Set theory vs Music

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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
(Hanson 1960).

Other theorists, such as Allen Forte, further developed the theory for
analyzing atonal music (Forte 1973),
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.

https://en.wikipedia.org/wiki/Set_(music)

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A set (pitch set, pitch-class set, set class, set form, set genus,
pitch collection) 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.[2]

https://en.wikipedia.org/wiki/Set_(music)[/url]

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Musicology is the scholarly analysis and research-based study of music.

Musicology departments traditionally belong to the humanities,
although some music research is scientific in focus
(psychological, sociological, acoustical, neurological, computational).

Some geographers and anthropologists have an interest in musicology so
the social sciences also have an academic interest.

A scholar who participates in musical research is a musicologist.[1][2][3]

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Music theory has no axiomatic foundation in modern mathematics,
although some interesting work has recently been done in this direction
(see the External Links),
yet the basis of musical sound can be described mathematically (in acoustics) and
exhibits "a remarkable array of number properties".[1]

Elements of music such as its form, rhythm and metre, the pitches of its notes
and the tempo of its pulse can be related to the measurement of time and frequency,
offering ready analogies in geometry.

https://en.wikipedia.org/wiki/Music_and_mathematics

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Set theory is the analytical technique we will use to analyze expressionist music.
The primary composers associated with expressionism are Arnold Schoenberg (1874–1951),
Anton Webern (1883–1945), and Alban Berg (1885–1935).

In this text, we will associate atonal music—music that avoids traditional harmonies
and scales—with expressionism.
Instead of scales and chords, intervals are the building blocks of Expressionist music.

Although composers began writing atonal music in 1908, there was no
widely-accepted systematic analytical approach that could show relationships
between different pieces until Allen Forte published his seminal
The Structure of Atonal Music in 1973,
in which Forte applied set theory mathematics to music.

However, our approach to normal form and prime form will follow
the slightly-modified approach set out by John Rahn in his Basic Atonal Theory (1980),
which is the approach followed by Joseph Straus in his well-known
and widely-used Introduction to Post-Tonal Theory.

https://musictheory.pugetsound.edu/m...rySection.html