, 1959, on Columbia Records in the United States. Recording sessions for the album took place at Columbia's 30th Street Studio in New York City on March 2 and April 22, 1959...
by
Miles DavisMiles Dewey Davis III was an American jazz musician, trumpeter, bandleader, and composer. Widely considered one of the most influential musicians of the 20th century, Miles Davis was, with his musical groups, at the forefront of several major developments in jazz music, including bebop, cool jazz,...
– recorded a
Grammy AwardA Grammy Award — or Grammy — is an accolade by the National Academy of Recording Arts and Sciences of the United States to recognize outstanding achievement in the music industry...
-winning album called
The Bill Evans AlbumThe Bill Evans Album is an album by jazz pianist Bill Evans, released in 1971.At the Grammy Awards of 1972, The Bill Evans Album won the Grammy Award for Best Jazz Instrumental Solo and the Best Jazz Performance by a Group awards....
, which included a composition called "T.T.T. (Twelve Tone Tune)" where Evans and his trio explored the jazz implications of using the twelve tone compositional technique.
More recently progressive metal guitarist
Ron JarzombekRon Jarzombek is an American guitarist best known for his work with Austin, Texas progressive metal trailblazers WatchTower, '90s madcap trio, Spastic Ink, technical extreme metal band Blotted Science, featuring Cannibal Corpse bassist Alex Webster and Obscura drummer Hannes Grossmann, and most...
(
WatchtowerWatchTower is an American progressive metal band based in Austin, Texas. The band were influenced by late 1970s progressive rock and acts such as Rush and UK as well as the burgeoning New Wave of British Heavy Metal...
,
Spastic InkSpastic Ink is a progressive technical metal band from the United States.-History:Spastic Ink was formed in 1993 by guitarist Ron Jarzombek of Watchtower after recovering from multiple hand surgeries that had sidelined him, unable to play, for a couple of years. He would be joined by brother Bobby...
,
Blotted ScienceBlotted Science is an instrumental technical death metal supergroup headed by Ron Jarzombek , bassist Alex Webster and drummer Hannes Grossmann...
) used the technique almost exclusively on the track "Oscillation Cycles" off of Blotted Science's album "The Machinations of Dementia". Ron also released a DVD titled "12 Tone Variations" in which similar techniques are explained.
Tone row
The basis of twelve-tone technique is the
tone rowIn music, a tone row or note row , also series and set, refers to a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.-History and usage:Tone rows are the basis of...
, an ordered arrangement of the twelve notes of the
chromatic scaleThe chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
(the twelve
equal temperedAn equal temperament is a musical temperament, or a system of tuning, in which every pair of adjacent notes has an identical frequency ratio. As pitch is perceived roughly as the logarithm of frequency, this means that the perceived "distance" from every note to its nearest neighbor is the same for...
pitch classIn music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
es). There are four postulates or preconditions to the technique which apply to the set on which a work or section is based:
- The set is a specific ordering of all twelve notes of the semitonal scale.
- No note is repeated within the set
- The set may be stated in any of its "linear aspects": prime, inversion, retrograde, and retrograde-inversion.
- The set in any of its four transformations may be started upon any degree of the semitonal scale.
When twelve-tone technique is strictly applied, a piece consists of statements of certain permitted
transformationsIn music, a transformation consists of any operation or process that may apply to a musical variable in composition, performance, or analysis. Transformations include multiplication, rotation, permutation In music, a transformation consists of any operation or process that may apply to a musical...
of the prime series. Note that these statements may appear consecutively, simultaneously, or may overlap, giving rise to
harmonyIn music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
.
In Hauer's system postulate 3 does not apply.
Transformations
The tone row chosen as the basis of the piece is called the
prime series (P). Untransposed, it is notated as P
0. Given the twelve
pitch classIn music, a pitch class is a set of all pitches that are a whole number of octaves apart, e.g., the pitch class C consists of the Cs in all octaves...
es of the chromatic scale, there are (12!) (
factorialIn mathematics, the factorial of a non-negative integer n, denoted by n!, is the product of all positive integers less than or equal to n...
, i.e. 479,001,600) tone rows, although 469,015,680 of these are merely transformations of other rows. There are 9,985,920 truly unique twelve-tone rows.
Appearances of P can be transformed from the original in three basic ways:
- transposition up or down, giving Pχ.
- reversal in time, giving the retrograde
In music, a permutation of a set is any ordering of the elements of that set. Different permutations may be related by transformation, through the application of zero or more of certain operations, such as transposition, inversion, retrogradation, circular permutation , or multiplicative operations...
(R)
- reversal in pitch, giving the inversion
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...
(I): I(χ) = P(12 -χ).
The various transformations can be combined. These give rise to a set-complex of forty-eight forms of the set, 12 transpositions of the
four basic forms: P, R, I, RI. The combination of the retrograde and inversion transformations is known as the
retrograde inversionIn 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,...
(
RI).
| RI is: |
RI of P, |
R of I, |
and I of R. |
| R is: |
R of P, |
RI of I, |
and I of RI. |
| I is: |
I of P, |
RI of R, |
and R of RI. |
| P is: |
R of R, |
I of I, |
and RI of RI. |
thus, each cell in the following table lists the result of the transformations, a four-group, in its row and column headers:
| P: |
RI: |
R: |
I: |
| RI: |
P |
I |
R |
| R: |
I |
P |
RI |
| I: |
R |
RI |
P |
However, there are only a few numbers by which one may multiply a row and still end up with twelve tones.
Example
Suppose the prime series is as follows:
Then the retrograde is the prime series in reverse order:
The inversion is the prime series with the
intervalIn music theory, an interval is a combination of two notes, or the ratio between their frequencies. Two-note combinations are also called dyads...
s inverted (so that a rising minor third becomes a falling minor third):
And the retrograde inversion is the inverted series in retrograde:
P, R, I and RI can each be started on any of the twelve notes of the
chromatic scaleThe chromatic scale is a musical scale with twelve pitches, each a semitone apart. On a modern piano or other equal-tempered instrument, all the half steps are the same size...
, meaning that 47
permutationIn music, a permutation of a set is any ordering of the elements of that set. Different permutations may be related by transformation, through the application of zero or more of certain operations, such as transposition, inversion, retrogradation, circular permutation , or multiplicative operations...
s of the initial tone row can be used, giving a maximum of 48 possible tone rows. However, not all prime series will yield so many variations because transposed transformations may be identical to each other. This is known as invariance. A simple case is the ascending chromatic scale, the retrograde inversion of which is identical to the prime form, and the retrograde of which is identical to the inversion (thus, only 24 forms of this tone row are available).
Note that in the above example, as is typical, the retrograde inversion contains three points where the sequence of two pitches are identical to the prime row. Thus the generative power of even the most basic transformations is both unpredictable and inevitable. Motivic development can be driven by this internal consistency both positively and negatively.
When rigorously applied, the technique demands that one statement of the tone row must be heard in full (otherwise known as aggregate completion) before another can begin. Adjacent notes in the row can be sounded at the same time, and the notes can appear in any
octaveIn music, an octave is the interval between one musical pitch and another with half or double its frequency. The octave relationship is a natural phenomenon that has been referred to as the "basic miracle of music", the use of which is "common in most musical systems"...
, but the order of the notes in the tone row must be maintained. Durations,
dynamicsIn music, dynamics normally refers to the volume of a sound or note, but can also refer to every aspect of the execution of a given piece, either stylistic or functional . The term is also applied to the written or printed musical notation used to indicate dynamics...
and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no rules about which tone rows should be used at which time (beyond their all being derived from the prime series, as already explained).
Derivation
Derivation is transforming segments of the full chromatic, less than 12 pitch classes, to yield a complete set, most commonly using trichords, tetrachords, and hexachords. A
derived setThe term "partition" is also French for the sheet music of a transcription.In music using the twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the...
can be generated by choosing appropriate transformations of any
trichordIn music theory, a trichord is a group of three different pitch classes found within a larger group . For example a continguous three note set from a musical scale or twelve-tone row. The term is derived by analogy from the 20th-century use of the word "tetrachord"...
except 0,3,6, the
diminishedDiminished is to make smaller or less or to cause to appear so.Diminished may also refer to:*Diminution in Music*Diminished: A song in alternative rock band R.E.M.'s 1998 album Up↑...
triad. A derived set can also be generated from any
tetrachordTraditionally, a tetrachord is a series of three intervals filling in the interval of a perfect fourth, a 4:3 frequency proportion. In modern usage a tetrachord is any four-note segment of a scale or tone row. The term tetrachord derives from ancient Greek music theory...
that excludes the interval class 4, a
major thirdIn classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...
, between any two elements. The opposite,
partitioning, uses methods to create segments from sets, most often through registral difference.
Combinatoriality
CombinatorialityIn music using the twelve tone technique combinatoriality is a quality shared by some twelve-tone tone rows whereby the row and one of its transformations combine to form a pair of aggregates...
is a side-effect of derived rows where combining different segments or sets such that the pitch class content of the result fulfills certain criteria, usually the combination of hexachords which complete the full chromatic.
Invariance
Invariant formations are also the side effect of derived rows where a segment of a set remains similar or the same under transformation. These may be used as "pivots" between set forms, sometimes used by
Anton WebernAnton 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...
and
Arnold SchoenbergArnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
.
Invariance describes the portions of
rowIn music, a tone row or note row , also series and set, refers to a non-repetitive ordering of a set of pitch-classes, typically of the twelve notes in musical set theory of the chromatic scale, though both larger and smaller sets are sometimes found.-History and usage:Tone rows are the basis of...
s which have been so designed that they remain invariant under the allowable
transformationIn music, a transformation consists of any operation or process that may apply to a musical variable in composition, performance, or analysis. Transformations include multiplication, rotation, permutation In music, a transformation consists of any operation or process that may apply to a musical...
s (inversion, retrograde, retrograde-inversion, multiplication). Another theorist has defined musical invariance differently, however, as "properties of a set that are preserved under [any given] operation, as well as those relationships between a set and the so-operationally transformed set that inhere in the operation", a definition very close to that of mathematical invariance.
George PerleGeorge Perle was a composer and music theorist. He was born in Bayonne, New Jersey. Perle was an alumnus of DePaul University...
describes their use as "pivots" or non-tonal ways of emphasizing certain
pitchPitch is an auditory perceptual property that allows the ordering of sounds on a frequency-related scale.Pitches are compared as "higher" and "lower" in the sense associated with musical melodies,...
es. Invariant rows are also
combinatorialIn music using the twelve tone technique combinatoriality is a quality shared by some twelve-tone tone rows whereby the row and one of its transformations combine to form a pair of aggregates...
and
derivedThe term "partition" is also French for the sheet music of a transcription.In music using the twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the...
.
Cross partition
A
cross partition is an often monophonic or homophonic technique which, "arranges the pitch classes of an aggregate (or a row) into a rectangular design," in which the vertical columns (harmonies) of the rectangle are derived from the adjacent segments of the row and the horizontal columns (melodies) are not (and thus may contain non-adjacencies).
For example, the layout of all possible 'even' cross partitions is as follows:
6
2 3
4 4
3 2
6
** *** **** ******
** *** **** ******
** *** ****
** ***
**
**
One possible realization out of many for the
order numbers of the 3
4 cross partition, and one variation of that, are:
0 3 6 9 0 5 6 e
1 4 7 t 2 3 7 t
2 5 8 e 1 4 8 9
Thus if one's tone row was 0 e 7 4 2 9 3 8 t 1 5 6, one's cross partitions from above would be:
0 4 3 1 0 9 3 6
e 2 8 5 7 4 8 5
7 9 t 6 e 2 t 1
Cross partitions are used in Schoenberg's Op. 33a
Klavierstück and also by Berg but Dallapicolla used them more than any other composer.
Other
In practice, the "rules" of twelve-tone technique have been bent and broken many times, not least by Schoenberg himself. For instance, in some pieces two or more tone rows may be heard progressing at once, or there may be parts of a composition which are written freely, without recourse to the twelve-tone technique at all. Offshoots or variations may produce music in which:
- the full chromatic is used and constantly circulates, but permutational devices are ignored
- permutational devices are used but not on the full chromatic
Also, some composers, including Stravinsky, have used
cyclic permutationA cyclic permutation or circular permutation is a permutation built from one or more sets of elements in cyclic order.The notion "cyclic permutation" is used in different, but related ways:- Definition 1 :right|mapping of permutation...
, or rotation, where the row is taken in order but using a different starting note. Stravinsky also preferred the inverse-retrograde, IR, to the retrograde-inverse, RI.
Although usually atonal, twelve tone music need not be—several pieces by Berg, for instance, have tonal elements.
One of the best known twelve-note compositions is
Variations for Orchestra by
Arnold SchoenbergArnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
. "Quiet", in
Leonard BernsteinLeonard Bernstein August 25, 1918 – October 14, 1990) was an American conductor, composer, author, music lecturer and pianist. He was among the first conductors born and educated in the United States of America to receive worldwide acclaim...
's
Candide, satirizes the method by using it for a song about boredom, and
Benjamin BrittenEdward Benjamin Britten, Baron Britten, OM CH was an English composer, conductor, and pianist. He showed talent from an early age, and first came to public attention with the a cappella choral work A Boy Was Born in 1934. With the premiere of his opera Peter Grimes in 1945, he leapt to...
used a twelve-tone row—a "tema seriale con fuga"—in his
Cantata Academica: Carmen Basiliense (1959) as an emblem of academicism.
Schoenberg's mature practice
Ten features of Schoenberg's mature twelve-tone practice are characteristic, interdependent, and interactive:
- Hexachord
In music, a hexachord is a collection of six pitch classes including six-note segments of a scale or tone row. The term was adopted in the Middle Ages and adapted in the twentieth-century in Milton Babbitt's serial theory.-Middle Ages:...
al inversionIn music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...
al combinatorialityIn music using the twelve tone technique combinatoriality is a quality shared by some twelve-tone tone rows whereby the row and one of its transformations combine to form a pair of aggregates...
- Aggregates
- Linear set
A set in music theory, as in mathematics and general parlance, is a collection of objects...
presentation
- Partitioning
The term "partition" is also French for the sheet music of a transcription.In music using the twelve-tone technique, derivation is the construction of a row through segments. A derived row is a tone row whose entirety of twelve tones is constructed from a segment or portion of the whole, the...
- Isomorphic partitioning
- Invariants
- Hexachordal levels
A level , also "tonality level", Gerhard Kubik's "tonal step", and John Blacking's "root progression") is a temporary modal frame contrasted with another temporary modal frame built on a different foundation note. It is more general and basic than a chord and is found in Asian, African, and Celtic...
- Harmony
In music, harmony is the use of simultaneous pitches , or chords. The study of harmony involves chords and their construction and chord progressions and the principles of connection that govern them. Harmony is often said to refer to the "vertical" aspect of music, as distinguished from melodic...
, "consistent with and derived from the properties of the referential set"
- Metre
Meter or metre is a term that music has inherited from the rhythmic element of poetry where it means the number of lines in a verse, the number of syllables in each line and the arrangement of those syllables as long or short, accented or unaccented...
, established through "pitch-relational characteristics"
- Multidimensional
In music, a simultaneity is more than one complete musical texture occurring at the same time, rather than in succession. This first appeared in the music of Charles Ives, and is common in the music of Conlon Nancarrow and others....
set presentations.
See also
- List of pieces that use serialism and twelve-tone
- All-interval twelve-tone chord
In music, an all-interval twelve-tone row is a twelve-tone tone row arranged so that it contains one instance of each interval within the octave, 1 through 11...
- All-interval hexachord
- All-interval tetrachord
An all-interval tetrachord is a tetrachord, a collection of four pitch classes, from which all six interval classes can be derived by means of various inversions. There are only two possible all-interval tetrachords. In set theory notation, these are [0,1,4,6] and [0,1,3,7]...
- Pitch interval
In musical set theory, a pitch interval is the number of semitones that separates one pitch from another, upward or downward.They are notated as follows:For example C4 to D4 is 3 semitones:While C4 to D5 is 15 semitones:...
Sources
- Alegant, Brian. 2010. The Twelve-Tone Music of Luigi Dallapiccola. Eastman Studies in Music 76. Rochester, NY: University of Rochester Press. ISBN 9781580463256.
- Babbitt, Milton. 1960. "Twelve-Tone Invariants as Compositional Determinants". Musical Quarterly 46, no. 2, Special Issue: Problems of Modern Music: The Princeton Seminar in Advanced Musical Studies (April): 246–59.
- Babbitt, Milton. 1961. "Set Structure as a Compositional Determinant". Journal of Music Theory 5, no. 1 (Spring): 72–94.
- Brett, Philip. "Britten, Benjamin." Grove Music Online ed. L. Macy (Accessed 8 January 2007), http://www.grovemusic.com.
- Chase, Gilbert. 1987. America's Music: From the Pilgrims to the Present, revised third edition. Music in American Life. Urbana: University of Illinois Press. ISBN 025200454X (cloth); ISBN 0-252-06275-2 (pbk).
- Haimo, Ethan. 1990. Schoenberg's Serial Odyssey: The Evolution of his Twelve-Tone Method, 1914-1928. Oxford [England] Clarendon Press; New York: Oxford University Press ISBN 0-19-3152-60-6.
- Hill, Richard S. 1936. "Schoenberg's Tone-Rows and the Tonal System of the Future". Musical Quarterly 22, no. 1 (January): 14–37.
- Lansky, Paul, George Perle, and Dave Headlam. 2001. "Twelve-note Composition". The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell. London: Macmillan Publishers.
- Leeuw, Ton de
Antonius Wilhelmus Adrianus de Leeuw was a Dutch composer. He was known for his experiments with microtonality....
. 2005. Music of the Twentieth Century: A Study of Its Elements and Structure, translated from the Dutch by Stephen Taylor. Amsterdam: Amsterdam University Press. ISBN 9053567658. Translation of Muziek van de twintigste eeuw: een onderzoek naar haar elementen en structuur. Utrecht: Oosthoek, 1964. Third impression, Utrecht: Bohn, Scheltema & Holkema, 1977. ISBN 9031302449.
- Neighbour, Oliver. 1955. "The Evolution of Twelve-Note Music". Proceedings of the Royal Musical Association, 81st Sess. (1954–1955): 49–61.
- Perle, George. 1977. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, fourth edition, revised. Berkeley, Los Angeles, and London: University of California Press. ISBN 0-520-03395-7
- Perle, George. 1991. Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, sixth edition, revised. Berkeley: University of California Press. ISBN 9780520074309.
- Reti, Rudolph. 1958. Tonality, Atonality, Pantonality: A Study of Some Trends in Twentieth Century Music. Westport, Connecticut: Greenwood Press. ISBN 0-313-20478-0.
- Rufer, Josef. 1954. Composition with Twelve Notes Related Only to One Another, translated by Humphrey Searle
Humphrey Searle was a British composer.-Biography:He was born in Oxford where he was a classics scholar before studying — somewhat hesitantly — with John Ireland at the Royal College of Music in London, after which he went to Vienna on a six month scholarship to become a private pupil of Anton...
. New York: The Macmillan Company. (Original German ed., 1952)
- Schoenberg, Arnold. 1975. Style and Idea, edited by Leonard Stein with translations by Leo Black. Berkeley & Los Angeles: University of California Press. ISBN 0-520-05294-3.
- 207–208 "Twelve-Tone Composition (1923)"
- 214–45 "Composition with Twelve Tones (1) (1941)"
- 245–49 "Composition with Twelve Tones (2) (c.1948)"
- Solomon, Larry. 1973. "New Symmetric Transformations", Perspectives of New Music 11, no. 2 (Spring-Summer): 257–64.
- Whittall, Arnold. 2008. The Cambridge Introduction to Serialism. Cambridge Introductions to Music. New York: Cambridge University Press. ISBN 978-0-521-86341-4 (cloth) ISBN 978-0-521-68200-8 (pbk).
Further reading
- Covach, John. 1996. "The Zwölftonspiel of Josef Matthias Hauer". Journal of Music Theory 36, no. 1 (Spring): 149–84.
- Covach, John. 2000. "Schoenberg's 'Poetics of Music', the Twelve-tone Method, and the Musical Idea". In Schoenberg and Words: The Modernist Years, edited by Russell A. Berman and Charlotte M. Cross, New York: Garland. ISBN 0815328303
- Covach, John. 2002, "Twelve-tone Theory". In The Cambridge History of Western Music Theory, edited by Thomas Christensen, 603–27. Cambridge: Cambridge University Press. ISBN 0521623715.
- Starr, Daniel. 1978. "Sets, Invariance and Partitions". Journal of Music Theory 22, no. 1 (Spring): 1–42.
- Wuorinen, Charles
Charles Peter Wuorinen is a prolific Pulitzer Prize-winning American composer born and living in New York City. His catalog of more than 250 compositions includes works for orchestra, opera, chamber music, as well as solo instrumental and vocal works...
. 1979. Simple Composition. New York: Longman. ISBN 0582280591. Reprinted 1991, New York: C. F. Peters. ISBN 0-938856-06-5.
External links