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The technique, part 2 (synthesis)

A full description of the composition technique, with examples.
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Chris Gibbs
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The technique, part 2 (synthesis)

Postby Chris Gibbs » Tue Dec 14, 2010 2:36 pm

Cambric Clouds - Example 1 (layered inversions)
Cambric Clouds - a piece comprised of many different inversions
Cambric Clouds - Example 2 (inverting both melody and chord sequence)
Midnight Rain - Example (synthesis within the same melody)
Us Prisoners - Example (layered inversions & inverting both melody and chord sequence)

I'll now describe the other core part of the inversion synthesis technique, the "synthesis" portion of the name.

Around the same time that I discovered the inversion technique, I was also listening to Bach's Goldberg Variations, and wondered what a "Quodlibet" was, which forms the 30th variation. It turns out a Quodlibet is a piece composed of several different melodies of well-known tunes. I then realised that it should be possible to build pieces by combining inversions of several melodies, which was proved correct with the first few Inner Version pieces I wrote.

So, inversion synthesis is a little like a quodlibet of inverted melodies, where the source melodies are often well-known songs (but this isn't a requirement, as any melody can be valid as source material). As far as I know, inversion synthesis has never been used before 2009. Even just the inversion part of the technique I described in part 1 only has the Rachmaninoff vs Paganini as the one well known example, which I still find stunning that inversion alone hasn't been done on a large scale before.

Anyway, the synthesis part of the technique is an area where there is a lot of freedom to be creative, and I'll go through some of the ways I've combined inversions in my existing pieces as examples. If you come across any more interesting combination methods then you are welcome to share those on this forum thread.

In most of my pieces, I link together inverted melodies from several parts of the same song for at least one of the source tunes. On quite a few occasions I even layer inversions on top of each other and my piece "Cambric Clouds" is a good example of this.

Cambric Clouds - Example 1 (layered inversions)

Here it might be handy to listen to the complete piece - Inner Version - Cambric Clouds (Piano Sketch) - and also take a look at the full sheet music for the piece here: ... Clouds.pdf

Let's take a few different sections of the piece as an example. Firstly, bars 3 and 4:


Here, we have the right hand playing the lower melody, which is an inversion to the opening guitar line of Radiohead - Street Spirit as described in part 1 of this technique.

The higher melody played with the left hand (i.e. by swapping hands) in bar 3 is an inversion of another melody that appears elsewhere in the same song Street Spirit. See if you can spot it in the Radiohead song here, it has exactly the same rhythm as the inverted form I used: (appears as an inside guitar melody at 3:19 in that video and again at 3:47)

For the next left hand melody that appears in bar 4, this is based on a single melody that appears in an early David Bowie song called "Come and Buy My Toys", which contains the lyric "You shall own a cambric shirt" (I had never heard the song before, and stumbled on it whilst searching the web for anything related to "cambric")

The melody appears at 1:14 in the following video:

I inverted just the melody that accompanies the lyric "You shall own a cambric shirt", and an exact inversion (with no rhythm changes) would result in this instead for Cambric Clouds bar 4:


This didn't seem to fit with the bar before so, so by removing the second quaver of the bar (B), and the initial C quaver shifted by one quaver to the right results in the actual bar 4 used in the piece (excerpt repeated from above for convenience):


I recommend manually doing the inversion of the Bowie melody here and playing both the inversion with one note omitted in Cambric Clouds and also the alternate exact inversion (playing just the melody on its own is fine, as the cross-hands intro to Cambric Clouds is technically difficult to play).

So from this I realised a key part of the technique is learning when to add or omit notes in order to create a more fluid piece and/or a more interesting overall melody. As with the core inversion part of technique, this should get easier with practice.

Cambric Clouds - a piece comprised of many different inversions

Cambric Clouds in particular was an ambitious piece in that I set myself the challenge of trying to fit as many inversions as possible into whilst still being a coherent piece of music. In the end it featured inversions of around 20 different pieces of music, several of which have multiple melodies that made their way into the final piece in their inverted form. (The full details are available in the Inner Version section of this forum)

Some of the source tunes include the traditional English song "Scarborough Fair" (which contains the lyric "cambric shirt"), "Claire de Lune" by Claude Debussy, "The Lark Ascending" by Ralph Vaughan Williams, "Gymnopédie #1" by Erik Satie, even the piece "Song of Storms" by Koji Kondo, from the Nintendo 64 video game "The Legend of Zelda: Ocarina of Time".

You may notice that most of the source pieces have titles that link to the concept of clouds, skies, weather in some form, or have links to the word "cambric", which means "cotton" or "made of cotton". Pretty much all of the titles of my works feature a multiple play on words, again which I go into greater detail in the Inner Version forum section.

Also note that all of my pieces I've written so far still contain linking sections which aren't based on inversions, although it should be possible in theory to build a piece from inversions and nothing else (there's a challenge for the members of this forum!)

Cambric Clouds - Example 2 (inverting both melody and chord sequence)

The next inversion that appears in Cambric Clouds begins at bar 15:


Here, the upper melody is based on an inversion of the tune to the traditional English song "Scarborough Fair". Have a listen to the main theme which appears around 13 seconds from the start of the Simon & Garfunkel version here:

The first half of bar 15 is an inversion of the following section of the Scarborough Fair tune:


Notice how the chord sequence in this case is also inverted. The Scarborough Fair tune goes from D minor to C major then back to D minor. Compare this with Cambric Clouds, where in the bass clef the left hand plays a D major chord, followed by a E minor then back to D major again half way through the bar.

For the rest of the 15th bar of Cambric Clouds, I added an arpeggiated D major chord to link to the next bar, which is a common theme that appears throughout the piece.

Continuing with this example, let's now take a look at the next bar of the piece, bar 16:


And the corresponding next section of the Scarborough Fair tune:


This is a much more exact inversion than the 15th bar, in both the rhythm (although the note durations are all halved) and the actual notes, plus there is one extra note added for the Cambric Clouds inversion (the initial A note for the upper melody). However, the inverted melody of just this section has been transposed up one octave from the exact inversion of the complete Scarborough Fair tune. This is a common part of composing using inversion and quite often you will need to try different sections of the melody moved up and down an octave until it fits the piece.

Again notice how the chord sequence has been inverted, the F major -> D minor -> G major -> D minor of Scarborough Fair becomes B minor -> (D major omitted here) -> A minor -> D major. As with omitting or adding notes from the melody, I omitted the second D major chord as it felt like too much harmonic movement, especially as my piece is intended to be played at a faster tempo than Scarborough Fair.

Midnight Rain - Example (synthesis within the same melody)

My piece "Midnight Rain" was the very first complete piece I composed using this technique, and has a simple but effective melody that first appears at bars 23-37 in the piece: ... t_Rain.pdf

This melody is based on the inversions of two different tunes. Firstly, the section from bars 24-26:


This is an inversion of a section of "You Are My Sunshine", at 38 seconds in to this video: (the melody that goes with "you make me happy when skies are grey").

Here it might be a useful exercise for you to invert the uppermost right-hand melody for the section of Midnight Rain, leaving the rhythm unchanged, and see how closely it matches the corresponding section of You Are My Sunshine.

This 4-bar melody then repeats once, but after that repeats again with a different melody during the 3rd and 4th bar (bars 33 and 34 of the piece, note the key signature is still 5 sharps in the following extract):


This is an exact inversion (with an identical rhythm) of the tune that goes with the second occurence of the lyric "saints go marching in", from the popular American song "When the Saints Go Marching In": (from 1:19 to 1:22 in the video)

This is a relatively short extract of five notes, so might be good practice to try doing this one in your head if possible. Don't worry if you aren't at that stage yet, but a helpful tip would be to notice that the notes are around a major chord (starting on the 5th) and ending on the 2nd note of the scale, so from this you can work out that the inversion will be around a minor chord (starting on the 1st) and ending on the 4th note of the scale (if inverting around the 3rd).

Us Prisoners - Example (layered inversions & inverting both melody and chord sequence)

Expanding on the introduction to my piece Us Prisoners as described in part 1 of this technique, let's now look at a larger section of the sheet music: ... soners.pdf

Take a listen to the full Radiohead song "No Surprises" here:

The section from bars 5-10 of Us Prisoners is close to an exact inversion of the section of the Radiohead song from 1:19 to 1:37 (i.e. up to and including the first occurence of "No alarms and no surprises"). Similarly, the section from bars 15-20 of my piece is very similar to an exact inversion of the part of No Surprises from 0:28 to 0:48 in the YouTube video. So, the order of the two sections of the Radiohead song is switched around in Us Prisoners, reinforcing the inversion idea further :)

Again, it would be a useful exercise to invert the upper melody of Us Prisoners bars 5-10 and bars 15-20 and see how close they sound to the original main melodies used in the Radiohead song. These two sections of Us Prisoners are sort of "verses", and they are linked by two repeats of the inverted introduction to No Surprises, whereas in the actual Radiohead track, the sung verses are linked by just one repeat of the guitar theme.

Also note that an almost exact inversion of the underlying chord sequence has been employed in my piece. For the Radiohead song, the verses have the chord sequence of F major -> D minor -> Bb major -> C major, whereas for Us Prisoners the chord sequence is F minor -> Ab major -> C minor -> Bb minor
(albeit with a few extra notes in places to imply slightly altered versions of the chords).

This example illustrates that it's sometimes possible to form a complete section of a piece from a melody and its underlying riff and/or chord sequence with relatively few changes to the both the rhythm and the inverted notes. And it reveals one of the most fascinating aspects of the technique: even when little is changed from an exact inversion, the inverted piece sounds completely different from the original.

In the next part, I go into more advanced ways of rearranging melodies, such as retrograde inversion.

Continue to The technique, part 3
Chris Gibbs (Inner Version)
Musician/Programmer at Inner Version Ltd

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