Editing Schenkerian analysis (section)

===Harmony===
The [[Klang (music)|tonic triad]], that from which the work as a whole arises, takes its model in the harmonic series. However,
<blockquote>the mere duplication of nature cannot be the object of human endeavour. Therefore ... the [[overtone series]] ... is transformed into a succession, a horizontal arpeggiation, which has the added advantage of lying within the range of the human voice. Thus the harmonic series is condensed, abbreviated for the purposes of art".<ref>''Free Composition'', § 1. See also ''Harmony'', § 13.</ref></blockquote>

Linking the (major) triad to the harmonic series, Schenker merely pays lip service to an idea common in the early 20th century.<ref>The same link is made, for instance, in [[Arnold Schönberg|Schoenberg]]'s ''Harmonielehre'', Wien, Universal, 1911, 7/1966, p. 16.</ref> He confirms that the same derivation cannot be made for the minor triad:
<blockquote>Any attempt to derive even as much as the first foundation of this [minor] system, i.e., the minor triad itself, from Nature, i.e., from the overtone series, would be more than futile. ... The explanation becomes much easier if artistic intention rather than Nature herself is credited with the origin of the minor mode.".<ref>''Harmony'', § 23</ref></blockquote>

The basic component of Schenkerian harmony is the ''Stufe'' (scale degree, scale-step), i.e. a chord having gained structural significance. Chords arise from within chords, as the result of the combination of passing notes and arpeggiations: they are at first mere embellishments, mere voice-leading constructions, but they become tonal spaces open for further elaboration and, once elaborated, can be considered structurally significant: they become scale-steps properly speaking. Schenker recognizes that "there are no rules which could be laid down once and for all" for recognizing scale-steps,<ref>''Harmony'', § 79.</ref> but from his examples one may deduce that a triad cannot be recognized as a scale-step as long as it can be explained by passing or neighboring voice-leading.

Schenkerian analyses label scale-steps with Roman numerals, a practice common in 19th- and 20th-century Vienna, developed by the theoretic work of [[Georg Joseph Vogler]] and his student [[Gottfried Weber]], transmitted by [[Simon Sechter]] and his disciple [[Anton Bruckner]], the classes of whom Schenker had followed in the Konservatorium in Vienna.<ref>Robert E. Wason, ''Viennese Harmonic Theory from Albrechtsberger to Schenker and Schoenberg'', Ann Arbor, London, UMI Research Press, 1982/1985.</ref>

Schenker's theory is monotonal: the ''Ursatz'', as the diatonic unfolding of the tonic triad, by definition cannot include modulation. Local "tonicisation" may arise when a scale-step is elaborated to the point of becoming a local tonic, but the work as a whole projects a single key and ultimately a single ''Stufe'' (the tonic).<ref>Matthew Brown, ''Explaining Tonality. Schenkerian Theory and Beyond'', Rochester, University of Rochester Press, 2005, p. 69, reproduces a chart showing that the "tonality of a given foreground can be generated from the diatony of the given background through various levels of the middleground".</ref>