separate sources. This information is presented in a context freed from
application within a specific analysis, or system of analytical thinking, and
was chosen to provide information that is of primary importance to the
most common and general analytical pursuits. Also included in this book
are significant references to individual set-classes in musical or theoretical
contexts, tables that allow quick comparisons between set-classes of similar
or differing numbers of elements, an extensive bibliography, and an index
of analytical styles. Brief explanations of fundamental assumptions and
instructions for each new section are given, but they assume the reader has
had, or is currently receiving, instruction in application of set-theory to
musical procedure. For an introduction to basic concepts in contemporary
analysis and pitch-structure, see Straus ( 1990), Lester ( 1989), or Rahn
( 1980). For an overall historical and general stylistic guide, see Antokoletz
( 1992), Morgan ( 1991a), or Watkins ( 1988). Composers and theorists will
benefit from compositional applications in Morris ( 1987).

A common resistance to this approach for developing insight into
musical possibilities stems from what may appear to be unnatural preoccu-
pation with, and an overabundance of, numbers with intimidatingly
mathematical appearances. But this impression is deceptive, because
complex mathematics is usually unnecessary. Numbers are used to repre-
sent pitches, allowing relations to be notated in a way that generalizes
possibility without being limited by enharmonic spellings peculiar to
specific contexts. Numbers can become familiar quickly, and are no more
arbitrary than the letter names from A to G that we easily accept. They
allow clarity of organization in charts and a compression of information in
concise and streamline manners impossible with letters and accidentals.
This use of numbers has similar advantages to the use of numbers in
measuring the passing of time. While this application of numbers is
primarily practical, it also helps model the cyclic qualities we perceive in
passing time. Numeric notation applied to pitches can help reveal the influ-
ence of cycles in music in analogous ways.

Central to the book's presentation of resources is the organizational
method of notation based on transpositional and inversional equivalence of
set-classes introduced by Allen Forte ( 1973). While influenced by several
pre-existing models, including at the very least Hauer ( 1926), Martino
( 1961), and Hanson ( 1960), Forte's set-class notation succeeded in provid-
ing a system of harmonic classification that was not completely dependent
upon analytical habits from tonal music. Many analysts based classifica-
tions on chord roots built from the bass using uniform interval sizes. This

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