John Rahn

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John Rahn, born on February 26, 1944, in New York City, is a music theorist, composer, bassoonist, and Professor of Music at the University of Washington School of Music, Seattle. A former student of Milton Babbitt and Benjamin Boretz, he was editor of Perspectives of New Music from 1983 to 1993 and since 2001 has been co-editor with Benjamin Boretz and Robert Morris.

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Forte number and prime form

There are three methods of computing Forte number and prime form. Allen Forte published the first in his book The Structure of Atonal Music (1973). The second was introduced in Rahn's Basic Atonal Theory and used in Joseph N. Straus's Introduction to Post-Tonal Theory,[ full citation needed ] where it was declared that the two algorithms only differed in five cases: 5-20, 6-Z29, 6-31, 7-20, and 8-26.

Forte (1973)[ full citation needed ] and Rahn (1980) both list the prime forms of a set as the most left-packed possible version of the set. Forte packs from the left and Rahn packs from the right ("making the small numbers smaller" versus making "the larger numbers smaller"). [1] Programmers tend to prefer Rahn's method. [2]

Bibliography

Related Research Articles

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 the early 20th-century to the present day, where a hierarchy of harmonies focusing on a single, central triad 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 European classical 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".

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.

Twelve-tone technique Musical composition method using all 12 chromatic scale notes equally often & not in a key

The twelve-tone technique—also known as dodecaphony, twelve-tone serialism, and 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 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 actively opposed the technique, such as Aaron Copland and Igor Stravinsky, eventually adopted it in their music.

Set theory (music) Branch of music 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 theory for analyzing atonal music, drawing on the twelve-tone theory of Milton Babbitt. The concepts of musical set theory are very general and can be applied to tonal and atonal styles in any equal temperament tuning system, and to some extent more generally than that.

Interval class

In musical set theory, an interval class, also known as unordered pitch-class interval, interval distance, undirected interval, or "(even completely incorrectly) as 'interval mod 6'", is the shortest distance in pitch class space between two unordered pitch classes. For example, the interval class between pitch classes 4 and 9 is 5 because 9 − 4 = 5 is less than 4 − 9 = −5 ≡ 7 (mod 12). See modular arithmetic for more on modulo 12. The largest interval class is 6 since any greater interval n may be reduced to 12 − n.

Benjamin Boretz American composer and music theorist

Benjamin Aaron Boretz is an American composer and music theorist.

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.

In music, transposition refers to the process or operation of moving a collection of notes up or down in pitch by a constant interval.

The shifting of a melody, a harmonic progression or an entire musical piece to another key, while maintaining the same tone structure, i.e. the same succession of whole tones and semitones and remaining melodic intervals.

Perspectives of New Music is a peer-reviewed academic journal specializing in music theory and analysis. It was established in 1962 by Arthur Berger and Benjamin Boretz.

Multiplication (music)

The mathematical operations of multiplication have several applications to music. Other than its application to the frequency ratios of intervals, it has been used in other ways for twelve-tone technique, and musical set theory. Additionally ring modulation is an electrical audio process involving multiplication that has been used for musical effect.

Set (music)

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.

Interval vector

In musical set theory, an interval vector is an array of natural numbers which summarize the intervals present in a set of pitch classes. Other names include: ic vector, PIC vector and APIC vector

Pentachord

A pentachord in music theory may be either of two things. In pitch-class set theory, a pentachord is defined as any five pitch classes, regarded as an unordered collection. In other contexts, a pentachord may be any consecutive five-note section of a diatonic scale. A pentad is a five-note chord.

<i>Five Pieces for Orchestra</i>

The Five Pieces for Orchestra, Op. 16, were composed by Arnold Schoenberg in 1909, and first performed in London in 1912. The titles of the pieces, reluctantly added by the composer after the work's completion upon the request of his publisher, are as follows:

Forte number

In musical set theory, a Forte number is the pair of numbers Allen Forte assigned to the prime form of each pitch class set of three or more members in The Structure of Atonal Music. The first number indicates the number of pitch classes in the pitch class set and the second number indicates the set's sequence in Forte's ordering of all pitch class sets containing that number of pitches.

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.

Elaine Barkin American composer, writer, and educator

Elaine Barkin née Radoff is an American composer, writer, and educator.

James K. Randall

James K. Randall was an American composer, music theorist, and early adopter of electronic music. At the time of his death he was Professor of Music Emeritus at Princeton University.

References

  1. Nelson, Paul (2004). "Two Algorithms for Computing the Prime Form", ComposerTools.com.
  2. Tsao, Ming (2007). Abstract Musical Intervals: Group Theory for Composition and Analysis, p.99, n.32. ISBN   9781430308355. Algorithms given in Morris, Robert (1991). Class Notes for Atonal Music Theory, p.103. Frog Peak Music.