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I am looking for retrograde and inverted remakes of classical pieces. Even better if they are being played simultaneously with the origina, like Pachelbel's Canon, Original Version and Retrograde Inversion Played Simultaneously.

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    Disagree that this was marked as "off-topic". This question is not about a particular song, it is about a class of songs that use a particular, well-defined method of composition.
    – Roland Bouman
    Commented Feb 27, 2014 at 0:12
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    I added this to the meta: meta.music.stackexchange.com/questions/731/…
    – Roland Bouman
    Commented Apr 26, 2014 at 19:53
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    I think it would be helpful if you could go to meta.music.stackexchange.com/questions/731/… and explain how you thought of your question, and what your expectations were w/re to the answers. Would be great if you could give your feedback. Thanks in advance!
    – Roland Bouman
    Commented Apr 27, 2014 at 20:12
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    @Hans: It would help if you provide a bit more background info on why you want this answered. It would help in how to phrase the answers and what kind of examples to provide, and to be more useful to others that might share your interest in this.
    – awe
    Commented Apr 29, 2014 at 10:29

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The earliest version I can think of is Bach's Musikalisches Opfer which is a series of canons Bach composed after given a theme by the King. The music can be played forwards and backwards simultaneously harmoniously in various ways (refer to the video).

I also remember reading a score of Mozart's violin duet piece called "The Mirror". To play this piece two violinists stand across from each other and play the same score from beginning to the end from their own angles.

In simplest words, for this kind of music to work the (roots of the) chords in the piece must be symmetrical, i.e. the first note(s) and last note(s) must be in the same chord, so that when they are played at the same time it will sound natural. Rhythm would be another key factor.

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As @Menglan pointed out, the crab canon from Bach's musical offering is probably the most famous example. I transcribed it and put it on musecore:

http://musescore.com/rpbouman/scores/143009

The art of fuge (Also Bach) has 2 fugues which can be inverted. Look for Contrapunctus XII and XIII (there's a rectus and an inversus version for both of them)

I wrote some mirror canons myself. Of course, I'm nowhere close to the grand wig himself, but I had a lot of fun writing these:

http://musescore.com/rpbouman/sets/mirrorcanon1 http://musescore.com/rpbouman/sets/mirrorcanon2

Both these canons are written so that you can put the page upside down and get the same piece again. And because of this property, you can play each piece in inverse too. So playing the rectus and the inversus right after each other yields a palindrome.

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  • Is there a way of playing the both of each mirror at a time?
    – Hans
    Commented Feb 19, 2014 at 1:32
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    Hi Hans, the mirror canons I posted here are both designed along the same plan: you have the original melody (rectus), then enters the retrograde, then enters the inverse, finally enteres the retrograde inverse. So you're already hearing all classical permutations all at the same time. And precisely because it was designed in this way, you can reverse or inverse the entire piece and get back a "new" one. However, it was not designed so as to sound both these pieces at the same time. You can certainly try but it'll sound horrendous.
    – Roland Bouman
    Commented Feb 19, 2014 at 3:10

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