The Combination of Harmony and Counterpoint
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Schenker's theory of harmony explains the tonal system as a collection of major triads derived from the harmonic series - these harmonic units represent the vertical aspect of music. His theory of counterpoint, on the other hand, sets out how simple two-voice progressions can be elegantly embellished by adhering to a series of rules on the succession of consonant and dissonant intervals - the horizontal or linear aspect of music.
The next and crucial stage of his theory explains how these two elements are brought together in tonal compositions. These ideas were developed over a series of yearbook articles and monographs, but the theory is formally set out in Free Composition, published in 1935.
Using the basic principles of consonance and dissonance from species counterpoint, Schenker identifies a number of common linear units that he calls diminutions. His analyses, at their most simple level, show how these linear units prolong harmonic units. Prolongation, in other words, is when a harmonic unit (such as the tonic or dominant) or a note from that harmonic unit (for example, the third of a tonic triad) is extended in time (by an arpeggio, for example).
The concept of prolongation is at the core of Schenkers' theory and the element of it that has been the most influential. Because diminutions must prolong a harmonic unit in Schenker's theory, only a note consonant with the prevailing harmony can give rise to a diminution.
Below are the four basic linear units that are found in tonal music, collectively they are called diminutions. The central link leads to a familiar example of these diminutions and an explanation of why they are important. Although most of the examples here show the diminution in the upper of the two voices, they are equally an important part of the bass line:
For more about putting this into practice, see stage two of How to do a Schenkerian Analysis.