Schenker's Theory of Counterpoint (cont.)
Consonance and Dissonance
The idea of consonance and dissonance in western music goes back to at least the 5th century BCE and is now commonly understood to stem from a combination of factors both acoustic and cultural. Consonant intervals have simpler ratios (the octave has the simplest of all - 2:1) and the more complex the ratio the more it is heard as a dissonance (the minor second has a ratio of 16:15).
It is probable that our perception of dissonance is to a large extent conditioned by the music with which we are brought up, but there are several acoustic phenomena that can help explain this cultural one.
Whatever the basis for the concept of consonant and dissonant intervals, a gradually changing consensus developed over the centuries that while some successions of intervals were pleasing to the ear, some were not.
Species counterpoint is a codification of this consensus, prescribing what intervals are allowed both within (from one note to the next) and between parts. Augmented fourths, for example, are neither allowed in the horizontal direction (within a part), nor in the vertical (between one part and another).
In the music of Palestrina, whose style species counterpoint attempts to reproduce, you will find that these rules are frequently broken. This is because species counterpoint is a teaching method not a theory - it was Schenker who took some of its principles and, in combination with other elements, constructed a theory.
Species counterpoint, as explained by Schenker, presumes the classification of intervals into three groups:
fourths (inversion of fifth)
third (inversion of sixth)
seventh (inversion of second)
Some of the rules governing various types of motion imply, at least to Schenker, important relationships between these different groups of intervals (see the full explanation of species counterpoint for more on these rules):
You may not have much patience with this sort of theorising (Schenker sometimes seems to have limitless patience for it!), but you should bear in mind that Schenker's theory does seem to explain how tonal music works. His insistence that tonal music is natural and therefore the only acceptable kind seems merely eccentric now, but that does not necessarily invalidate his understanding of tonality.
- The rules governing dissonance - Dissonant intervals are only allowed on weak beats in between consonant intervals (although fourth species introduces an exception). Intervals of seconds, sevenths and fourths are therefore in a sense dependent upon consonances - they require a consonant point of departure and resolution. This idea that dissonances are subordinate - attached to structurally more important consonances is absolutely central to Schenker's theory of music. One reason this is so important is because it means that a dissonant note cannot be decorated. The significance of this will soon become clear.
- The rule probiting parallel fifths - Schenker gives a number of reasons why parallel fifths are not allowed. The most important is that counterpoint requires two independent voices and, because the fifth and octave are the first and second overtones of the harmonic series, parallel motion involving these intervals sounds like a shadowing of the lower voice. The same point could conceivably be made about thirds, but Schenker considers the perfect fifth a special case. He calls it a 'boundary interval' because it, 'demarcates the harmonic content of the bass note' (Schenker, Counterpoint, p. 125) - in other words because it spans the interval between the top and bottom notes of a root position triad, it implies that triad in a way that other intervals (such as a third) do not (more explanation
). What, you may ask, is wrong with that? Schenkerian theory explains tonal music as harmonic units (i.e. triads) decorated and extended through time according to the principles of counterpoint (see The Combination of Harmony and Counterpoint); parallel fifths imply a succession of undecorated triads which perhaps upsets this model.