Editing Schenkerian analysis (section)

==Techniques of prolongation==
{{Main|Prolongation}}
The meat of a Schenkerian analysis is in showing how a background structure expands until it results in the succession of musical events on the surface of the composition itself. Schenker refers to this process under the term ''Auskomponierung'', literally "composing out", but more often translated as "elaboration". Modern Schenkerians usually prefer the term "prolongation", stressing that elaborations develop the events along the time axis.

Schenker writes:
<blockquote>In practical art the main problem is how to realize the concept of harmony in a live content. In Chopin's Prelude, Op. 28, No 6, thus, it is the motif [[File:ChopinOp28no6.png|thumb|center|upright=1.8|<br />[[File:ChopinOp28no6.mid|thumb|150px|left|Chord]][[File:ChopinOp28no6 score bass.mid|thumb|150px|Arpeggio]]]]
:that gives life to the abstract concept of the triad, B, D, F-sharp.<ref>''Harmonielehre'', p. 281; English translation, p. 211.</ref></blockquote>
The elaboration of the triad, here mainly in the form of an arpeggio, loads it with "live content", with meaning. Elaborations take the form of ''diminutions'', replacing the total duration of the elaborated event by shorter events in larger number. By this, notes are displaced both in pitch and in rhythmic position. The analysis to some extent aims at restoring displaced notes to their "normal" position and explaining how and why they were displaced.<ref name = idea/>

{{anchor|HaydnFmajor}}<!-- This section is linked from [[Schenkerian analysis]] -->

[[File:TonalSpace.png|thumb|Elaboration of the F major chord[[File:TonalSpace.mid]]]]
One aspect of Schenkerian analysis is that it does not view the work as built from a succession of events, but as the growth of new events from within events of higher level, much as a tree develops twigs from its branches and branches from its trunk: it is in this sense that Schenkerian theory must be considered organicist. The example shown here may at first be considered a mere elaboration of an F major chord, an arpeggiation in three voices, with passing notes (shown here in black notes without stem) in the two higher voices: it is an exemplification of the tonal space of F major. The chord labelled (V) at first merely is a "[[#Divider|divider at the fifth]]". However, the meeting of the fifth (C) in the [[bass arpeggiation]] with the passing notes may also be understood as producing a dominant chord, V, arising from within the tonic chord I. This is the situation found at the beginning of Haydn's Sonata in F major, Hob. XVI:29, where the (incomplete) dominant chord appears at the very end of bar 3, while the rest of the fragment consists of arpeggios (with neighbor notes) of the F chord:<ref>See http://nicolas.meeus.free.fr/Cours/2012Elaborations.pdf, examples 5 a and b, pp. 3 and 4.</ref>
[[File:HaydnHobXVI29.png|thumb|center|upright=1.8|[[File:HaydnHobXVI29.mid]]]]

===Arpeggiation, neighbour note, passing note===
Arpeggiation is the simplest form of elaboration. It delimits a tonal space for elaboration, but lacks the melodic dimension that would allow further developments: it "remains a harmonic phenomenon".<ref>Heinrich Schenker, "Elucidations", ''Der Tonwille'' 8–9, English translation, vol. II, p. 117 (translation by [[Ian Bent]])</ref> From the very structure of triads (chords), it follows that arpeggiations remain disjunct and that any filling of their space involves conjunct motion. Schenker distinguishes two types of filling of the tonal space: 1) neighbor notes (''Nebennoten''), ornamenting one single note of the triad by being adjacent to it. These are sometimes referred to generically as "adjacencies";
2) passing notes, which pass by means of stepwise motion from one note to another and fill the space in between, and are thus sometimes referred to as "connectives".
Both neighbor notes and passing notes are dissonances. They may be made consonant by their coinciding with other notes (as in the [[#HaydnFmajor|Haydn]] example above) and, once consonant, may delimit further tonal spaces open to further elaborations. Insofar as chords consist of several voices, arpeggiations and passing notes always involve passing from one voice to another.

===Linear progression===
{{Main|Linear progression}}
A linear progression (''Zug'') is the stepwise filling of some consonant interval. It usually is underlined in graphic analyses with a slur from the first note of the progression to the last.
The most elementary linear progressions are determined by the tonal space that they elaborate: they span from the prime to the third, from the third to the fifth or from the fifth to the octave of the triad, in ascending or descending direction. Schenker writes: "there are no other tonal spaces than those of 1–3, 3–5, and 5–8. There is no origin for passing-tone- progressions, or for melody"<ref>"Erläuterungen", ''Der Tonwille'' 8–9, English translation, vol. I, p. 117 (translation by [[Ian Bent]]).</ref> Linear progressions, in other words, may be either third progressions (''Terzzüge'') or fourth progressions (''Quartzüge''); larger progressions result from a combination of these.
{{anchor|BeethovenOp109}}<!-- This section is linked from [[Schenkerian analysis]] -->Linear progressions may be incomplete (deceptive) when one of their tones is replaced by another, but nevertheless suggested by the harmony. In the example below, the first bars of Beethoven's Sonata Op. 109, the bass line descends from E<sub>3</sub> to E<sub>2</sub>. F{{music|#}}<sub>2</sub> is replaced by B<sub>1</sub> in order to mark the cadence, but it remains implicit in the B chord. In addition, the top voice answers the bass line by a voice exchange, E<sub>4</sub>–F{{music|#}}<sub>4</sub>–G{{music|#}}<sub>4</sub> above G{{music|#}}<sub>2</sub>–(F{{music|#}}<sub>2</sub>)–E<sub>2</sub>, in bar 3, after a descending arpeggio of the E major chord. The bass line is doubled in parallel tenths by the alto voice, descending from G{{music|#}}<sub>4</sub> to G{{music|#}}<sub>3</sub>, and the tenor voice alternatively doubles the soprano and the bass, as indicated by the dotted slurs. It is the bass line that governs the passage as a whole: it is the "leading progression", on which all the other voices depend and which best expresses the elaboration of the E major chord.<ref>''Free composition'', p. 78, §221.</ref>
[[File:BeethovenOp109.png|thumb|center|upright=2|<br />[[File:BeethovenOp109.mid|thumb|120px|left|Reduction]][[File:BeethovenOp109 score.mid|thumb|120px|Original]]]]

Schenker describes lines covering a seventh or a ninth as "illusory",<ref>''Free Composition'', pp. 74–75, §§ 205–207. Schenker's German term is ''scheinbare Züge'', literally "apparent linear progressions"; Oster's translation as "illusory" may overstate the point.</ref> considering that they stand for a second (with a register transfer): they do not fill a tonal space, they pass from one chord to another.<ref>The matter of the elaboration of seventh chords remains ambiguous in Schenkerian theory. See Yosef Goldenberg, ''Prolongation of Seventh Chords in Tonal Music'', Lewinston, The Edwin Mellen Press, 2008.</ref>

===Lines between voices, reaching over<!--[[Reaching over]] and [[Übergreifen]] redirect directly here.-->===
Passing tones filling the intervals of a chord may be considered forming lines between the voices of this chord. At the same time, if the chord tones themselves are involved in lines from one chord to another (as usually is the case), lines of lower level unfurl between lines of higher level. The most interesting case is when the lines link an inner voice to the upper voice. This may happen not only in ascending (a case usually described as a "line from an inner voice"), but also in descending, if the inner voice has been displaced above the upper line by a [[#Transfer|register transfer]], a case known as "reaching over" (''Übergreifen'', also translated as ''superposition'' or ''overlapping'').<ref>{{Cite Grove |last=Drabkin |first=William |title=Reaching over}}. See also Nicolas Meeùs, "[https://trace.tennessee.edu/gamut/vol8/iss1/6/ Übergreifen]," ''Gamut: Online Journal of the Music Theory Society of the Mid-Atlantic'', vol. 8, iss. 1, article 6.</ref> In the example from Schubert's ''[[#SchubertOp4no3|Wanderers Nachtlied]]'' below, the descending line G{{music|b}}–F–E{{music|b}}–D{{music|b}} at the end of the first bar may be read as a reaching over.

===Unfolding===
{{main|Unfolding (music)}}
{{anchor|SchubertOp4no3}}<!-- This section is linked from [[Schenkerian analysis]] -->Unfolding (''Ausfaltung'') is an elaboration by which several voices of a chord or of a succession of chords are combined in one single line "in such a manner that a tone of the upper voice is connected to a tone of the inner voice and then moves back, or the reverse".<ref>''Free composition'', p.&nbsp;50, §140.</ref> At the end of Schubert's ''Wanderers Nachtlied'' op. 4 no. 3, the vocal melody unfolds two voices of the succession I–V–I; the lower voice, B{{music|b}}–A{{music|b}}–G{{music|b}}, is the main one, expressing the tonality of G{{music|b}} major; the upper voice, D{{music|b}}–C{{music|b}}–B{{music|b}}, is doubled one octave lower in the right hand of the accompaniment:
[[File:SchubertOp4no3.png|thumb|center|upright=3|[[File:SchubertOp4no3.mid|thumb|left|Reduction]][[File:SchubertOp4no3 score.mid|thumb|Original]]]]

In his later writings (from 1930 onwards), Schenker sometimes used a special sign to denote the unfolding, an oblique beam connecting notes of the different voices that are conceptually simultaneous, even if they are presented in succession in the single line performing the unfolding.<ref>For a detailed study of "unfolding", see Rodney Garrison, ''Schenker's ''Ausfaltung'' Unfolded: Notation, Terminology, and Practice'', PhD Thesis, State University of New York at Buffalo, 2012.</ref>

===Register transfer, coupling<!--[[Register transfer]], [[Obligatory register]], [[Octave transfer]], and [[Coupling (Schenker)]] redirect directly here.-->===
{{anchor|Transfer}}<!-- This section is linked from [[Schenkerian analysis]] -->"Register transfer" is the motion of one or several voices into a different octave (i.e. into a different register). Schenker considers that music normally unfolds in one register, the "obligatory register" (Ger. ''Obligate Lage''), but at times is displaced to higher or lower registers. These are called, respectively, "ascending register transfer" (Ger. ''Höherlegung'') and "descending register transfer" (Ger. ''Tieferlegung'').<ref>{{Cite Grove |last=Drabkin |first=William |title=Register transfer}}</ref> Register transfers are particularly striking in piano music (and that for other keyboard instruments), where contrasts of register (and the distance between the two hands) may have a striking, quasi orchestral effect.<ref>See David Gagné, "The Compositional Use of Register in Three Piano Sonatas by Mozart", ''Trends in Schenkerian Research,'' A. Cadwallader ed., New York, Schirmer, 1990, pp. 23–39.</ref>
"Coupling" is when the transferred parts retain a link with their original register. The work, in this case, appears to unfold in two registers in parallel.

===Voice exchange===
{{main|Voice exchange}}
Voice exchange is a common device in counterpoint theory. Schenkerians view it as a means of elaborating a chord by modifying its position. Two voices exchange their notes, often with passing notes in between. At the end of the example of [[#BeethovenOp109|Beethoven's Op. 109]] above, the bass and soprano exchange their notes: G{{music|#}} is transferred from bass to soprano, while E is transferred from soprano to bass. The exchange is marked by crossed lines between these notes.<ref>''Free Composition'', §§ 236–237.</ref>