John Rahn, born on February 26, 1944, in New York City, is a

music theorist Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. '' The Oxford Companion to Music'' describes three interrelated uses of the term "music theory": The first is the " rudiments", that ...

composer A composer is a person who writes music. The term is especially used to indicate composers of Western classical music, or those who are composers by occupation. Many composers are, or were, also skilled performers of music. Etymology and def ...

bassoon The bassoon is a musical instrument in the woodwind family, which plays in the tenor and bass ranges. It is composed of six pieces, and is usually made of wood. It is known for its distinctive tone color, wide range, versatility, and virtuosity ...

ist, and Professor of Music at the

University of Washington The University of Washington (UW and informally U-Dub or U Dub) is a public research university in Seattle, Washington, United States. Founded in 1861, the University of Washington is one of the oldest universities on the West Coast of the Uni ...

School of Music, Seattle. A former student of

Milton Babbitt Milton Byron Babbitt (May 10, 1916 – January 29, 2011) was an American composer, music theorist, mathematician, and teacher. He was a Pulitzer Prize and MacArthur Fellowship recipient, recognized for his serial and electronic music. Biography ...

and

Benjamin Boretz Benjamin Aaron Boretz (born October 3, 1934) is an American composer and Music theory, music theorist. Life and work Benjamin Boretz was born in Brooklyn, New York, to Abraham Jacob Boretz and Leah (Yullis) Boretz. He graduated with a degree in ...

, he was editor of ''

Perspectives of New Music ''Perspectives of New Music'' (PNM) is a peer-reviewed academic journal specializing in music theory Music theory is the study of theoretical frameworks for understanding the practices and possibilities of music. ''The Oxford Companion to Musi ...

'' from 1983 to 1993 and since 2001 has been co-editor with Benjamin Boretz and

Robert Morris Robert or Bob Morris may refer to: :''Ordered chronologically within each section.'' Politics and the law * Robert Hunter Morris (1700–1764), lieutenant governor of Colonial Pennsylvania * Robert Morris (financier) (1734–1806), one of the Foun ...

Forte number and prime form

There are three methods of computing

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'' (1973, ). The first number indicates the number of pitch cl ...

and

prime form In algebraic geometry, the Schottky–Klein prime form ''E''(''x'',''y'') of a compact Riemann surface ''X'' depends on two elements ''x'' and ''y'' of ''X'', and vanishes if and only if ''x'' = ''y''. The prime form ''E'' is not quite ...

Allen Forte Allen Forte (December 23, 1926 – October 16, 2014) was an American music theorist and musicologist. He was Battell Professor Emeritus of the Theory of Music at Yale University and specialized in 20th-century atonal music and music analysis. ...

published the first in his 1973 book ''The Structure of Atonal Music'', citing a 1961 article by

. The second was introduced in Rahn's ''Basic Atonal Theory'' and used in Joseph N. Straus's ''Introduction to Post-Tonal Theory'', where it was declared that the two algorithms only differed in five cases: 5-20, 6-Z29, 6-31, 7-20, and 8-26. and both list the prime forms of a

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 ...

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").Nelson, Paul (2004).
Two Algorithms for Computing the Prime Form
, ''ComposerTools.com''. Programmers tend to prefer Rahn's method, because the Rahn prime is easily computed by comparing sets in binary, whereas Forte's prime requires a more complex algorithm.Tsao, Ming (2007). ''Abstract Musical Intervals: Group Theory for Composition and Analysis'', p.99, n.32. . Algorithms given in Morris, Robert (1991). ''Class Notes for Atonal Music Theory'', p.103. Frog Peak Music.

References

Bibliography

* * *Rahn, John (2000). ''Music Inside Out: Going Too Far in Musical Essays''. intro. and comment. by Benjamin Boretz. Amsterdam: G+B Arts International. p. 177. . OCLC 154331400. *Rahn, John (1989). "New Research Paradigms", ''Music Theory Spectrum'', xi/1, 84-94. *

External links

John Rahn's home page
, ''Faculty.Washington.Edu''. American music theorists Year of birth missing (living people) Living people Babbitt scholars {{US-music-bio-stub