Editing Schenkerian analysis (section)

==={{anchor|Ursatz}}Ursatz===<!-- This section is linked from [[Schenkerian analysis]] -->
{{Main|Ursatz}}
[[File:The Schenkerian Ursatz.png|thumb|upright|Minimal ''Ursatz'': a line {{music|scale|3}} {{music|scale|2}} {{music|scale|1}} supported by an arpeggiation of the bass[[File:Ursatz.mid]]]]
''Ursatz'' (usually translated as "fundamental structure") is the name given by Schenker to the underlying structure in its simplest form, that from which the work as a whole originates. In the canonical form of the theory, it consists of the ''Urlinie'', the "fundamental line", supported by the ''Bassbrechung'', the "arpeggiation of the bass". The fundamental structure is a two-voice counterpoint and as such belongs to strict composition.<ref>The canonical ''Ursatz'' is discussed in ''Free Composition'', §§ 1–44, but it was first described in ''Das Meisterwerk in der Musik'', vol. III (1930), pp. 20–21 (English translation, p. 7-8). The word ''Ursatz'' already appeared in Schenker's writings in 1923 (''Der Tonwille'' 5, p. 45; English translation, vol. I, p. 212).</ref> In conformity with the theory of the tonal space, the fundamental line is a line starting from any note of the triad and descending to the tonic itself. The arpeggiation is an arpeggiation through the fifth, ascending from I to V and descending back to I. The ''Urlinie'' unfolds the tonal space in a melodic dimension, while the ''Bassbrechung'' expresses its harmonic dimension.<ref>''Free Composition'', pp. 4–5.</ref>

The theory of the fundamental structure is the most criticized aspect of Schenkerian theory: it has seemed unacceptable to reduce all tonal works to one of a few almost identical background structures. This is a misunderstanding: Schenkerian analysis is not about demonstrating that all compositions can be reduced to the same background, but about showing how each work elaborates the background in a unique, individual manner, determining both its identity and its "meaning". Schenker has made this his motto: ''Semper idem, sed non eodem modo'', "always the same, but never in the same manner".<ref>Schenker himself mentioned and refuted the criticism, in § 29 (p. 18) of ''Free Composition''</ref>

===={{anchor|Fundamental line}}Fundamental line====
{{main|Fundamental line}}
The idea of the fundamental line comes quite early in the development of Schenker's theory. Its first printed mention dates from 1920, in the edition of [[Piano Sonata No. 28 (Beethoven)|Beethoven's Sonata Op. 101]], but the idea obviously links with that of "fluent melody", ten years earlier.<ref>''Counterpoint'', vol. I, 1910, quoted above.</ref> Schenker first conceived the ''Urlinie'', the "fundamental line", as a kind of motivic line characterized by its fluency, repeated under different guises throughout the work and ensuring its homogeneity. He later imagined that a musical work should have only one fundamental line, unifying it from beginning to end. The realization that such fundamental lines usually were descending led him to formulate the canonical definition of the fundamental line as necessarily descending. It is not that he rejected ascending lines, but that he came to consider them hierarchically less important. "The fundamental line begins with {{music|scale|8}}, {{music|scale|5}} or {{nobreak|{{music|scale|3}},}} and moves to {{music|scale|1}} via the descending leading tone {{music|scale|2}}".<ref>''Free Composition'', § 10.</ref> The initial note of the fundamental line is called its "head tone" (''Kopfton'') or "[[primary tone]]". The head note may be elaborated by an upper neighbour note, but not a lower one.<ref>Free Composition, § 106.</ref> In many cases, the head note is reached through an ascending line (''Anstieg'', "initial ascent") or an ascending arpeggiation, which do not belong to the fundamental structure properly speaking.<ref name="FreeComposition">''Free Composition'', § 120.</ref>

===={{anchor|Divider}}Arpeggiation of the bass and the divider at the fifth====
{{Main|Bass arpeggiation}}
The arpeggiation through the fifth is an imitation of the overtone series, adapted to man [sic] "who within his own capacities can experience sound only in a succession".<ref>Free Composition, § 16.</ref> The fifth of the arpeggiation coincides with the last passing note {{music|scale|2}} of the fundamental line. This at first produces a mere "divider at the fifth", a complex filling in of the tonal space. However, as a consonant combination, it defines at a further level a new tonal space, that of the dominant chord, and so doing opens the path for further developments of the work. It would appear that the difference between the divider at the fifth and the dominant chord properly speaking really depends on the level at which the matter is considered: the notion of the divider at the fifth views it as an elaboration of the initial tonal space, while the notion of dominant chord conceives it as a new tonal space created within the first. But the opinions of modern Schenkerians diverge on this point.<ref>William Rothstein, "Articles on Schenker and Schenkerian Theory in ''[[The New Grove Dictionary of Music and Musicians]]'', 2nd edition," ''[[Journal of Music Theory]]'' 45/1 (2001), pp. 218–219.</ref>