# 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:

**C**, D, **E flat**, F, **F#**, G#, **A**, B: repeating
2 + 1 = 3 semitones (*fully diminished* chord)

or
**C**, C#, D#, **E**, F, G, **G#**, A, B: repeating
1 + 2 + 1 = 4 semitones (augmented triad)

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.

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