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 aspe ...
, 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 posit ...
es, 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
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 and most types of
serial music. Tone rows were widely used in 20th-century contemporary music, like
Dmitri Shostakovich's use of twelve-tone rows, "without dodecaphonic transformations."
A tone row has been identified in the A minor prelude,
BWV 889, from book II of
J.S. Bach's ''
The Well-Tempered Clavier'' (1742) and by the late eighteenth century it is found in works such as
Mozart'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 classic ...
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''.
Hans Keller 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
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 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.
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 ca ...
—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 disenfranchi ...
.
Alban Berg, however, sometimes incorporated tonal elements into his twelve-tone works. The main tone row of his
Violin Concerto 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. This whole tone scale reappears in the second movement when the
chorale "
Es ist genug" (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'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 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 pr ...
called the
generator, 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'' name ...
(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 pr ...
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 classes. An "array" is a succession of aggregates.
The term is also used to refer to
lattices.
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 ...
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'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
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'' which contains a repeated note making it a 'thirteen-tone row':
Igor Stravinsky 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'' 17, no. 2 (Spring 1999): 231–271, citation on 242.] as for example in his ''
Requiem Canticles'':
Ben Johnston Ben Johnston may refer to:
* Ben Johnston (rugby union) (born 1978), British rugby player
* Ben Johnston (composer) (1926–2019), American contemporary composer of concert music
* Bennett Johnston, Jr. (born 1932), Washington, D.C.-based lobbyist ...
uses a "just tone row" (see
just intonation) 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 chord (music), chords whose pitch classes are the harmonics or subharmonics of a given fixed root (chord), tone (identity (tuning), identity), respectively. For ...
or utonality on A+ utonality, C otonality and utonality, and E- otonality, outlining a
diminished triad.
See also
*
Musical set theory
*
Unified field
*
Side-slipping
*
Pitch interval
*
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
;Eleve ...
References
Sources
*
*
*
*
*
*
Further reading
*
External links
Database on tone rows and tropes Harald Fripertinger, Peter Lackner
{{DEFAULTSORT:Tone Row
Twelve-tone technique
Musical symmetry