Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle, though analysis as a formal concept is a relatively recent development.
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. 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.
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".
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 ; the second is learning scholars' views on music from antiquity to the present; the third is a sub-topic of musicology that "seeks to define processes and general principles in music". The musicological approach to theory differs from music analysis "in that it takes as its starting-point not the individual work or performance but the fundamental materials from which it is built."
Schenkerian analysis is a method of analyzing tonal music based on the theories of Heinrich Schenker (1868–1935). The goal is to demonstrate the organic coherence of the work by showing how the "foreground" relates to an abstracted deep structure, the Ursatz. This primal structure is roughly the same for any tonal work, but a Schenkerian analysis shows how, in each individual case, that structure develops into a unique work at the foreground. A key theoretical concept is "tonal space". The intervals between the notes of the tonic triad in the background form a tonal space that is filled with passing and neighbour tones, producing new triads and new tonal spaces that are open for further elaborations until the "surface" of the work is reached.
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.
In music, a hexachord is a six-note series, as exhibited in a scale or tone row. The term was adopted in this sense during the Middle Ages and adapted in the 20th century in Milton Babbitt's serial theory. The word is taken from the Greek: ἑξάχορδος, compounded from ἕξ and χορδή, and was also the term used in music theory up to the 18th century for the interval of a sixth.
Allen Forte 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.
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.
In music theory, prolongation is the process in tonal music through which a pitch, interval, or consonant triad is considered to govern spans of music when not physically sounding. It is a central principle in the music-analytic methodology of Schenkerian analysis, conceived by Austrian theorist Heinrich Schenker. The English term usually translates Schenker's Auskomponierung. According to Fred Lerdahl, "The term 'prolongation' [...] usually means 'composing out' ."
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
David Benjamin Lewin was an American music theorist, music critic and composer. Called "the most original and far-ranging theorist of his generation", he did his most influential theoretical work on the development of transformational theory, which involves the application of mathematical group theory to music.
Drei Klavierstücke, Op. 11, is a set of pieces for solo piano written by the Austrian composer Arnold Schoenberg in 1909. They represent an early example of atonality in the composer's work.
Music Theory Spectrum is a peer-reviewed, academic journal specializing in music theory and analysis. It is the official journal of the Society for Music Theory, and is published by Oxford University Press. The journal was first published in 1979 as the official organ of the Society for Music Theory, which had been founded in 1977 and had its first conference in 1978. Unlike many other journals, Music Theory Spectrum was initially published in an oblong (landscape) page format, to better accommodate such musical graphics as Schenkerian graphs.
Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period. It revolves around the idea of 'emancipating dissonance', that is, freeing the structure of music from the familiar harmonic patterns that are derived from natural overtones. As music becomes more complex, dissonance becomes indistinguishable from consonance.
Daniel Harrison is a music theorist, author, and former Chairman of the Department of Music at Yale University. Most interested in tonal theory, Harrison wrote his dissertation on the music of Max Reger at Yale, which eventually became Harmonic Function in Chromatic Music: A Renewed Dualist Theory and an Account of Its Precedents (1994). Also interested in pop music, particularly The Beach Boys, he appeared in the Don Was documentary Brian Wilson: I Just Wasn't Made for These Times (1995). During his tenure at Yale, he was named the Allen Forte Professor of Music Theory in 2006 and Chairman in 2007. From 2001 to 2003 he was editor-in-chief of Music Theory Spectrum.
The Society for Music Theory (SMT) is an American organization devoted to the promotion of music theory as a scholarly and pedagogical discipline. It currently has a membership of over 1200, primarily in the United States.
Ernst Oster was a German pianist, musicologist, and music theorist. A specialist in the use of Schenkerian Analysis, he was the English translator of Heinrich Schenker's final work, Free Composition.
Timothy L. Jackson is an American professor of music theory who has spent most of his career at the University of North Texas and specializes in music of the eighteenth through twentieth centuries, Schenkerian theory, politics and music. He is the co-founder of the Journal of Schenkerian Studies. In 2020, he became controversial for editing a special issue of that journal containing articles criticizing Philip Ewell's plenary talk "Music Theory's White Racial Frame".
