Editing Schenkerian analysis (section)

==Elaboration of the fundamental structure==
The elaborations of the fundamental structure deserve a specific discussion because they may determine the form of the work in which they occur.

===Initial ascent, initial arpeggiation<!--[[Head note (Schenker)]], [[Kopfton]], [[Übergreifen]], [[Anstieg]], and [[Initial ascending line]] redirect directly here.-->===

The starting point of the fundamental line, its "head note" (''Kopfton''), may be reached only after an ascending motion, either an initial ascending line (''Anstieg'') or an initial arpeggiation, which may take more extension than the descending fundamental line itself. This results in melodies in arch form. Schenker decided only in 1930 that the fundamental line should be descending: in his earlier analyses, initial ascending lines often are described as being part of the ''Urlinie'' itself.<ref name="FreeComposition" />

===First-order neighbor note===
Schenker stresses that the head note of the fundamental line often is decorated by a neighbor note "of the first order", which must be an upper neighbor because "the lower neighboring note would give the impression of the interruption". The neighbor note of the first order is {{music|scale|3}}–{{music|scale|4}}–{{music|scale|3}} or {{music|scale|5}}–{{music|scale|6}}–{{music|scale|5}}: the harmony supporting it often is the IVth or VIth degree, which may give rise to a section of the work at the subdominant.<ref>''Free Composition'', §106.</ref>

===Articulation of the span from I to V in the bass arpeggiation===
The canonic form of the bass arpeggiation is I–V–I. The second interval, V–I, forms under {{music|scale|2}}–{{music|scale|1}} the perfect authentic cadence and is not susceptible of elaboration at the background level. The first span, I–V, on the other hand, usually is elaborated. The main cases include:<ref>The cases described in the following paragraphs are discussed in Heinrich Schenker, "Further Consideration of the Urlinie: II", translated by John Rothgeb, ''The Masterwork in Music'', vol. II, Cambridge, Cambridge University Press, 1996, pp. 1–22.</ref>

====I–III–V====
This is the complete arpeggiation of the triad. Once elaborated, it may consist in a succession of three tonalities, especially in pieces in minor. In these cases, III stands for a tonicisation of the major relative. This often occurs in Sonata forms in minor, where the first thematic group elaborates degree I, the second thematic group is in the major relative, degree III, and the development leads to V before the recapitulation in the tonic key.

====I–IV–V or I–II–V====
[[File:I IV V I.png|thumb|250px|Bass elaboration I–IV–V–I[[File:I-IV-V-I.mid]]]]

Even though he never discussed them at length, these elaborations occupy a very special place in Schenker's theory. One might even argue that no description of an ''Ursatz'' properly speaking is complete if it does not include IV or II at the background level. Schenker uses a special sign to denote this situation, the double curve shown in the example hereby, crossing the slur that links IV (or II) to V. That IV (here, F) is written as a quarter note indicates that it is of lower rank than I and V, notated as half notes. Here there is an unexpected link between Schenkerian theory and Riemann's theory of tonal functions, a fact that might explain Schenker's reluctance to be more explicit about it. In modern Schenkerian analysis, the chord of IV or II is often dubbed the "predominant" chord, as the chord that prepares the dominant one, and the progression may be labelled "T–P–D–T", for tonic–predominant–dominant–tonic.

====I–II–III–IV–V====
The dominant chord may be linked to the tonic by a stepwise linear progression. In such case, one of the chords in the progression, II, III or IV, usually takes preeminence, reducing the case to one or the other described above.

===Interruption===
The interruption (''Unterbrechung'') is an elaboration of the fundamental line, which is interrupted at its last passing note, {{music|scale|2}}, before it reaches its goal. As a result, the bass arpeggiation itself is also interrupted at the divider at the fifth (V). Both the fundamental line and the bass arpeggiation are bound to return to their starting point and the fundamental structure repeats itself, eventually reaching its goal. The interruption is the main form-generating elaboration: it often is used in binary forms (when the first part ends on the dominant) or, if the elaboration of the "dividing dominant", {{music|scale|2}} above V, takes some importance, it may produce ternary form, typically sonata form.<ref>''Free Composition'', §§ 87–101.</ref>

===Mixture===
Schenker calls "mixture" (''Mischung'') the change of mode of the tonic, i.e. the replacement of its major third by the minor one, or of its minor third by the major one. The elaboration of the resulting chord may give rise to a section in minor within a work in major, or the reverse.<ref>''Free Composition'', § 193.</ref>

===Transference of the fundamental structure===
The forms of the fundamental structure may be repeated at any level of the work. "Every transferred form [of the fundamental structure] has the effect of a self-contained structure within which the upper and lower voices delimit a single tonal space".<ref>''Free Composition'', p. 87, §242.</ref> That is to say that any phrase in a work could take the form of a complete fundamental structure. Many classical themes (e.g. the theme to the set of variations in Mozart's K. 331 piano sonata) form self-contained structure of this type. This resemblance of local middleground structures to background structures is part of the beauty and appeal of Schenkerian analysis, giving it the appearance of a recursive construction.<ref>Matthew Brown, ''Explaining Tonality. Schenkerian Theory and Beyond'', Rochester, University of Rochester Press, pp. 96–98.</ref>