What is inversion?
My next inversion
The composition technique is called inversion synthesis, so firstly let's have a look at the "inversion" part of the name.
What is inversion?
Inversion in the musical sense is basically playing melodies upside-down. This means to create an inverted version of a melody, for every movement that the original melody makes (such as a semitone or a major 3rd), the inverted melody also makes exactly the same degree of movement, but in the opposite direction.
So, if a melody goes from C to D to E, then an inverted version of this melody starting on C would be C to Bb to Ab, i.e. two whole tone movements for each melody but in the opposite direction. Likewise, a melody that goes from C up to F then G, when inverted would go C down to G below then F, i.e. movements of a perfect fourth and then a whole tone in each case.
The key result of this type of inversion is that when the inverted melody goes in the opposite direction exactly the same number of semitones as the original melody, then the result is a tune that sounds nothing like the original, even when the rhythm is left unchanged. This inversion method is known as "chromatic inversion", as it involves dealing with the full chromatic scale (i.e. all semitones are allowed).
The most famous example of chromatic inversion is the 18th variation from Rhapsody on a Theme of Paganini by Sergei Rachmaninoff, which is based on an inversion of the melody of Caprice No. 24 by Niccolò Paganini. This was also the primary inspiration for the development of the composition technique, which started in early 2009 when I became curious about inversion and how exactly these two pieces were related.
Take a moment to listen to the main melody of each piece here:
Paganini's 24th caprice: http://www.youtube.com/watch?v=vPcnGrie__M
Rachmaninoff's 18th variation: http://www.youtube.com/watch?v=h_BArG3ollw
Both pieces are very famous and widely performed pieces in their own right, but before 2009 I had no idea they were so closely connected. You may recognise the 18th variation from a number of films (including Groundhog Day and Somewhere in Time).
I suggest at this point actually sitting down at a piano or your instrument of choice, and try playing through the two extracts of the melodies:
Notice that the step between each note is the exact opposite for these two melodies. Also, if you are able to play by ear then when you play the rest of the melodies, then you may notice that it is not an absolutely exact inversion, as the rhythm is different and one or two notes have been added or removed in Rachmaninoff's version. So essentially the 18th variation is based around an inversion of the theme, but is not an exact inversion, which I come onto shortly.
After playing the above two pieces, I then wondered how successful this technique would be when applied to any other melody. The very first piece I attempted to invert was the song "No Surprises" by Radiohead, as the intro has a simple rhythm.
Take a listen to the introduction to this song here, the first 30 seconds or so: http://www.youtube.com/watch?v=u5CVsCnxyXg
The top guitar line is in the key of F major, starting on the note A:
I then sat down at a piano and worked out note-by-note the exact chromatic inversion of this melody, starting on the note Ab two octaves below:
This forms the introduction to one of the early pieces composed using the technique, take a listen to the first 30 seconds or so here: Inner Version - Us Prisoners (Piano Sketch).
Notice that the underlying chord sequence has also been inverted: the F major / Bb minor chords (No Surprises) turn into F minor / C major chords (Us Prisoners). If applying the inversion strictly to both the melody and the underlying chord sequence, then in general any major chord becomes a minor chord, and vice versa. Note that while I could have used any initial note (and corresponding minor key) as the starting point for my version, I found that in this case the Ab note (and F minor) seemed to be around the right pitch to create a suitable mood for the piece.
You also may notice how the uplifting guitar melody of the Radiohead song becomes a beautiful melancholic melody in the inverted form. This inversion of the mood of the piece becomes a regular pattern as more inverted melodies are discovered within existing tunes.
My next inversion
Next, I tried to invert a more gloomy piece also by Radiohead, the song "Street Spirit (Fade Out)". Again, I just took the guitar line of the introduction, take a listen to the first 20 seconds: http://www.youtube.com/watch?v=LCJblaUkkfc
In this case, the acoustic guitar melody is in the key of A minor, and like the first song No Surprises, also has a simple rhythm and is repeated a few times during the introduction:
And sure enough, the inversion results in this uplifting melody, here in the key of D major:
To me this melody seems to sound like it is floating on clouds, and forms the introduction to another one of the early Inner Version pieces, take a listen to the start here: Inner Version - Cambric Clouds (Piano Sketch).
At this point I strongly recommend taking these two examples and making sure you are fully familiar with how the (chromatic) inversion process works, as this is the most important part of the technique. Don't worry if you find it time consuming initially - it should get a lot easier and faster with practice.
In the next part, I go into the "synthesis" part of the technique, along with how to begin forming a complete piece.
Continue to The technique, part 2