My post “A search for interesting canons part 2” (part 1) is getting longer and longer so I decided to spin off a couple of minor parts into separate posts to keep everything manageable. This post is probably not interesting to you if you’re not into musical theory.
Retrograde refers to playing music backwards. For at least 500 years (without exception as far as I know except the literal signal reversal that exists in electronic music), this is done as such:
These 3 examples show some of the most basic movements, a rising figure, a back and forth figure and a cross figure. You can see how the rising figure in ex.1 become a back and forth figure. And the back and forth figure becomes a falling figure in ex.2. And how the cross figure in ex.3 is broken in two separate pieces.
These motive-breaking transformations are considered a fact of life when playing something in retrograde and they are generally the basis of much critism against retrograde (it being just a intellectual visual trick) It is probably also an important contributor to the rarity of retrograde as a contrapuntal device (compared to inversion or augmention) as it is hard to write melodies that sound good in retrograde, especially in counterpoint.
So I want to propose a more audible retrograde, the main problem with the visual retrograde is that the note durations are wrong, when looking at a theme played backwards and looking at the space between adjacent notes it becomes intuitively obvious that you should use the time value of the next note as duration for the current:
This creates a retrograde much closer to an actual sound-retrograde. The duration of the first note can be anything when it’s the actual last note to be played. When the reversed music is repeated you simply use the time value of the first(retrograde first) duration.
The audible retrograde of the example motives is written as such:
While it does not look as striking it does retain all the basic motives. Making it easier on the ear, easier to hear as a transformation and easier to write for. And so it’s the retrograde that I will focus on in my future posts.