Twelve-tone technique

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Schoenberg, inventor of twelve-tone technique Arnold Schoenberg la 1948.jpg
Schoenberg, inventor of 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 of the twelve tones" in 1919. In 1923, Arnold Schoenberg (1874–1951) developed his own, better-known version of 12-tone technique, which became associated with the "Second Viennese School" composers, who were the primary users of the technique in the first decades of its existence. 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 one note [3] through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. Over time, the technique increased greatly in popularity and eventually became widely influential on 20th-century composers. Many important composers who had originally not subscribed to or even actively opposed the technique, such as Aaron Copland and Igor Stravinsky,[ clarification needed ] eventually adopted it in their music.

Musical composition aesthetic ordering and disposing of musical information

Musical composition, or simply composition, can refer to an original piece or work of music, either vocal or instrumental, the structure of a musical piece, or to the process of creating or writing a new piece of music. People who create new compositions are called composers. Composers of primarily songs are usually called songwriters; with songs, the person who writes lyrics for a song is the lyricist. In many cultures, including Western classical music, the act of composing typically includes the creation of music notation, such as a sheet music "score," which is then performed by the composer or by other instrumental musicians or singers. In popular music and traditional music, songwriting may involve the creation of a basic outline of the song, called the lead sheet, which sets out the melody, lyrics and chord progression. In classical music, orchestration is typically done by the composer, but in musical theatre and in pop music, songwriters may hire an arranger to do the orchestration. In some cases, a pop or traditional songwriter may not use written notation at all, and instead compose the song in their mind and then play, sing and/or record it from memory. In jazz and popular music, notable sound recordings by influential performers are given the weight that written or printed scores play in classical music.

Josef Matthias Hauer Austrian composer

Josef Matthias 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 was also an important early theorist of twelve-tone music and composition.

Arnold Schoenberg Austrian-American composer

Arnold Schoenberg or Schönberg was an Austrian, and later American, composer, music theorist, teacher, writer, and painter. He was associated with the expressionist movement in German poetry and art, and leader of the Second Viennese School. With the rise of the Nazi Party, Schoenberg's works were labeled degenerate music, because they were modernist and atonal. He immigrated to the United States in 1934.

Contents

Schoenberg himself described the system as a "Method of composing with twelve tones which are related only with one another". [4] It is commonly considered a form of serialism.

In music, serialism is a method of composition using series of pitches, rhythms, dynamics, timbres or other musical elements. Serialism began primarily with Arnold Schoenberg's twelve-tone technique, though some of his contemporaries were also working to establish serialism as a form of post-tonal thinking. Twelve-tone technique orders the twelve notes of the chromatic scale, forming a row or series and providing a unifying basis for a composition's melody, harmony, structural progressions, and variations. Other types of serialism also work with sets, collections of objects, but not necessarily with fixed-order series, and extend the technique to other musical dimensions, such as duration, dynamics, and timbre.

Schoenberg's fellow countryman and contemporary Josef Matthias Hauer also developed a similar system using unordered hexachords or tropes —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. [5]

In music, a hexachord is a six-note series, as exhibited in a scale 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 theory. The word is taken from the Greek: ἑξάχορδος, compounded from ἕξ and χορδή, and was also the term used in music theory up to the 18th century for the interval of a sixth.

History of use

Though most sources will say it was invented by Austrian composer Arnold Schoenberg in 1921 and first described privately to his associates in 1923, in fact Josef Matthias Hauer published his "law of the twelve tones" in 1919, and should be credited with inventing the technique, requiring that all twelve chromatic notes sound before any note is repeated. [8] The method was used during the next twenty years almost exclusively by the composers of the Second Viennese SchoolAlban Berg, Anton Webern, and Schoenberg himself.

The 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. Their music was initially characterized by late-Romantic expanded tonality and later, following Schoenberg's own evolution, a totally chromatic expressionism without firm tonal centre, often referred to as atonality; and later still, Schoenberg's serial twelve-tone technique. Though this common development took place, it neither followed a common time-line nor a cooperative path. Likewise, it was not a direct result of Schoenberg's teaching—which, as his various published textbooks demonstrate, was highly traditional and conservative. Schoenberg's textbooks also reveal that the Second Viennese School spawned not from the development of his serial method, but rather from the influence of his creative example.

Alban Berg Austrian composer

Alban Maria Johannes Berg was an Austrian composer of the Second Viennese School. His compositional style combined Romantic lyricism with twelve-tone technique.

Anton Webern Austrian composer and conductor

Anton Friedrich Wilhelm von Webern was an Austrian composer and conductor. Along with his mentor Arnold Schoenberg and his colleague Alban Berg, Webern was in the core of those in the circle of the Second Viennese School, including Ernst Krenek and Theodor W. Adorno. As an exponent of atonality and twelve-tone technique, Webern exerted influence on contemporaries Luigi Dallapiccola, Křenek, and even Schoenberg himself. As a tutor, Webern guided and variously influenced Arnold Elston, Frederick Dorian, Matty Niël, Fré Focke, Karl Amadeus Hartmann, Philipp Herschkowitz, René Leibowitz, Humphrey Searle, Leopold Spinner, and Stefan Wolpe.

The twelve tone technique was preceded by "freely" atonal pieces of 1908–1923 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". [9] The twelve-tone technique was also preceded by "nondodecaphonic serial composition" used independently in the works of Alexander Scriabin, Igor Stravinsky, Béla Bartók, Carl Ruggles, and others. [10] 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. [11] "Essentially, Schoenberg and Hauer systematized and defined for their own dodecaphonic purposes a pervasive technical feature of 'modern' musical practice, the ostinato". [10] Additionally, John Covach argues that the strict distinction between the two, emphasized by authors including Perle, is overemphasized:

Atonality Music that lacks a tonal center or key

Atonality in its broadest sense is 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 function independently of one another. More narrowly, the term atonality describes music that does not conform to the system of tonal hierarchies that characterized classical European music between the seventeenth and nineteenth centuries. "The repertory of atonal music is characterized by the occurrence of pitches in novel combinations, as well as by the occurrence of familiar pitch combinations in unfamiliar environments".

Cell (music) small rhythmic and melodic design

The 1957 Encyclopédie Larousse defines a cell in music as a "small rhythmic and melodic design that can be isolated, or can make up one part of a thematic context." The cell may be distinguished from the figure or motif: the 1958 Encyclopédie Fasquelle defines a cell as "the smallest indivisible unit", unlike the motif, which may be divisible into more than one cell. "A cell can be developed, independent of its context, as a melodic fragment, it can be used as a developmental motif. It can be the source for the whole structure of the work; in that case it is called a generative cell."

Alexander Scriabin Russian pianist and composer

Alexander Nikolayevich Scriabin was a Russian composer and pianist. Scriabin, who was influenced early in his life by the works of Frédéric Chopin, composed works that are characterised by a highly tonal idiom. Later in his career, independently of Arnold Schoenberg, Scriabin developed a substantially atonal and much more dissonant musical system, which accorded with his personal brand of mysticism. Scriabin was influenced by synesthesia, and associated colours with the various harmonic tones of his atonal scale, while his colour-coded circle of fifths was also influenced by theosophy. He is considered by some to be the main Russian Symbolist composer.

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. [12]

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." [13]

Rudolph Reti, 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, [14] [ page needed ] providing a "positive premise" for atonality. [3] 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. [13]

Schoenberg's idea in developing the technique was for it to "replace those structural differentiations provided formerly by tonal harmonies". [4] As such, twelve-tone music is usually atonal, and treats each of the 12 semitones of the chromatic scale with equal importance, as opposed to earlier classical music which had treated some notes as more important than others (particularly the tonic and the dominant note).

The technique became widely used by the fifties, taken up by composers such as Milton Babbitt, Luciano Berio, Pierre Boulez, Luigi Dallapiccola, Ernst Krenek, Riccardo Malipiero, and, after Schoenberg's death, Igor Stravinsky. 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 Wuorinen 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." [15]

American composer Scott Bradley, best known for his musical scores for work like Tom & Jerry and Droopy Dog , utilized the 12-tone technique in his work. Bradley had learned the concept as a student of Schoenberg. [16] Bradley described his use thus:

The Twelve-Tone System provides the ‘out-of-this-world’ progressions so necessary to under-write the fantastic and incredible situations which present-day cartoons contain. [17]

An example of Bradley's use of the technique to convey building tension occurs in the Tom & Jerry short "Puttin' on the Dog", from 1953. In a scene where the mouse, wearing a dog mask, runs across a yard of dogs "in disguise", a chromatic scale represents both the mouse's movements, and the approach of a suspicious dog, mirrored octaves lower. [18] Apart from his work in cartoon scores, Bradley also composed tone poems that were performed in concert in California. [19]

Theodore Norman played the guitar part in Columbia Records' 1957 recordings of Schoenberg's Serenade, Opus 24 and Pierre Boulez's Le Marteau sans maître (The Hammer Without a Master). He went on to compose a number of twelve-tone pieces for solo guitar. [20]

Tone row

The basis of the twelve-tone technique is the tone row , an ordered arrangement of the twelve notes of the chromatic scale (the twelve equal tempered pitch classes). There are four postulates or preconditions to the technique which apply to the row (also called a set or series), on which a work or section is based: [21]

  1. The row is a specific ordering of all twelve notes of the chromatic scale (without regard to octave placement).
  2. No note is repeated within the row.
  3. The row may be subjected to interval-preserving transformations—that is, it may appear in inversion (denoted I), retrograde (R), or retrograde-inversion (RI), in addition to its "original" or prime form (P).
  4. The row in any of its four transformations may begin on any degree of the chromatic scale; in other words it may be freely transposed. (Transposition being an interval-preserving transformation, this is technically covered already by 3.) Transpositions are indicated by an integer between 0 and 11 denoting the number of semitones: thus, if the original form of the row is denoted P0, then P1 denotes its transposition upward by one semitone (similarly I1 is an upward transposition of the inverted form, R1 of the retrograde form, and RI1 of the retrograde-inverted form).

(In Hauer's system postulate 3 does not apply.) [2]

A particular transformation (prime, inversion, retrograde, retrograde-inversion) together with a choice of transpositional level is referred to as a set form or row form. Every row thus has up to 48 different row forms. (Some rows have fewer due to symmetry; see the sections on derived rows and invariance below.)

Example

Suppose the prime form of the row is as follows:

Example tone row.png

Then the retrograde is the prime form in reverse order:

Retrograde tone row.png

The inversion is the prime form with the intervals inverted (so that a rising minor third becomes a falling minor third, or equivalently, a rising major sixth):

Inversion tone row.png

And the retrograde inversion is the inverted row in retrograde:

Retrograde inversion tone row.png

P, R, I and RI can each be started on any of the twelve notes of the chromatic scale, meaning that 47 permutations 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).

Prime, retrograde, inverted, and retrograde-inverted forms of the ascending chromatic scale. P and RI are the same (to within transposition), as are R and I. P-R-I-RI.png
Prime, retrograde, inverted, and retrograde-inverted forms of the ascending chromatic scale. P and RI are the same (to within transposition), as are R and I.

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 such internal consistency.

Application in composition

Note that rules 1–4 above apply to the construction of the row itself, and not to the interpretation of the row in the composition. (Thus, for example, postulate 2 does not mean, contrary to common belief, that no note in a twelve-tone work can be repeated until all twelve have been sounded.) While a row may be expressed literally on the surface as thematic material, it need not be, and may instead govern the pitch structure of the work in more abstract ways. Even when the technique is applied in the most literal manner, with a piece consisting of a sequence of statements of row forms, these statements may appear consecutively, simultaneously, or may overlap, giving rise to harmony.

Schoenberg's annotated opening of his Wind Quintet Op. 26 shows the distribution of the pitches of the row among the voices and the balance between the hexachords, 1-6 and 7-12, in the principal voice and accompaniment Schoenberg - Wind Quintet opening.png
Schoenberg's annotated opening of his Wind Quintet Op. 26 shows the distribution of the pitches of the row among the voices and the balance between the hexachords, 1–6 and 7–12, in the principal voice and accompaniment

Needless to say, durations, dynamics and other aspects of music other than the pitch can be freely chosen by the composer, and there are also no general rules about which tone rows should be used at which time (beyond their all being derived from the prime series, as already explained). However, individual composers have constructed more detailed systems in which matters such as these are also governed by systematic rules (see serialism).

Properties of transformations

The tone row chosen as the basis of the piece is called the prime series (P). Untransposed, it is notated as P0. Given the twelve pitch classes of the chromatic scale, there are 12 factorial [23] (479,001,600 [13] ) tone rows, although this is far higher than the number of unique tone rows (after taking transformations into account). There are 9,985,920 classes of twelve-tone rows up to equivalence (where two rows are equivalent if one is a transformation of the other). [24]

Appearances of P can be transformed from the original in three basic ways:

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 inversion (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:PIR
R:IPRI
I:RRIP

However, there are only a few numbers by which one may multiply a row and still end up with twelve tones. (Multiplication is in any case not interval-preserving.)

Derivation

Derivation is transforming segments of the full chromatic, fewer than 12 pitch classes, to yield a complete set, most commonly using trichords, tetrachords, and hexachords. A derived set can be generated by choosing appropriate transformations of any trichord except 0,3,6, the diminished triad. A derived set can also be generated from any tetrachord that excludes the interval class 4, a major third, between any two elements. The opposite, partitioning, uses methods to create segments from sets, most often through registral difference.

Combinatoriality

Combinatoriality 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 Webern and Arnold Schoenberg. [26]

Invariance is defined as the "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", [27] a definition very close to that of mathematical invariance. George Perle describes their use as "pivots" or non-tonal ways of emphasizing certain pitches. Invariant rows are also combinatorial and derived.

Cross partition

Aggregates spanning several local set forms in Schoenberg's Von Heute auf Morgen. Aggregate Von Heute auf Morgen.png
Aggregates spanning several local set forms in Schoenberg's Von Heute auf Morgen .

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). [29]

For example, the layout of all possible 'even' cross partitions is as follows: [30]

62  43   34    26 **  ***  ****  ****** **  ***  ****  ****** **  ***  **** **  *** ** **

One possible realization out of many for the order numbers of the 34 cross partition, and one variation of that, are: [30]

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. [31]

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:

Also, some composers, including Stravinsky, have used cyclic permutation, or rotation, where the row is taken in order but using a different starting note. Stravinsky also preferred the inverse-retrograde, rather than the retrograde-inverse, treating the former as the compositionally predominant, "untransposed" form. [32]

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 Schoenberg. "Quiet", in Leonard Bernstein's Candide , satirizes the method by using it for a song about boredom, and Benjamin Britten used a twelve-tone row—a "tema seriale con fuga"—in his Cantata Academica: Carmen Basiliense (1959) as an emblem of academicism. [33]

Schoenberg's mature practice

Ten features of Schoenberg's mature twelve-tone practice are characteristic, interdependent, and interactive: [34]

  1. Hexachordal inversional combinatoriality
  2. Aggregates
  3. Linear set presentation
  4. Partitioning
  5. Isomorphic partitioning
  6. Invariants
  7. Hexachordal levels
  8. Harmony, "consistent with and derived from the properties of the referential set"
  9. Metre, established through "pitch-relational characteristics"
  10. Multidimensional set presentations.

See also

Related Research Articles

In music, a tone row or note row, also series or set, is 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.

In music, the mystic chord or Prometheus chord is a six-note synthetic chord and its associated scale, or pitch collection; which loosely serves as the harmonic and melodic basis for some of the later pieces by Russian composer Alexander Scriabin. Scriabin, however, did not use the chord directly but rather derived material from its transpositions.

The term "partition" is also French for the sheet music of a transcription.

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. Much as the pitches of an aggregate created by a tone row do not need to occur simultaneously, the pitches of a combinatorially created aggregate need not occur simultaneously. Arnold Schoenberg, creator of the twelve-tone technique, often combined P-0/I-5 to create "two aggregates, between the first hexachords of each, and the second hexachords of each, respectively."

Complement (music)

In music theory, complement refers to either traditional interval complementation, or the aggregate complementation of twelve-tone and serialism.

Permutation (music)

In music, a permutation (order) of a set is any ordering of the elements of that set. A specific arrangement of a set of discrete entities, or parameters, such as pitch, dynamics, or timbre. Different permutations may be related by transformation, through the application of zero or more operations, such as transposition, inversion, retrogradation, circular permutation, or multiplicative operations. These may produce reorderings of the members of the set, or may simply map the set onto itself.

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." Retrograde reverses the order of the motive's pitches: what was the first pitch becomes the last, and vice versa. This is a technique used in music, specifically in twelve-tone technique, where the inversion and retrograde techniques are performed on the same tone row successively, "[t]he inversion of the prime series in reverse order from last pitch to first."

Set (music) collection of objects in music theory

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.

An all-interval tetrachord is a tetrachord, a collection of four pitch classes, containing all six interval classes. There are only two possible all-interval tetrachords, when expressed in prime form. In set theory notation, these are [0,1,4,6] (4-Z15) and [0,1,3,7] (4-Z29). Their inversions are [0,2,5,6] (4-Z15b) and [0,4,6,7] (4-Z29b). The interval vector for all all-interval tetrachords is [1,1,1,1,1,1].

Trope (music) Concepts in music

A trope or tropus may refer to a variety of different concepts in medieval, 20th-, and 21st-century music.

<i>Composition for Four Instruments</i>

Composition for Four Instruments (1948) is an early serial music composition written by American composer Milton Babbitt. It is Babbitt’s first published ensemble work, following shortly after his Three Compositions for Piano (1947). In both these pieces, Babbitt expands upon the methods of twelve-tone composition developed by Arnold Schoenberg. He is notably innovative for his application of serial techniques to rhythm. Composition for Four Instruments is considered one of the early examples of “totally serialized” music. It is remarkable for a strong sense of integration and concentration on its particular premises—qualities that caused Elliott Carter, upon first hearing it in 1951, to persuade New Music Edition to publish it.

Fritz Heinrich Klein was an Austrian composer.

Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period. It revolves around the idea of 'emancipating dissonance', that is, freeing the structure of music from the familiar harmonic patterns that are derived from natural overtones. As music becomes more complex, dissonance becomes indistinguishable from consonance.

Suite for Piano (Schoenberg) twelve tone piece for piano composed between 1921 and 1923

Arnold Schoenberg's Suite for Piano, Op. 25, is a twelve tone piece for piano composed between 1921 and 1923.

In music, the "Ode-to-Napoleon" hexachord is the hexachord named after its use in the twelve-tone piece Ode to Napoleon Buonaparte (1942) by Arnold Schoenberg. Containing the pitch-classes 014589 it is given Forte number 6-20 in Allen Forte's taxonomic system. The primary form of the tone row used in the Ode allows the triads of G minor, E minor, and B minor to easily appear.

<i>A Sermon, a Narrative and a Prayer</i>

A Sermon, a Narrative and a Prayer is a cantata for alto and tenor singers, a narrator, chorus, and orchestra by Igor Stravinsky, composed in 1960–61. It belongs to the composer’s serial period, and lasts a little over a quarter of an hour in performance.

The Tone Clock, and its related compositional theory Tone-Clock Theory, is a post-tonal music composition technique, developed by composers Peter Schat and Jenny McLeod. Music written using tone-clock theory features a high economy of musical intervals within a generally chromatic musical language. This is because tone-clock theory encourages the composer to generate all their harmonic and melodic material from a limited number of intervallic configurations. Tone-clock theory is also concerned with the way that the three-note pitch-class sets can be shown to underlie larger sets, and considers these triads as a fundamental unit in the harmonic world of any piece. Because there are twelve possible triadic prime forms, Schat called them the 'hours', and imagined them arrayed in a clock face, with the smallest hour in the 1 o'clock position, and the largest hour in the 12 o'clock position. A notable feature of Tone-Clock Theory is 'tone-clock steering': transposing and/or inverting hours so that each note of the chromatic aggregate is generated once and once only.

References

Notes

  1. Whittall 2008, 26.
  2. 1 2 Perle 1991, 145.
  3. 1 2 Perle 1977, 2.
  4. 1 2 Schoenberg 1975, 218.
  5. Whittall 2008, 25.
  6. Leeuw 2005, 149.
  7. Leeuw 2005, 155–57.
  8. Schoenberg 1975, 213.
  9. Perle 1977, 9–10.
  10. 1 2 Perle 1977, 37.
  11. Neighbour 1955, 53.
  12. John Covach quoted in Whittall 2008, 24.
  13. 1 2 3 Whittall 2008, 24.
  14. Reti 1958
  15. Chase 1987, 587.
  16. "Scott Bradley – Biography & History – AllMusic". AllMusic.
  17. Yowp (7 January 2017). "Tralfaz: Cartoon Composer Scott Bradley".
  18. Goldmark, Daniel (2 April 2007). "Tunes for 'Toons: Music and the Hollywood Cartoon". Univ of California Press via Google Books.
  19. "Scott Bradley". IMDb.
  20. "Theodore Norman – Compositions". www.parfaitole.com.
  21. Perle 1977, 3.
  22. Whittall 2008, 52.
  23. Loy 2007, 310.
  24. Benson 2007, 348.
  25. Haimo 1990, 27.
  26. Perle 1977, 91–93.
  27. Babbitt 1960, 249–50.
  28. Haimo 1990, 13.
  29. Alegant 2010, 20.
  30. 1 2 Alegant 2010, 21.
  31. Alegant 2010, 22 and 24.
  32. Spies 1965, 118.
  33. Brett 2007.
  34. Haimo 1990, 41.

Sources

Further reading