In music, a linear progression (Auskomponierungszug or Zug, German: train, abbreviated: Zg.) is a passing note elaboration involving stepwise melodic motion in one direction between two harmonic tones. "The compositional unfolding of a specific interval, one of the intervals of the chord of nature." For example: -- over the tonic. According to Schenker: "The linear progression always presupposes a passing tone; there is no linear progression without a passing tone and no passing tone without a linear progression." In German zug may be combined with prefixes to create related words such as untergreifzug (German: under-reaching linear progression), a linear progression rising from a lower voice, or terzzug (German: third linear progression), linear progression through a third. The term "zug" may best be translated as, "a direct, unimpeded motion from one place to another."
Linear progressions prolong harmonies and through elaboration, or filling-in with dissonant notes, of a leap between two consonant notes from different voices in a chord. In English they may be abbreviated "prg." such as 3-prg. for 'third progression' (rather than "zg.").
Note that the Mozart example above that the passing tones are dissonant and unable to be embellished, however, in the Urlinie example to the right the passing tone is supported harmonically, allowing for embellishment. Also note the Schenkerian notation indicating relative hierarchical depth, surface or structural importance, where structural notes are indicated through stems and beams and surface notes are indicated through note heads only which are then slurred to stemmed and beamed notes. Thus in the bottom right example the third progression from D is a decoration of the deeper third progression from E.
See also 
- Pankhurst (2008), p.28-30.
- Pankhurst, Tom (2008). Schenker Guide: A Brief Handbook and Website for Schenkerian Analysis, p.243 and 27. ISBN 0-415-97398-8.
- Jonas, Oswald (1982). Introduction to the Theory of Heinrich Schenker, p.62. (1934: Das Wesen des musikalischen Kunstwerks: Eine Einführung in Die Lehre Heinrich Schenkers). Trans. John Rothgeb. ISBN 0-582-28227-6.
- Schenker, Heinrich (1969). Five Graphic Music Analyses, p.14. ISBN 0-486-22294-2.
- Schenker (1969), p.25.
- Snarrenberg, Robert (1997). Schenker's Interpretive Practice, p.19. ISBN 0-521-49726-4.
- Pankhurst (2008), p.28.