In music Music is an art form whose medium is sound. Common elements of music are pitch , rhythm (and its associated concepts tempo, meter, and articulation), dynamics, and the sonic qualities of timbre and texture. The word derives from Greek μουσική (mousike), "(art) of the Muses.", a tone row or note row (German German (Deutsch, [ˈdɔʏtʃ] ) is a West Germanic language, thus related to and classified alongside English and Dutch. It is one of the world's major languages and the most widely spoken first language in the European Union. Globally, German is spoken by approximately 120 million native speakers and also by about 80 million non-native speakers: Reihe or Tonreihe), also series and set,[2] refers to a non-repetitive ordering of the twelve notes (pitch-classes 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. "The pitch class C stands for all possible Cs, in whatever octave position." Thus, using scientific pitch notation, the pitch class "C" is the infinite set in musical set theory 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 (1973), drawing on the work in twelve-tone theory of Milton) of the chromatic scale The chromatic scale is a musical scale with twelve equally spaced pitches, each a semitone apart. A chromatic scale is a nondiatonic scale having no tonic due to the symmetry of its equally spaced tones. Tone rows are the basis of Arnold Schoenberg Arnold Schoenberg (13 September 1874 – 13 July 1951) was an Austrian and later American composer, associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School. He used the spelling Schönberg until after his move to the United States in 1934 (Steinberg 1995, 463), "in deference to American's twelve-tone technique Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any through the use of tone rows, an ordering of the 12 pitches. All 12 notes are thus given and most types of serial music 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 post-tonal thinking (Whittall 2008, 1). Twelve-tone. 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 (31 March 1685 [O.S. 21 March] – 28 July 1750) (often referred to simply as Bach) was a German composer, organist, harpsichordist, violist, and violinist whose ecclesiastical and secular works for choir, orchestra, and solo instruments drew together the strands of the Baroque period and brought it to its ultimate maturity,[3] 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).[4] 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".[5] It is clear from Schoenberg's own writings that he must have been aware of this practice.[6]

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.[7]

P-6 tone row melody from Schoenberg's Op. 25, P-0 transposed up 6 semitones[8]

A twelve-tone or serial composition will take one or more tone rows, called the prime form, as its basis plus their transformations In music, a transformation consists of any operation or process that a composer, performer, or analyst may apply to a musical variable . Transformations include multiplication, rotation, permutation (i.e. transposition, inversion, and retrograde), and combinations thereof (inversion In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices. The concept of inversion also plays a role in musical set theory, retrograde In music, a permutation of a set is a transformation of its prime form by applying zero or more of certain operations, specifically transposition, inversion, and retrograde, retrograde inversion, as well as transposition In music transposition refers to the process 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. Similarly, one might transpose a tone row or an unordered collection of pitches such as a chord so that it begins on another pitch. See also Transposing; see twelve-tone technique Twelve-tone technique is a method of musical composition devised by Arnold Schoenberg. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any through the use of tone rows, an ordering of the 12 pitches. All 12 notes are thus given 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 is a method of musical composition devised by Arnold Schoenberg. The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any through the use of tone rows, an ordering of the 12 pitches. All 12 notes are thus given.

I-0 tone row melody from Schoenberg's Op. 25, P-0 inverted[8]

Initially, Schoenberg required the avoidance of suggestions of 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 (Reti, 1958; Simms 1975, 119; Judd, 1998; Dahlhaus 1990). Although Fétis used it as a general term for a—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. Alban Berg Alban Maria Johanne 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, however, sometimes incorporated tonal elements into his twelve-tone works, and the main tone row of his Violin Concerto hints at this tonality:

This tone row consists of alternating minor and major triads In music, a chord is any set of harmonically-related notes that is heard as if sounding simultaneously (a "harmonic simultaneity", see Simultaneity ). The most frequently encountered chords in theory and music are triads: major and minor and then the augmented and diminished triads. The descriptions "major", "minor", & 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 Chorales tend to have simple and singable tunes, because they were originally intended to be sung by the congregation rather than a professional choir. They generally have rhyming words and are in a strophic form . Within a verse, most chorales follow the AAB pattern of melody that is known as the German Bar form "It is enough" (Es ist genug) from Bach's Johann Sebastian Bach (31 March 1685 [O.S. 21 March] – 28 July 1750) (often referred to simply as Bach) was a German composer, organist, harpsichordist, violist, and violinist whose ecclesiastical 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 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 pitch, rhythm and dynamics were formative in the's Concerto Opus 24:

Webern's Concerto Op. 24 tone row,[9] composed of four trichords Depending on the context, a trichord is either a contiguous segment of a musical scale or of a twelve-tone row, or a musical triad, that is, any three-note pitch collection: P RI R I 
B, B♭, D, E♭, G, F♯, G♯, E, F, C, C♯, A

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 In music, a chord is any set of harmonically-related notes that is heard as if sounding simultaneously (a "harmonic simultaneity", see Simultaneity ). The most frequently encountered chords in theory and music are triads: major and minor and then the augmented and diminished triads. The descriptions "major", "minor", & or tetrachord Traditionally, a tetrachord is a series of four tones 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. It literally means four strings, originally in reference to harp-like instruments called the generator 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 inverses, is called a derived row. The tone rows of many of Webern's other late works are similarly intricate.

Webern's String Quartet Op. 28 tone row, composed of three tetrachords Traditionally, a tetrachord is a series of four tones 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. It literally means four strings, originally in reference to harp-like instruments: P I RI, with P = the BACH motif.

The set-complex is the forty-eight forms of the set generated by stating each "aspect" or transformation on each pitch class.[2]

An all-interval row is a tone row arranged so that it contains one instance of each interval In music theory, the term interval describes the relationship between the pitches of two notes within the octave, 0 through 11. For example, the first all-interval row, devised by Fritz Heinrich Klein: F, E, C, A, G, D, A♭, D♭, E♭, G♭, B♭, C♭.[10]

In integers, this row is represented as

0 e 7 4 2 9 3 8 t 1 5 6

with the interval between each note being

e 8 9 t 7 6 5 2 3 4 1

This row was also used by Alban Berg Alban Maria Johanne 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 in his Lyric Suite

The total chromatic (aggregate[11]) is the set A set in music theory, as in mathematics and general parlance, is a collection of objects. In musical contexts the term is traditionally applied most often to collections of pitches or pitch-classes, but theorists have extended its use to other types of musical entities, so that one may speak of sets of durations or timbres, for example of all twelve pitch classes 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. "The pitch class C stands for all possible Cs, in whatever octave position." Thus, using scientific pitch notation, the pitch class "C" is the infinite set. An array is a succession of aggregates[11].

First array of four aggregates (numbered 1-4 at bottom) from Babbitt's Composition for Four Instruments, each vertical line (four trichords labeled a-d) is an aggregate while each horizontal line (four trichords labeled a-d) is also an aggregate[11]

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[12]. For example, the row form consisting of two hexachords (one in italics and one in bold):

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]

Contents

Nonstandard tone rows

Prime form of five note tone row from Igor Stravinsky Igor Fyodorovich Stravinsky (17 June [O.S. 5 June] 1882 – 6 April 1971) was a Russian composer, pianist, and conductor, widely acknowledged as one of the most important and influential composers of 20th century music. He was a quintessentially cosmopolitan Russian who was named by Time magazine as one of the 100 most influential people and of's In memoriam Dylan Thomas[13]

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 which 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's Nones which contains a repeated note making it a 'thirteen tone row':

Thirteen note tone row from Nones,[14] symmetrical about the central tone with one note (D) repeated

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),[15][16][17] as for example in his Requiem Canticles:

Basic row forms from Stravinsky's Requiem Canticles[17]: P R I IR

See also

A literary parallel of the tone row is found in Georges Perec Georges Perec was a French novelist, filmmaker and essayist. He was 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 Arabic music or Arab music is the music of the Arab World, including several genres and styles of music ranging from Arabic classical to Arabic pop music and from secular to sacred music.

Sources

  1. ^ Arnold Whittall, The Cambridge Introduction to Serialism, Cambridge Introductions to Music (New York: Cambridge University Press, 2008): 2. ISBN 978-0-521-68200-8 (pbk).
  2. ^ a b George Perle, Serial Composition and Atonality: An Introduction to the Music of Schoenberg, Berg, and Webern, fourth Edition (Berkeley, Los Angeles, and London: University of California Press, 1977): 3. ISBN 0-520-03395-7.
  3. ^ . Weekend Edition Sunday, NPR, 6 Sep 2009.
  4. ^ Hans Keller, "Strict Serial Technique in Classical Music", Tempo, New Series, no. 37 (Autumn, 1955): 12–24; citations on 14–21.
  5. ^ Keller 1955, 22–23.
  6. ^ Keller 1955, 23.
  7. ^ George Perle, Twelve-Tone Tonality, second edition, revised and expanded (Berkeley: University of California Press, 1996): 3. ISBN 0-520-20142-6.
  8. ^ a b Whittall 2008, 5.
  9. ^ Whittall 2008, 97.
  10. ^ Whittall 2008, 271 and 68–69.
  11. ^ a b c Whittall 2008, 271.
  12. ^ Perle 1977, 100; Perle 1996, 20.
  13. ^ Whittall 2008, 127.
  14. ^ Whittall 2008, 195.
  15. ^ Claudio Spies, "Notes on Stravinsky's Abraham and Isaac", Perspectives of New Music 3, no. 2 (Spring-Summer 1965): 104–26. Citation on p. 118.
  16. ^ Joseph N. Strauss, "Stravinsky's Serial 'Mistakes'", The Journal of Musicology 17, no. 2 (Spring 1999): 231–71, citation on 242.
  17. ^ a b Whittall 2008, 139.

External links

Categories: Twelve-tone technique | Post-tonal music theory

 

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