Take these final three bars of the Gymnopédie No.1, for example:
In the final measure, assuming beat 3 becomes beat 1 and vice versa by going right to left, one could choose to play the chord right away on the new downbeat since the sound continues through beat 3 in the original. OR, one could choose to wait until beat 3 which is the proper "edge" of the measure where the note occurred as a rhythmic event. (Technically, the attack would occur right at the very end of beat 3.) If you have a look at the first bar above, the problem gets more complex. That F-natural is the "melody note" and it sounds through the measure in the original so it could be played along with the final chord at the beginning of the bar in a backwards version - but, in the original, we experience that measure as having three separate rhythmic events, and we don't experience that F-natural simultaneously with the beat 3 chord. If you want three rhythmic events, one would play the chord with G on top first, then the chord with D on top, and finally the F-natural with the D in the bass. This is all kind of mundanely confusing and hard to put into words elegantly, but it's always a bit of a revelation to me to realize what a moving target "backwards" is in musical performance.
Nevertheless, I decided it would be fun to perform this Gymnopédie as backwardly as seemed reasonable, making a variety of interpretive decisions along the way as to where the longer notes should be played. I created my own score (with backwards page numbers) which you can see below and download here. (The original Satie is here.)
The most "controversial" decision I made was to play R.H. melodic dotted half-notes at the beginnings of bars while placing the L.H. dotted-half bass notes on beat 3. I'm not sure I have a great argument for this decision other than I liked the way it came out. I suppose my argument would be that those melodic notes need to sound for three beats to "feel' right in relation to the quarter-note pitches, whereas the bass notes are always dotted-halves - it seemed right to feature them as rhythmic events on the "other" side of the measure from the original. Whoa, this is getting confusing again. Just listen:
I think it's really quite lovely and "works" pretty much from beginning to end - or, rather, from end to beginning. I can't really say this is a composition of mine or even an arrangement - more like a discovery of potential energy in an existing work. If nothing else, Eitas Kire is a cool name.
* There's also this.
UPDATE: This performance is now conveniently embedded on a page where you can view either Satie's score backwards or my score forwards.