Non-retrogradable rhythms

These are palindromic rhythms. For example:

Messiaen gives two definitions of non-retrogradable rhythms:

1. 'Whether one reads them from right to left or from left to right, the order of their values remains the same'.
2. 'All rhythms divisible into two groups, one of which is the retrograde of the other, with a central common value, are non-retrogradable' (1944, 20).

Non-retrogradable rhythms also appear in a more complicated compound form, where individual values within the rhythm can be combinations of two or more notes or chords tied together. There are examples in Messiaen's music of rhythms that may not appear at first to be non-retrogradable, but in fact are. These compound rhythms produce a more subtle effect than in the above example and, as is the case with many of Messiaen's techniques, become less noticeable when incorporated into larger musical structures. The following example is taken from Regard de I'Esprit de joie, (bar 33):

To hear this example, click here.

Added values

An added value is where an addition to a rhythm makes its value irregular. Much favoured by Messiaen, this technique allows him to build prime-numbered groupings from an even-numbered rhythmic cell, making Messiaen's rhythms both flexible and unpredictable. A very common occurrence of added value is shown below.

Rhythmic canons

These are similar to normal canons, but the element of pitch is not involved. There can be two or more entries, with each a prescribed distance apart. To qualify as a rhythmic canon, each entry must have the same rhythm, but not the same pitch. Entries in the following example are at the distance of a crotchet.

Rhythmic pedals

These ostinato figures repeat a set rhythm as many times as is required; the rhythm of the pedal can be, and often is, entirely independent from any of the other rhythms involved. The following example has four pedals, marked A, B, C and D.

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Added notes

This technique derives from Debussy. Messiaen mentions finding in Debussy 'appoggiaturas without resolution, of passing notes with no issue .... foreign notes, with neither preparation nor resolution, without particular expressive accent, which tranquilly make part of the chord, changing its colour, giving it a spice, a new perfume .... they are added notes' (1944: 47). The added sixth and augmented fourth are important parts of Messiaen's language (the chord of F-sharp major with an added sixth forms the harmonic basis of the Vingt regards), so his explanation is worth quoting in detail. The first stage is to add a sixth to a chord:

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A seventh and then a ninth can be added:

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Messiaen then argues that the next note in this harmonic sequence should be an F sharp:

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The final result is a chord containing a sixth and an augmented fourth that resolves to a chord with an added 6th:

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Agrandissement asymétrique

Messiaen uses this technique to develop a small cell through the alteration of pitches by various means. Some pitches rise, some fall, and some remain the same, a technique that can be found in the fugal subject of the sixth Regard, 'Par Lui tout a été fait', but its most extended use occurs in the third Regard: 'L'échange', which is almost entirely based on this technique. The octaves in groups of three on the lowest stave progress using agrandissement asymétrique. The following shows the start of the procedure:

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