261021 Chronochromie

Batch ‘Door opening procedure’

  1. play chronochromie
  2. read ordering the disordered
  3. read treatise on rhythm, color and ornitology

ABSTRACT FROM ORDERING THE DISORDERED

1 The invention of the symmetrical permutation scheme, unique in its engagement of 32 durations, 4 enables the astronomical number of permutations (‘interversions’ in Messiaen’s term) derivable from the reshuffling of durations to be reduced drastically. This is evidently an impressive addition to his stock of charm of impossibilities

2 The top layer employs 32 revolving chords (accords tournants), the middle layer 32 chords of transposed inversions on the same
bass note (accords à renversements transposés sur la même note de basse) and the bottom layer 32 chords of contracted resonance (accords à résonance contractée)

3 Messiaen described the colours of these chords and added that there are twelve tables of revolving chords just as there are twelve
tables each of the chords of transposed inversions and the first chords of contracted resonance.

4 To sum up: there are five categories of chords and altogether 60 chord tables, twelve each for the revolving chords, the chords of transposed inversions, the chord of total chromaticism, and the first and second chords of contracted resonance.

5 if we focus on only one set of twelve tables, it is terribly straightforward. For example, the twelve transpositions of the revolving chords are entered into twelve tables by following a chromatic sequence. The revolving chords of the first table lie a semitone above the revolving chords of the second table and so on and so forth. But if we compare the five different sets of tables, we become perplexed. It is not at all clear as to why the first chords of the respective first tables should be as they are. They do not seem to have anything in common: the treble is different, the bass is different, they do not have even one note in common. The rationale seems to lie elsewhere.

6 In attempting to answer the question as to why the twelve transpositions of each category of chords should be written out as twelve tables, it becomes clear that a number of factors may have been in play. The disparate ways in which Messiaen categorizes these chords might have led him to write out all chord tables. While the twelve transpositions of any one category of chords are entered into twelve chord tables by following an orderly chromatic sequence, we do not know what determines whether the second table should lie one semitone above or one semitone below the first table. There seems to be no standardized practice: two of the five categories of chords have tables that trace a chromatic descent, all other chord tables trace a chromatic ascent.

7 There is another important change in the way Messiaen uses these chords. At the time of Technique, the component chords of a table are usually articulated as a progression. Chronochromie brings a drastic change in this regard, for the chord layers of strophes I and II frequently use the component chords as discrete entities.

8 In conclusion, we may well ask what the chord tables, and the chords tabled, tell us. These chords stand out in importance in the
sense that they, but no other chords, are formally tabled in Traité. The chord tables show also that mirror inversions are not treated as equivalent. For example, the twelve tables of the revolving chords list only the twelve transpositions of the three referential octads; the mirror inversions of these are not included. In the special case of the chords of transposed inversions, not only the content but the spacing of chords also determine the tabling of them. The twelve tables of the chords of transposed inversions are occupied by 48 chords although there are only twelve chords of distinct content. Each of these twelve chords, differently inverted, appears in four different tables. The creation of 48 chords thus rests on the factor of chord inversion, which boils down to spacing.

tags: symmetrical permutation, revolving chords, transposed inversions, contracted resonance

Batch ‘Inside view’

bonus

and here am I

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