![Schoenberg - Variations for Orchestra op](https://upload.wikimedia.org/wikipedia/commons/2/2d/Schoenberg_-_Variations_for_Orchestra_op._31_tone_row_mirror_forms.png)
In
music
Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...
, a tone row or note row (german: Reihe or '), also series or set,
is a non-repetitive ordering of a set of
pitch-class
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positi ...
es, typically of the twelve notes in
musical set theory
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the ...
of the
chromatic scale
The chromatic scale (or twelve-tone scale) is a set of twelve pitches (more completely, pitch classes) used in tonal music, with notes separated by the interval of a semitone. Chromatic instruments, such as the piano, are made to produce the ...
, though both larger and smaller sets are sometimes found.
History and usage
![Stockhausen Gruppen für drei Orchester series](https://upload.wikimedia.org/wikipedia/commons/e/e9/Stockhausen_Gruppen_f%C3%BCr_drei_Orchester_series.png)
Tone rows are the basis of
Arnold Schoenberg
Arnold Schoenberg or Schönberg (, ; ; 13 September 187413 July 1951) was an Austrian-American composer, music theorist, teacher, writer, and painter. He is widely considered one of the most influential composers of the 20th century. He was as ...
's
twelve-tone technique
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law o ...
and most types of
serial music
In music, serialism is a method of Musical composition, composition using series of pitches, rhythms, dynamics, timbres or other elements of music, musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, thou ...
. Tone rows were widely used in 20th-century contemporary music, like
Dmitri Shostakovich
Dmitri Dmitriyevich Shostakovich, , group=n (9 August 1975) was a Soviet-era Russian composer and pianist who became internationally known after the premiere of his Symphony No. 1 (Shostakovich), First Symphony in 1926 and was regarded throug ...
's use of twelve-tone rows, "without dodecaphonic transformations."
A tone row has been identified in the A minor prelude,
BWV
The (BWV; ; ) is a catalogue of compositions by Johann Sebastian Bach. It was first published in 1950, edited by Wolfgang Schmieder. The catalogue's second edition appeared in 1990. An abbreviated version of that second edition, known as BWV2a ...
889, from book II of
J.S. Bach
Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late baroque music, Baroque period. He is known for his orchestral music such as the ''Brandenburg Concertos''; instrumental compositions such as the Cello Suite ...
's ''
The Well-Tempered Clavier
''The Well-Tempered Clavier'', BWV 846–893, consists of two sets of preludes and fugues in all 24 major and minor keys for keyboard by Johann Sebastian Bach. In the composer's time, ''clavier'', meaning keyboard, referred to a variety of in ...
'' (1742) and by the late eighteenth century it is found in works such as
Mozart
Wolfgang Amadeus Mozart (27 January 17565 December 1791), baptised as Joannes Chrysostomus Wolfgangus Theophilus Mozart, was a prolific and influential composer of the Classical period (music), Classical period. Despite his short life, his ra ...
's
C major String Quartet, K. 157 (1772),
String Quartet in E-flat major, K. 428,
String Quintet in G minor, K. 516 (1790), and the
Symphony in G minor, K. 550 (1788).
Beethoven
Ludwig van Beethoven (baptised 17 December 177026 March 1827) was a German composer and pianist. Beethoven remains one of the most admired composers in the history of Western music; his works rank amongst the most performed of the classical ...
also used the technique but, on the whole, "Mozart seems to have employed serial technique far more often than Beethoven".
Franz Liszt
Franz Liszt, in modern usage ''Liszt Ferenc'' . Liszt's Hungarian passport spelled his given name as "Ferencz". An orthographic reform of the Hungarian language in 1922 (which was 36 years after Liszt's death) changed the letter "cz" to simpl ...
used a twelve-tone row in the opening of his ''
Faust Symphony
''A Faust Symphony in three character pictures'' (german: Eine Faust-Symphonie in drei Charakterbildern), S.108, or simply the "''Faust Symphony''", is a choral symphony written by Hungarian composer Franz Liszt inspired by Johann Wolfgang von Go ...
''.
Hans Keller
Hans (Heinrich) Keller (11 March 19196 November 1985) was an Austrian-born British musician and writer, who made significant contributions to musicology and music criticism, as well as being a commentator on such disparate fields as psychoana ...
claims that Schoenberg was aware of this serial practice in the
classical period and that "Schoenberg repressed his knowledge of classical serialism because it would have injured his
narcissism
Narcissism is a self-centered personality style characterized as having an excessive interest in one's physical appearance or image and an excessive preoccupation with one's own needs, often at the expense of others.
Narcissism exists on a co ...
."
Theory and compositional techniques
![Webern - Piano Variations op](https://upload.wikimedia.org/wikipedia/commons/f/f9/Webern_-_Piano_Variations_op._27_tone_row.png)
Tone rows are designated by letters and subscript numbers (e.g.: RI
11, which may also appear as RI11 or RI–11). The numbers indicate the initial (P or I) or final (R or RI) pitch-class number of the given row form, most often with ''c'' = 0.
* "P" indicates prime, a forward-directed right-side up form.
* "I" indicates
inversion
Inversion or inversions may refer to:
Arts
* , a French gay magazine (1924/1925)
* ''Inversion'' (artwork), a 2005 temporary sculpture in Houston, Texas
* Inversion (music), a term with various meanings in music theory and musical set theory
* ...
, a forward-directed upside-down form.
* "R" indicates
retrograde, a backwards right-side up form.
* "RI" indicates
retrograde-inversion, a backwards upside-down form.
*
Transposition is indicated by a ''T number'', for example P8 is a T(4) transposition of P4.
A twelve-tone composition will take one or more tone rows, called the "prime form", as its basis plus their
transformations (inversion, retrograde, retrograde inversion, as well as transposition; see
twelve-tone technique
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law o ...
for details). These forms may be used to construct a melody in a straightforward manner as in Schoenberg's
Piano Suite Op. 25 Minuet Trio, where P-0 is used to construct the opening melody and later varied through transposition, as P-6, and also in articulation and dynamics. It is then varied again through inversion, untransposed, taking form I-0. However, rows may be combined to produce melodies or harmonies in more complicated ways, such as taking successive or multiple pitches of a melody from two different row forms, as described at
twelve-tone technique
The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and (in British usage) twelve-note composition—is a method of musical composition first devised by Austrian composer Josef Matthias Hauer, who published his "law o ...
.
Initially, Schoenberg required the avoidance of suggestions of
tonality
Tonality is the arrangement of pitches and/or chords of a musical work in a hierarchy of perceived relations, stabilities, attractions and directionality. In this hierarchy, the single pitch or triadic chord with the greatest stability is call ...
—such as the use of consecutive imperfect consonances (thirds or sixths)—when constructing tone rows, reserving such use for the time when the dissonance is completely
emancipated
Emancipation generally means to free a person from a previous restraint or legal disability. More broadly, it is also used for efforts to procure economic and social rights, political rights or equality, often for a specifically disenfranchis ...
.
Alban Berg
Alban Maria Johannes Berg ( , ; 9 February 1885 – 24 December 1935) was an Austrian composer of the Second Viennese School. His compositional style combined Romantic lyricism with the twelve-tone technique. Although he left a relatively sma ...
, however, sometimes incorporated tonal elements into his twelve-tone works. The main tone row of his
Violin Concerto
A violin concerto is a concerto for solo violin (occasionally, two or more violins) and instrumental ensemble (customarily orchestra). Such works have been written since the Baroque period, when the solo concerto form was first developed, up thro ...
hints at this tonality:
:
This tone row consists of alternating minor and major
triads starting on the
open strings of the violin, followed by a portion of an ascending
whole tone scale
In music, a whole-tone scale is a scale in which each note is separated from its neighbors by the interval of a whole tone. In twelve-tone equal temperament, there are only two complementary whole-tone scales, both six-note or ''hexatonic'' sc ...
. This whole tone scale reappears in the second movement when the
chorale
Chorale is the name of several related musical forms originating in the music genre of the Lutheran chorale:
* Hymn tune of a Lutheran hymn (e.g. the melody of "Wachet auf, ruft uns die Stimme"), or a tune in a similar format (e.g. one of the t ...
"
Es ist genug
"" ("It is enough") is a German Lutheran hymn, with text by Franz Joachim Burmeister, written in 1662. The melody, Zahn number, Zahn No. 7173, was written by Johann Rudolph Ahle who collaborated with the poet. It begins with a sequence of thre ...
" (It is enough) from J.S. Bach's cantata
''O Ewigkeit, du Donnerwort'', BWV 60 is quoted literally in the woodwinds (mostly clarinet).
Some tone rows have a high degree of internal organization. An example is the tone row from
Anton Webern
Anton Friedrich Wilhelm von Webern (3 December 188315 September 1945), better known as Anton Webern (), was an Austrian composer and conductor whose music was among the most radical of its milieu in its sheer concision, even aphorism, and stea ...
's
Concerto for Nine Instruments Op. 24, shown below.
:
In this tone row, if the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion, the next three are retrograde, and the last three are its inversion. A row created in this manner, through variants of a
trichord
In music theory, a trichord () is a group of three different pitch classes found within a larger group. A trichord is a contiguous three-note set from a musical scale or a twelve-tone row.
In musical set theory there are twelve trichords given ...
or
tetrachord
In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency propo ...
called the
generator
Generator may refer to:
* Signal generator, electronic devices that generate repeating or non-repeating electronic signals
* Electric generator, a device that converts mechanical energy to electrical energy.
* Generator (circuit theory), an eleme ...
, is called a ''
derived row
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 generator. Anton Webern often ...
''.
The tone rows of many of Webern's other late works are similarly intricate. The tone row for Webern's
String Quartet Op. 28 is based on the
BACH motif
In music, the BACH motif is the motif, a succession of notes important or characteristic to a piece, ''B flat, A, C, B natural''. In German musical nomenclature, in which the note ''B natural'' is named ''H'' and the ''B flat'' named ...
(B, A, C, B) and is composed of three
tetrachord
In music theory, a tetrachord ( el, τετράχορδoν; lat, tetrachordum) is a series of four notes separated by three intervals. In traditional music theory, a tetrachord always spanned the interval of a perfect fourth, a 4:3 frequency propo ...
s:
:
The "set-complex" is the forty-eight forms of the set generated by stating each "aspect" or transformation on each pitch class.
The
all-interval twelve-tone row is a tone row arranged so that it contains one instance of each interval within the octave, 0 through 11.
The
"total chromatic" (or "aggregate")
is the
set
Set, The Set, SET or SETS may refer to:
Science, technology, and mathematics Mathematics
*Set (mathematics), a collection of elements
*Category of sets, the category whose objects and morphisms are sets and total functions, respectively
Electro ...
of all twelve
pitch class
In music, a pitch class (p.c. or pc) is a set of all pitches that are a whole number of octaves apart; for example, the pitch class C consists of the Cs in all octaves. "The pitch class C stands for all possible Cs, in whatever octave positio ...
es. An "array" is a succession of aggregates.
The term is also used to refer to
lattices.
![Array - Babbitt's Composition for Four Instruments](https://upload.wikimedia.org/wikipedia/commons/a/a9/Array_-_Babbitt%27s_Composition_for_Four_Instruments.png)
An aggregate may be achieved through
complementation or
combinatoriality
In music using the twelve tone technique, combinatoriality is a quality shared by twelve-tone tone rows whereby each section of a row and a proportionate number of its transformations combine to form aggregates (all twelve tones). Whittall, Arnold ...
, such as with
hexachord
In music, a hexachord (also hexachordon) is a six-note series, as exhibited in a scale (hexatonic or hexad) or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theor ...
s.
A "secondary set" is a tone row which is derived from or, "results from the reversed coupling of hexachords", when a given row form is immediately repeated. For example, the row form consisting of two hexachords:
''0 1 2 3 4 5'' / ''6 7 8 9 t e''
when repeated immediately results in the following succession of two aggregates, in the middle of which is a new and complete aggregate beginning with the second hexachord:
''0 1 2 3 4 5'' / ''6 7 8 9 t e'' / ''0 1 2 3 4 5'' / ''6 7 8 9 t e''
secondary set:
'6 7 8 9 t e'' / ''0 1 2 3 4 5''
A "weighted aggregate" is an aggregate in which the twelfth pitch does not appear until at least one pitch has appeared at least twice, supplied by segments of different set forms. It seems to have been first used in
Milton Babbitt
Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, mathematician, and teacher. He is particularly noted for his Serialism, serial and electronic music.
Biography
Babbitt was born in Philadelphia t ...
's
String Quartet No. 4. An aggregate may be vertically or horizontally weighted. An "all-partition array" is created by combining a collection of hexachordally combinatorial arrays.
Nonstandard tone rows
![Pierre Boulez - Second Piano Sonata series](https://upload.wikimedia.org/wikipedia/commons/9/96/Pierre_Boulez_-_Second_Piano_Sonata_series.png)
Schoenberg specified many strict rules and desirable guidelines for the construction of tone rows such as number of notes and intervals to avoid. Tone rows that depart from these guidelines include the above tone row from Berg's Violin Concerto which contains triads and tonal emphasis, and the tone row below from
Luciano Berio
Luciano Berio (24 October 1925 – 27 May 2003) was an Italian composer noted for his experimental work (in particular his 1968 composition ''Sinfonia'' and his series of virtuosic solo pieces titled ''Sequenza''), and for his pioneering work ...
's ''
Nones Nones may refer to:
* ''Nones'' (Auden), a 1951 book of poems by W. H. Auden
* ''Nones'' (Berio), a 1954 orchestral composition by Luciano Berio
*Nones (calendar), or ''Nonae'', days of the Roman Calendar
*None (liturgy)
Nones (), also known as N ...
'' which contains a repeated note making it a 'thirteen-tone row':
Igor Stravinsky
Igor Fyodorovich Stravinsky (6 April 1971) was a Russian composer, pianist and conductor, later of French (from 1934) and American (from 1945) citizenship. He is widely considered one of the most important and influential composers of the ...
used a five-tone row, chromatically filling out the space of a major third centered tonally on C (C–E), in one of his early serial compositions, ''In memoriam Dylan Thomas''.
In his twelve-tone practice, Stravinsky preferred the inverse-retrograde (IR) to the retrograde-inverse (RI),
[Joseph N. Strauss, "Stravinsky's Serial 'Mistakes' ", '']The Journal of Musicology
''The Journal of Musicology'' is a quarterly peer-reviewed academic journal of musicology published by University of California Press
The University of California Press, otherwise known as UC Press, is a publishing house associated with the Un ...
'' 17, no. 2 (Spring 1999): 231–271, citation on 242. as for example in his ''
Requiem Canticles
''Requiem Canticles'' is a 15-minute composition by Igor Stravinsky, for contralto and bass soli, chorus, and orchestra. Stravinsky completed the work in 1966, and it received its first performance that same year.
The work is a partial setting o ...
'':
Ben Johnston uses a "just tone row" (see
just intonation
In music, just intonation or pure intonation is the tuning of musical intervals
Interval may refer to:
Mathematics and physics
* Interval (mathematics), a range of numbers
** Partially ordered set#Intervals, its generalization from numbers to ...
) in works including String Quartets Nos. 6 and 7. Each permutation contains a just chromatic scale, however, transformations (transposition and inversion) produce pitches outside of the primary row form, as already occurs in the inversion of P0. The pitches of each hexachord are drawn from different
otonality
''Otonality'' and ''utonality'' are terms introduced by Harry Partch to describe chords whose pitch classes are the harmonics or subharmonics of a given fixed tone (identity), respectively. For example: , , ,... or , , ,....
Definition ...
or utonality on A+ utonality, C otonality and utonality, and E- otonality, outlining a
diminished triad
In music theory, a diminished triad (also known as the minor flatted fifth) is a triad consisting of two minor thirds above the root. It is a minor triad with a lowered ( flattened) fifth. When using chord symbols, it may be indicated by the s ...
.
See also
*
Musical set theory
Musical set theory provides concepts for categorizing musical objects and describing their relationships. Howard Hanson first elaborated many of the concepts for analyzing tonal music. Other theorists, such as Allen Forte, further developed the ...
*
Unified field
In music, unified field is the 'unity of musical space' created by the free use of melodic material as harmonic material and vice versa.
The technique is most associated with the twelve-tone technique, created by its 'total thematicism' where a t ...
*
Side-slipping
In jazz improvisation, outside playing describes an approach where one plays over a scale, mode or chord that is harmonically distant from the given chord. There are several common techniques to playing outside, that include side-stepping or ...
*
Pitch interval
In musical set theory, a pitch interval (PI or ip) is the number of semitones that separates one pitch from another, upward or downward.Schuijer, Michiel (2008). ''Analyzing Atonal Music: Pitch-Class Set Theory and Its Contexts'', Eastman Studie ...
*
List of tone rows and series
This is a list of tone rows and series. For a list of unordered collections, see set (music), Forte number, list of set classes, and trope (music).
Twelve tone rows
Other lengths
Fewer than twelve
;Five
;Six
;Eight
;Nine
;Ten
;Elev ...
References
Sources
*
*
*
*
*
*
Further reading
*
External links
Database on tone rows and tropes Harald Fripertinger, Peter Lackner
{{DEFAULTSORT:Tone Row
Twelve-tone technique
Musical symmetry