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You probably know what counterpoint is - a compositional technique in which multiple independent and equally important melodies are sounding at the same time. This is in contrast to homophonic music, where there is a single prominent melody with other (most often lower) voices as a subservient accompaniment.
Invertible counterpoint is counterpoint in which two or more melodies can swap their registers (one is initially higher than the other, then they swap) but it all still works out harmonically. Just one example today...
Beethoven Symphony #6, 5th movement
This is a glorious passage in the middle of the last moment of Beethoven's wonderful Symphony #6, "The Pastoral".
There are 3 phrases here, building in intensity. It's made up of 3 melodies or motifs which I have color-coded in the scores below. At least two of the three motifs swap positions (and instruments) across the 3 phrases.
Phrase 1
The yellow motif with meandering 16th notes is the highest, in the first violins.
The lilting blue motif comes in groups of 4 eighth notes, played in pizzicato by the second violins, and
The steady red 2-notes eighth-quarter in the cellos (and double bass), also pizzicato.
Try to hear them all at the same time!
beeth 6_5 phrase1.mp3
Phrase 2
Now the yellow and blue have swapped positions.
Red still anchoring in the bass.
First violins now playing arco. And wow - I don't think I ever noticed before that the violas have the blue motif offset by 2 beats, still pizzicato. You can listen to music like this all your life and always hear something new in it.
Beeth 6_5 phrase2.mp3
Phrase 3
Big crescendo in the pickup to phrase 3! Yellow meandering motif goes to the cellos!
Winds and 2nd horns get the red 2-note theme.
Blue theme in the 1st horns. A slight modification, here the notes are sustained, but it's still a derivative of the 2-note motif.
Beeth 6_5 phrase3.mp3
All together now!
Challenge yourself to hear all parts.
Beeth 6_5.mp3
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