Structural analysis of M418M

Based on the clear tonal centre of the base key A major, thirteen smaller parts with the duration of a few minutes titled sections 1-11 form, which are framed in the beginning and end by the pulses 1 and 2. Section 3 is again partitioned in section 3A and section 3B. Between the pulses and sections there is no pause, the transitions are seamless.

The basic structure is made up by eleven chords that in the order ABCDCBA all sound in the pulses and form a prologue and an epilogue. In each section one of these chords is picked out and its triad a small piece is built. Therefore, almost all of these sections consist of the same sounds, but in a different order. Predominantly the notes A, B (in German notation: H), D, E and also C, F and G are used. The notes always vary only slightly what allows the morphing of their structural form into another and back again. The shape of the triad is looked at in the context of the bar and the shape of the bar structure within a repetition. These repetitions as the content of a segment and the distinct but similar sections within the whole piece, they all are akin to themselves. The form of the triads gradually mutates (with the bass clarinet or the vibraphone as indicator for the change) from one chord to the next and thus from section to section.

Also, the rhythm of the single parts of the pulse is always treated slightly differently. The instruments for the same lead melody are changed or the vocals start to mimic instruments and slowly replace them. Everything is in transition and mutates through iteration and thus from few pieces a complex pattern is generated.

Developing the grid

On the eight corners of the cuboid, the key A major was distributed. On its six sides, the 18 instruments were arranged, three on each side. Based on the corners the eight notes converge in the centre of the cuboid: A-A, C#-F#, E-H, G#-D. For the base note A, a whole diagonal of the cuboid is available, for each of the other notes half a diagonal. These diagonals are further partitioned in (using the example of D): D-2, D-1, D1, D2, D3. The three instruments per side of the cuboid are distributed on the unfolded cube in such a way that their positions approximate the plan of the performance. Thereby, one instrument lies on one of the square’s four corners and the other two on the centre of the opposing sides. In the cube (folded again), one instrument is marked by drawing a line from the instrument’s point of origin through a control point, the side’s centre, and from there on to the note the instrument plays and back to the point of origin. If several notes are played by one instrument simultaneously, all notes are traced consecutively before the line is returned to its point of origin. Thus, an area is delineated that describes which instrument plays which note.

For a two-dimensional design grid, the pattern was continued on the unfolded cube. As a periodic pattern, it by all means equates to the clear tonal centre and rhythm of the source music. However, here the aspect of iteration and mutation is not present as it is the case with quasicrystals. Though, regarding the sections, this aspect is intended to be produced analogously to the structure of Music for 18 Musicians, in the construction of different applications with and on this grid.