Sometimes when attempting to explain a musical idea or compositional device the most obvious and potentially boring example is actually the best example. Augmentation is the idea of taking a melodic gesture and multiplying the durations of the notes. As simple demonstrations of melodic augmentation goes it would be impossible to find a simpler or more effective example than "Dear Prudence" off the White Album. Yes, dear readers, we're going to be that obvious.
The sun is up
the sky is blue
and so are you
You all know the words, and you all know that the vocal line draws out all these notes at double their previous duration at the end of the song. Interspersed with this drawn-out form of the chorus are rising guitar riffs that form a response to the vocal call. As pop songs go it's genius, a combination of augmentation of a simple gesture with an antiphonal instrumental response decorating, expanding on, and sequentially developing a mirror-phrase to the augmented melody.
But there's something about augmentation of a melodic line that can be easy to overlook that makes or breaks whether or not the device is possible or effective. That "something" is that the melodic idea you expand rhythmically has to have a harmonic rhythm that you can play with. You have to be able to draw it out linearly in space and time, and when you do that there has to be more room to play with. To put it in reverse, the musical idea that sounds good all long and drawn out also has to make sense musically in a much tighter, more compressed harmonic rhythm. In other words you need a rocking chord change implicit or explicit in whatever you're subjecting to augmentation or diminution of harmonic and melodic durations. Surely after about half a century we know that "Dear Prudence" delivers this by the truckload.
If you don't know the song "Dear Prudence" and haven't heard it, well, even this not-necessarily-a-Beatles-fan might have to wonder what you've done with your life! Listen to the song (again) and I think you'll find that the experience of hearing with your own ears can better illustrate the concept of augmentation than mere words on a blog could provide (especially since the song is under copyright and all that). I might digress into the subject of the descending bass line as foundation to a passacaglia or how descending linear progressions show up in other Beatles songs ... but this blog entry is going to just stick to "Dear Prudence" here in the Emerald City where the sun is most definitely not up, the sky is definitely not blue, but it gets to beautiful and you do, too. ;-)
Don't come out to play, though. Seattle drivers are lame in the rain.