Editing Schenkerian analysis (section)

===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>