Non-tonal Centricity

September 16 & 17, 1997

Messiaen and his Technique. Messiaen composer, teacher, organist, bird watcher, interested in ancient and non-Western musical cultures, neumatic notation, etc.

His ideas regarding Rhythmic structure and notation.

Four ways of notating complex rhythms
- non-measured phrases, without time signatures (recitation, senza misura
- time signatures which change frequently
- rhythmic symbols (conducting patterns) marked in the score
- "false" meter with accents and ties (4/4 with syncopations)
rhythmic transformations of motives
added value rhythms
- extra value (sound)
- added silence
- added "dot"
augmentation/diminution based on a variety of factors
irregular but constant values (similar to aksak)
rhythmic canons
rhythmic pedal (ostinato)
polyrhythms
non-retrogradable rhythms (palindromes)

His ideas regarding pitch structure

Modes with limited transpositions
- symmetries
- equal partitions of the chromatic scale (12 divided by 1,2,3,4, and 6)
- the charm of impossibilities.
added notes
clusters
chords
- 13th chords
- "resonance" chords and "natural harmony"
- chord progressions litanie

A mode with limited transpositions is a scale which is divided in segments of the same size and containing the same exact arrangement of steps and halfsteps. Whithin an octave (12 semitones), there are a number of such divisions possible:

12 : 2 = 6 (the repeating segment is a tritone -6 semitones- long)
12 : 3 = 4 (the repeating segment is a major third -4 semitones- long)
12 : 4 = 3 (the repeating segment is a minor third -3 semitones- long)
12 : 6 = 2 (the repeating segment is a major second -2 semitones- long)
12 : 12 = 1 (the repeating segment is a minor second -1 semitone- long)

The last case produces the chromatic scale - not a very interesting result. The mode whose repeating segment is a major second long is the wholetone scale and there are only 2 such scales possible. Dividing the octaves by 4 leads to scales build around the pillars represented by a fully diminished chord and there are 4 possible transpositions for each of them. When the octave is divided by 3, the mode is built around an augmented triad and there are 3 possible transpositions of that scale. For modes built around the interval of a tritone there are 6 possible transpositions.

Example:

E flat

fully diminished

Messiaen combines modes with limited transpositions with nonretrogradable rhythms in order to create a sense of "failure of the rational thinking", an impasse created by a logical proceedure. Compare this with certain images (optical illusions) created by the artist Escher.

For more details, see Olivier Messiaen - Technique of my musical language on reserve.