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The technique, part 3 (retrograde inversion)

A full description of the composition technique, with examples.
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Chris Gibbs
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The technique, part 3 (retrograde inversion)

Postby Chris Gibbs » Tue Dec 14, 2010 1:24 pm

What does retrograde mean?
Cambric Clouds - Example (retrograde inversion)
Reflection #1 - Example (variations using retrograde inversion)
Reflection #4 - Example (retrograde rhythm as well as inverted melody)

In this part I'll describe the four versions of any melody - normal, inverted, retrograde and retrograde inverted - and provide some examples to demonstrate the potential source of inspiration of retrograde melodies.

What does retrograde mean?

Retrograde in the musical sense means playing the notes (or chords, rhythms for that matter) in reverse order. Like inversion, this can produce some interesting results, but since a purely retrograde melody still has all the same notes from the same musical scale(s), it will sound more familiar than the purely inverted melody, so it often has to be combined with inversion to produce the best effect.

So, this means that there are four forms of a melody:

1) Normal - the regular melody.
2) Inversion - the notes played in the same order, with the interval between each successive note applied in the opposite direction.
3) Retrograde - the regular melody, but with the notes played in reverse order from last to first.
4) Retrograde Inversion - the notes inverted and played in reverse order (it's easier to think about this as two distinct steps).

For my Inner Version project, so far I've only used inverted and retrograde inverted forms of melodies (2 and 4 above), but I recommend trying out all three of the alternatve versions of any melody, as I expect purely retrograde versions of melodies will generate some interesting results.

What may turn out to be effective is a particular form of a melody (e.g. inverted) played over a different form of the underlying chord sequence (e.g. retrograde). I haven't experimented with this yet, but this is certainly an extension to the technique that could work well. In fact I've only recently started experimenting with retrograde inversion to a significant extent (with my Reflections pieces from Reflection #4 onwards), but the results so far have been excellent and I'll definitely be using it more often in future.

Another potential idea which could work well is to splice up a melody into groups of a certain size (say one or bars in length), and then apply the retrograde or retrograde inversion process on each of those groups, but maintain the same order of the groups. Feel free to post your own suggestions for new ways of applying this particular method, as I expect there is a lot more to be discovered in this area (I'll update this forum post over time with any new ones I discover).

Let's take some examples of retrograde inversion from my Inner Version pieces to show how effective the retrograde transformation of a melody can be.

Cambric Clouds - Example (retrograde inversion)

During the development of my piece Cambric Clouds, I was wondering if a retrograde inversion of an introduction could provide a suitable ending to a piece. Let's take a look at part of the introduction again here, bars 3-4:


Using these two bars, I created an almost exact retrograde inversion, transposed a perfect fifth down to the key of G major:


The upper melody in bars 151 and 152 is an exact retrograde form of the upper melody in bars 3 and 4, i.e. it's a retrograde inversion of the two source melodies from "Radiohead - No Surprises" and "David Bowie - Come and Buy My Toys" respectively (described in part 2 of this technique).

Notice that the lower melody in the retrograde version has been shifted by one semiquaver to the right. An exact retrograde inversion, transposed down to G major again, would be as follows:


However, this results in too much emphasis on the note D, as it occurs as the first note of each group of 4 semiquavers and thus the same note is played on every beat of the bar (and also every half-beat for that matter). This is less musically interesting than the same melody rotated by one semiquaver to the right, which results in G, C, B, A starting each 4 semiquaver group and the D note occurring only on off-beats. As with modifying inversions by adding or omitting notes, cycling the order of notes of melodies can be a useful technique to create a more interesting result.

You can now listen to how this theme has been expanded into a full ending for Cambric Clouds here: (from 6:23 onwards)

This corresponds to bar 146 onwards of the full sheet music: ... Clouds.pdf

Reflection #1 - Example (variations using retrograde inversion)

Now let's look at a short extract from my piece "Reflection #1 (Tomorrow)", bar 176:


In this example, the melody in the bass clef is divided into two sections of six quavers. The first section is an inversion of a melody that appears at the very start of "Birthday" by The Beatles, the first few notes here:

The second section is a retrograde form of the first section, i.e. it's a retrograde inversion of the Beatles melody. Like with the Cambric Clouds example above, this has been rotated by one note to the right, to provide a more fluid link with the first section.

If you take a look at the full sheet music to this piece (it comes included with an album download at, you may be able to spot that the upper melody for bars 176-182 is an inversion of the tune to the famous Beatles song "Yesterday", although the rhythm has been altered by a reasonable amount. This is a reprise of the same inverted theme which appears earlier in the piece, from bars 11 to 23, but with another different rhythm. Also note that the inverted theme at bar 11 covers a slightly longer section of the tune, up to and including "I believe in yesterday" from the first verse.

It's also one of the main reasons why the piece has the subtitle "Tomorrow" - for those interested in my naming scheme - and the full details of the source songs used (which all happen to be by The Beatles in this case) are described in the Inner Version section of this forum.

Reflection #4 - Example (retrograde rhythm as well as inverted melody)

Here are first two bars of my piece Reflection #3 (the full sheet music is available exclusively with the Reflections album download at


Compare this with penultimate bar of the next piece, Reflection #4 (the key signature is B major, likewise with the other reflections, help to support this forum and download the full Reflections album to get the full sheet music):


The upper melody here is based on a retrograde inversion of the respective melody in the two bars of Reflection #3 above. If you take the second crotchet in bar 2 of Reflection #3 and work backwards, then we have crotchet-crotchet-crotchet-dotted crotchet-dotted crochet, i.e. the same rhythm used in Reflection #4 extract. So, the retrograde transformation here has also been applied to the rhythm as well as the inverted notes.

Also note that the bass-clef melody is an exact inversion (but not retrograde) of the corresponding melody in Reflection #3 from the start up to half way through the second bar. And if you take a look at the full sheet music for both these pieces, you may be able to spot that the first bar of Reflection #4 is very close to an exact retrograde inversion of the final arpeggiated chord in Reflection #3, i.e. the start of Reflection #4 is based on retrograde inverted ending to Reflection #3, and vice versa as shown in the examples above.

In the next part, I describe some advanced topics, including ideas for how use the technique for complete pieces, using my composition process as an example.

Continue to The technique, part 4
Chris Gibbs (Inner Version)
Musician/Programmer at Inner Version Ltd

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