Tone row
Encyclopedia
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...
, 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
Chromatic scale
The 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...
, though both larger and smaller sets are sometimes found.
History and usage
Tone rows are the basis of Arnold SchoenbergArnold Schoenberg
Arnold Schoenberg was an Austrian composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School...
's twelve-tone technique
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
and most types of serial music
Serialism
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...
. Tone rows were widely used in 20th century contemporary music, though one has been identified in a 1742 composition of Johann Sebastian Bach
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...
, and by the late eighteenth century was a well-established technique, found in works such as Mozart's C Major String Quartet, K. 156 (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 also used the technique, for example in the finale of his Ninth Symphony but, on the whole, "Mozart seems to have employed serial technique far more often than Beethoven". It is clear from Schoenberg's own writings that he must have been aware of this practice.
Theory and compositional techniques
Tone rows are designated by letters and subscript numbers (ex.: RI11, also may appear 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, 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.
Transformation (music)
In 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...
(inversion
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...
, retrograde
Permutation (music)
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...
, retrograde inversion
Retrograde inversion
Retrograde inversion is a musical term that literally means "backwards and upside down": "The inverse of the series is sounded in reverse order." This is a technique used in music, specifically in twelve-tone technique, where the inversion and retrograde techniques are performed on the same tone...
, as well 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...
; see twelve-tone technique
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
for details). These forms may be used to construct a melody in a straightforward manner as in Schoenberg's 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
Twelve-tone technique
Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg...
.
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...
—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 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...
. Alban Berg
Alban Berg
Alban 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...
, however, sometimes incorporated tonal elements into his twelve-tone works, and the main tone row of his Violin Concerto
Violin Concerto (Berg)
Alban Berg's Violin Concerto was written in 1935 . It is probably Berg's best-known and most frequently performed instrumental piece.-Conception and composition:...
hints at this tonality:
Chord (music)
A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...
starting on the open strings of the violin, followed by a portion of an ascending whole tone scale
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 step. There are only two complementary whole tone scales, both six-note or hexatonic scales:...
. This whole tone scale reappears in the second movement when the chorale
Chorale
A chorale was originally a hymn sung by a Christian congregation. In certain modern usage, this term may also include classical settings of such hymns and works of a similar character....
"It is enough" (Es ist genug) from Bach's
Johann Sebastian Bach
Johann Sebastian Bach was a German composer, organist, harpsichordist, violist, and violinist whose sacred and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity...
cantata no. 60, which opens with consecutive whole tones, is quoted literally in the woodwinds (mostly clarinet).
Some tone rows have a high degree of internal organisation. Here is the tone row from 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...
's Concerto
Concerto (Webern)
Anton Webern's Concerto for Nine Instruments, Op. 24 is a twelve-tone concerto for nine instruments: flute, oboe, clarinet, horn, trumpet, trombone, violin, viola, and piano; containing three movements: I. Etwas lebhaft, II. Sehr langsam, and III...
Opus 24:
If the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion (backwards and upside down), the next three are retrograde (backwards), and the last three are its inversion (upside down). A row created in this manner, through variants of a trichord
Chord (music)
A chord in music is any harmonic set of two–three or more notes that is heard as if sounding simultaneously. These need not actually be played together: arpeggios and broken chords may for many practical and theoretical purposes be understood as chords...
or tetrachord
Tetrachord
Traditionally, 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...
called the generator
Generating set of a group
In abstract algebra, a generating set of a group is a subset that is not contained in any proper subgroup of the group. Equivalently, a generating set of a group is a subset such that every element of the group can be expressed as the combination of finitely many elements of the subset and their...
, is called a derived row
Derived row
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...
. The tone rows of many of Webern's other late works are similarly intricate.
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 chord
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...
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 (music)
A set in music theory, as in mathematics and general parlance, is a collection of objects...
of all twelve pitch class
Pitch class
In 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. An array is a succession of aggregates.
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]
Nonstandard tone rows
Luciano Berio
Luciano 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...
's Nones
Nones (Berio)
Nones is a composition by Luciano Berio scored for orchestra. The piece is named for the poem, "Nones", by W. H. Auden, and was originally intended to be an oratorio, inspired by the poem, representing not only the Passion of Christ, but also the agony of modern man...
which contains a repeated note making it a 'thirteen tone row':
In his twelve-tone practice Stravinsky preferred the inverse-retrograde (IR) to the retrograde-inverse (RI), as for example in his Requiem Canticles
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....
:
Just intonation
In music, just intonation is any musical tuning in which the frequencies of notes are related by ratios of small whole numbers. Any interval tuned in this way is called a just interval. The two notes in any just interval are members of the same harmonic series...
) in works including String Quartet No. 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
Otonality and Utonality are terms introduced by Harry Partch to describe chords whose notes are the overtones or "undertones" of a given fixed tone. For example: 1/1, 2/1, 3/1,.....
or utonality on A+ utonality, C otonality and utonality, and E- otonality, outlining a diminished triad.
See also
A literary parallel of the tone row is found in Georges PerecGeorges Perec
Georges Perec was a French novelist, filmmaker, documentalist and essayist. He is a member of the Oulipo group...
's poems which use each of a particular set of letters only once.
Tone row may also be used to describe other musical collections or scales such as in Arabic music.
- Musical set theory
- Unified fieldUnified fieldIn music, unified field is often used to refer to the "unity of musical space" created by the free use of melodic material as harmonic material and vice-versa....
- Side-slippingSide-slippingIn jazz improvisation, to play outside, or out, is to intentionally stray from the key or chord changes of the song form. The term refers to a soloist taking some of the harmonic liberties of free jazz within a hard bop or modal context...
- Pitch intervalPitch intervalIn 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:...
External links
- "How Rare Is Symmetry in Musical 12-Tone Rows?" by David J. Hunter and Paul T. von Hippel.