What are the principles for improvising over an ostinato?
An ostinato or repeating riff is a basis of improvisation for everything from Elizatbethan music (Grounde) to classical music (basso ostinato) to jazz and rock. It's quite different from improvising over chord changes.
Aside from the differences in the different musical forms, how do you improvise pleasing lines over an ostinato? Is it just analyzing the ostinato for chord tones and key centers or is it something more? Are there a set of classical music rules for improvising over a basso ostinado?
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For jazz and rock, the principles appear to be phrasing and space, and to some degree, implied harmonic movement.
Since the underlying riff is not shifting around the harmony very much (it would produce an unpleasant vertigo effect), the melody can enter and exit when it chooses. But these choices define a larger rhythmic structure. Frenquently, the melody will take a short rest periodically to wait for the beat to turn around. The relative lengths of these rests with their associated melodic fragments evoke some degree of space.
Having no rests at all, especially when syncopated, so that the coda butts up flush to the next anacrusis, like a melodic ouroborous, produces a very closed space. If the melody is being sung, there is literally very little room to breathe. Conversely, long-rest lyrical codas, give a more open space, where the rhythm can be enjoyed more as a separate part (== rhythm must be interesting enough to stand on its own).
If the repeated riff has a sparse harmonic content, dyads or single-notes, then the melody can also make use of implied harmonic movement. For a bluesy minor pentatonic bassline, the melody can play as if a 12-bar blues or other form were being played, because the bassline is simple enough that it can be reinterpreted in the context of the implied chord/key.
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