Editing Schenkerian analysis (section)

==Fundamentals==

===Goals===
Schenker intended his theory as an exegesis of musical "genius" or the "masterwork", ideas that were closely tied to German nationalism and [[monarchism]].<ref>''Free Composition'', pp. xxi–xxiv, 158–162. ''Der Tonwille'', English translation, Vol. I, 17.</ref> The canon represented in his analytical work therefore is almost entirely made up of German music of the [[common practice period]] (especially that of [[Johann Sebastian Bach]], [[Carl Philipp Emanuel Bach]], [[Joseph Haydn]], [[Wolfgang Amadeus Mozart]], [[Ludwig van Beethoven]], [[Franz Schubert]], and [[Johannes Brahms]]),<ref>For a complete list of the works discussed by Schenker, see Larry Laskowski, ''Heinrich Schenker. An Annotated Index to his Analyses of Musical Works'', New York, Pendragon, 1978. Influential early exponents of Schenker's theory in the United states, [[Adele T. Katz]] and [[Felix Salzer]], opposed Schenker's musical conservatism and expanded the analytical method to more modern repertoire. See {{section link||Early reception in the US}}</ref> and he used his methods to oppose more modern styles of music such as that of [[Max Reger]] and [[Igor Stravinsky]].<ref>''Das Meisterwerk in der Musik'', vol. II, pp. 17–18, 192 (English translation, p. 1–22, 117)</ref> This led him to seek the key to an understanding of music in the traditional disciplines of counterpoint and figured bass, which was central to the compositional training of these composers. Schenker's project was to show that free composition (''freier Satz'') was an elaboration, a "[[prolongation]]", of strict composition (''strenger Satz''), by which he meant species counterpoint, particularly two-voice counterpoint. He did this by developing a theory of hierarchically organized levels of elaboration (''Auskomponierung''), called prolongational levels, voice-leading levels (''Stimmführungsschichten''), or transformations (''Verwandlungen''), the idea being that each of the successive levels represents a new freedom taken with respect to the rules of strict composition.<ref>See Schenker's "instructional plan" described in his Introduction to ''Free Composition'', pp. xxi–xxii. The steps of this plan are: "Instruction in strict writing (according to Fux-Schenker), in thorough-bass (according to J.S. and C.P.E. Bach) and in free writing (according to Schenker), that finally combines all studies and places them in the service of the law of organic coherence as it reveals itself in the ''Ursatz'' (''Urlinie'' and bass arpeggiation) as background, in the voice-leading transformations as middelground and ultimately through the foreground." (Translation modified following ''Der freie Satz'', 1935, p. 2.)</ref>

Because the first principle of the elaboration is the filling in of the tonal space by passing notes, an essential goal of the analysis is to show linear connections between notes which, filling a single triad at a given level, remain closely related to each other but which, at subsequent levels, may become separated by many measures or many pages as new triads are embedded in the first one. The analyst is expected to develop a "distance hearing" (''Fernhören''),<ref>''Der Tonwille'' 1 (1921), p. 23; 2 (1922), pp. 31 and 35; ''Der Tonwille'', English translation, vol. I, pp. 22, 77 and 82. The term has been taken over by Wilhelm Furtwängler, ''Wort und Ton'', Wiesbaden, Brockhaus, 1954, pp. 201–202.</ref> a "structural hearing".<ref>[[Felix Salzer]], ''Structural Hearing'', New York, Boni, 1952.</ref>

===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>

===Counterpoint, voice-leading===
Two-voice [[counterpoint]] remains for Schenker the model of strict writing. Free composition is a freer usage of the laws of strict counterpoint. One of the aims of the analysis is to trace how the work remains subject to these laws at the deepest level, despite the freedom taken at subsequent levels.<ref>Heinrich Schenker, ''Counterpoint'', vol. I, p. 12: "In the present day, when it is necessary to distinguish clearly between composition and that preliminary school represented by strict counterpoint, we must use the eternally valid of those rules for strict counterpoint, even if we no longer view them as applicable to composition".</ref>

One aspect of strict, two-voice writing that appears to span Schenker's theory throughout the years of its elaboration is the rule of "fluent melody" (''fließender Gesang''), or "melodic fluency".<ref>N. Meeùs, "[http://periodicos.udesc.br/index.php/orfeu/article/download/10538/7525 Schenker's ''fließender Gesang'' and the Concept of Melodic Fluency]", ''Orfeu'' 2/1, 2017, pp. 160–170.</ref> Schenker attributes the rule to [[Luigi Cherubini]], who would have written that "fluent melody is always preferable in strict counterpoint."<ref>''Counterpoint'', vol. I, p. 74. J. Rothgeb and J. Thym, the translators, quote Cherubini from the original French, which merely says that "conjunct motion better suits strict counterpoint than disjunct motion", but Schenker had written: ''der fliessende Gesang ist im strengen Stile immer besser as der sprungweise'' (''Kontrapunkt'', vol. I, p. 104) ("the fluent melody is always better in strict style than the disjunct one"). ''Fliessender Gesang'' not only appears in several 19th-century German translations of Cherubini, but is common in German counterpoint theory from the 18th century and might go back to Fux' description of the ''flexibili motuum facilitate'', the "flexible ease of motions" (''Gradus'', Liber secundus, Exercitii I, Lectio quinta) or even earlier. N. Meeùs, [http://periodicos.udesc.br/index.php/orfeu/article/view/10538 Schenker's ''Fliessender Gesang'' and the Concept of Melodic Fluency], ''Orfeu'' 2/1 (2017), pp. 162–63.</ref> Melodic fluency, the preference for conjunct (stepwise) motion, is one of the main rules of [[voice leading]], even in free composition. It avoids successive leaps and produces "a kind of wave-like melodic line which as a whole represents an animated entity, and which, with its ascending and descending curves, appears balanced in all its individual component parts".<ref>''Counterpoint'', vol. I, p. 94.</ref> This idea is at the origin of that of [[linear progression]] (''Zug'') and, more specifically, of that of the Fundamental Line (''Urlinie'').

==={{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>