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In all seriousness, that clown can teach us something about musical structure. He's an inventive fellow who appears to have figured out every possible way to relate to that barrel. During the show he employs each of them:
- He begins by standing in the barrel--he and the barrel are right-side up.
- Then he stands on his head in the barrel--he's inverted but the barrel is not.
- Next he turns the barrel over and stands on top of it--he is right-side up, but the barrel is inverted.
- Then he stands on his hands on top of the upside-down barrel--he and the barrel are inverted
Whew! If you're getting confused, just remember that, so far, the barrel has always been underneath the little guy...but that's about to change.
Did you catch all that? What a clown! Of the eight ways to juggle the barrel, in the first four, the barrel was beneath the clown, while in the second four he was beneath it. Notice that TWO objects (clown & barrel) were required to do this. Two or more objects exchanging places might be called "multiple-object inversion." By contrast, "Single-object inversion" happens when one or both objects flip without exchanging places. In "single-object inversion" the object inverts in relation to itself, but maintains its position in relation to objects around it. The clown's act shows that two objects may exchange places (multiple-object inversion) with or without inverting themselves (single-object inversion).
- Next he jumps to the floor and lifts the barrel over his head--he and the barrel are right-side up.
- Then he flips the barrel over and lowers it so all you can see are his floppy feet--the barrel is inverted but he is not.
- Then he stands on his hands with the barrel draped over his feet--both he and the barrel are inverted.
- Then, with a kick, the little guy flips the barrel one more time--he is inverted but the barrel is not!
One focal point of Monet's "Poplars in Summer" is the splash of color where yellow rushes along the shore are reflected in the lake. How many objects does this detail represent? Does the detail exemplify single- or multiple-object inversion? (Click the detail to see the larger picture.)
But you're probably wondering what this has to do with musical invention. Believe it or not, single- and multiple-object inversions are two of the most important techniques for inventing new motives and varying old textures and motives. For example, a single musical object (a melody) can be inverted by turning its intervals in the opposite direction. This is known as Melodic Inversion. Or, two musical objects (two melodies) can be inverted by exchanging registers. This is known as Contrapuntal Inversion. Sometimes both things happen--two melodies invert registers AND interval directions simultaneously. Bach called this the Evolutio.