Editing Music theory (section)

===Analysis===
{{Main|Musical analysis|Schenkerian analysis|Transformational theory}}
[[File:Debussy Pelleas et Melisande prelude opening.PNG|thumb|upright=1.3|Typically a given work is analyzed by more than one person and different or divergent analyses are created. For instance, the first two bars of the prelude to [[Claude Debussy]]'s ''[[Pelléas et Mélisande (opera)|Pelléas et Melisande]]''
are analyzed differently by Leibowitz, Laloy, van Appledorn, and Christ. Leibowitz analyses this succession harmonically as D minor:I–VII–V, ignoring melodic motion, Laloy analyses the succession as D:I–V, seeing the G in the second measure as an [[musical ornamentation|ornament]], and both van Appledorn and Christ analyse the succession as D:I–VII.
{{audio|Debussy Pelleas et Melisande-prelude opening.mid|Play}}]]
Musical analysis is the attempt to answer the question ''how does this music work?'' The method employed to answer this question, and indeed exactly what is meant by the question, differs from analyst to analyst, and according to the purpose of the analysis. According to [[Ian Bent]], "analysis, as a pursuit in its own right, came to be established only in the late 19th century; its emergence as an approach and method can be traced back to the 1750s. However, it existed as a scholarly tool, albeit an auxiliary one, from the [[Middle Ages]] onwards."{{sfn|Bent|1987|loc=6}}{{incomplete short citation|date=December 2021}} [[Adolf Bernhard Marx]] was influential in formalising concepts about composition and music understanding towards the second half of the 19th century. The principle of analysis has been variously criticized, especially by composers, such as [[Edgard Varèse]]'s claim that, "to explain by means of [analysis] is to decompose, to mutilate the spirit of a work".<ref>Quoted in {{harvnb|Bernard|1981|loc=1}}</ref>

[[Schenkerian analysis]] is a method of musical analysis of tonal music based on the theories of [[Heinrich Schenker]] (1868–1935). The goal of a Schenkerian analysis is to interpret the underlying structure of a tonal work and to help reading the score according to that structure. The theory's basic tenets can be viewed as a way of defining [[tonality]] in music. A Schenkerian analysis of a passage of music shows hierarchical relationships among its pitches, and draws conclusions about the structure of the passage from this hierarchy. The analysis makes use of a specialized symbolic form of musical notation that Schenker devised to demonstrate various [[Schenkerian analysis#Techniques of prolongation|techniques of elaboration]]. The most fundamental concept of Schenker's theory of tonality may be that of ''tonal space''.<ref>Schenker described the concept in a paper titled ''Erläuterungen'' ("Elucidations"), which he published four times between 1924 and 1926: ''Der Tonwille'' (Vienna, Tonwille Verlag, 1924) vol. 8–9, pp. 49–51, vol. 10, pp. 40–42; ''Das Meisterwerk in der Musik'' (München, Drei Masken Verlag), vol. 1 (1925), pp. 201–05; 2 (1926), pp. 193–97. English translation, ''Der Tonwille'', Oxford University Press, vol. 2, pp. 117–18 (the translation, although made from vols. 8–9 of the German original, gives as original pagination that of ''Das Meisterwerk'' 1; the text is the same). The concept of tonal space is still present in {{harvtxt|Schenker|1979|loc=especially p. 14, § 13}}, but less clearly than in the earlier presentation.</ref> The intervals between the notes of the tonic triad form a ''tonal space'' that is filled with passing and neighbour notes, producing new triads and new tonal spaces, open for further elaborations until the surface of the work (the score) is reached.

Although Schenker himself usually presents his analyses in the generative direction, starting from the [[fundamental structure]] (''Ursatz'') to reach the score, the practice of Schenkerian analysis more often is reductive, starting from the score and showing how it can be reduced to its fundamental structure. The graph of the ''Ursatz'' is arrhythmic, as is a strict-counterpoint cantus firmus exercise.{{sfn|Schenker|1979|loc=p. 15, § 21}} Even at intermediate levels of the reduction, rhythmic notation (open and closed noteheads, beams and flags) shows not rhythm but the hierarchical relationships between the pitch-events. Schenkerian analysis is ''subjective''. There is no mechanical procedure involved and the analysis reflects the musical intuitions of the analyst.{{sfn| Snarrenberg|1997|loc={{Page needed|date=July 2015}}}} The analysis represents a way of hearing (and reading) a piece of music.

Transformational theory is a branch of music theory developed by [[David Lewin]] in the 1980s, and formally introduced in his 1987 work, ''Generalized Musical Intervals and Transformations''. The theory, which models [[Transformation (music)|musical transformations]] as elements of a [[Group theory|mathematical group]], can be used to analyze both [[tonality|tonal]] and [[atonal music]]. The goal of transformational theory is to change the focus from musical objects—such as the "C [[major chord]]" or "G major chord"—to relations between objects. Thus, instead of saying that a C major chord is followed by G major, a transformational theorist might say that the first chord has been "transformed" into the second by the "[[dominant (music)|Dominant]] operation." (Symbolically, one might write "Dominant(C major) = G major.") While traditional [[set theory (music)|musical set theory]] focuses on the makeup of musical objects, transformational theory focuses on the [[interval (music)|intervals]] or types of musical motion that can occur. According to Lewin's description of this change in emphasis, "[The transformational] attitude does not ask for some observed measure of extension between reified 'points'; rather it asks: 'If I am ''at'' s and wish to get to t, what characteristic ''gesture'' should I perform in order to arrive there?'"{{sfn|Lewin|1987|loc=159}}