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

music theorist Music theory is the study of 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 are needed to understand music notation (ke ...

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 Defi ...

bassoon The bassoon is a woodwind instrument in the double reed 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 virtuo ...

ist, and Professor of Music at the

University of Washington The University of Washington (UW, simply Washington, or informally U-Dub) is a public research university in Seattle, Washington. Founded in 1861, Washington is one of the oldest universities on the West Coast; it was established in Seattle a ...

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 is particularly noted for his Serialism, serial and electronic music. Biography Babbitt was born in Philadelphia t ...

and

Benjamin Boretz Benjamin Aaron Boretz (born October 3, 1934) is an American composer and 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 music from Br ...

, he was editor of ''

Perspectives of New Music ''Perspectives of New Music'' (PNM) is a peer-reviewed academic journal specializing in music theory and analysis. It was established in 1962 by Arthur Berger and Benjamin Boretz (who were its initial editors-in-chief). ''Perspectives'' was first ...

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

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 c ...

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, Allen's or Allens may refer to: Buildings * Allen Arena, an indoor arena at Lipscomb University in Nashville, Tennessee * Allen Center, a skyscraper complex in downtown Houston, Texas * Allen Fieldhouse, an indoor sports arena on the Univer ...

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'', 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) 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.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.

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.

References

External links

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