The spectralist Grisey wishes to use both harmonic and inharmonic spectra, and the inharmonic are either compressed (4 overtone series where the intervals are slightly diminished) or they are extended (4 overtone series where the intervals are slightly augmented).
The 4 harmonic series (with the fundamentals on F#, Eb, C and A - making a diminished 7th-chord) have the 4 quartertones as coinciding pitches (as their 11th and 13th partials), and these same pitches are also found in the inharmonic series. In this way, the quarter-low C, the quarter-high D, the quarter-high F and the quarter-low A are central pitches through the whole work.
Grisey chose to octavate some of the pitches, because he wished to have the possibility of microtonal sounds in different ranges of the piano.
Grisey's 4 quarter tones make up a diminished 7th chord. This chord has usually little to do with the harmonic spectrum, but as the spectralists often make use of the 3 quartertones interval (neutral 2nd) which is the minor 3rd devided in two, I chose to play with the 3 quartertones interval in the following examples.
The quartertone is used melodically and tonally (C major) as the 11th harmonic.
Examples of quartertone high/ low octaves.
Hervé, Jean-Luc 1999: L'image sonore: Regard sur la création musicale.
Université Lille III - Charles-de-Gaulle. U.F.R. d'Arts et Culture.
Kverndokk, Kristin 2003: Klang og prosess i Gérard Griseys Vortex Temporum
Hovedoppgave i musikkvitenskap - Institutt for musikk og teater, Universitetet i Oslo