Piano Study No. 1
Piano Study No. 1, one minute and eleven seconds long, was written for Raymond Deane on the occasion of his fortieth birthday in 1993.The form of the piece is derived from an icosahedron, a polygon made up of twenty equally sized equilateral triangles, of which a maximum of ten can be seen at any one time. If we project an icosahedron onto a flat plane we see the following image, one of three possible symmetries (diagram 1):
Diagram 1.
The piece traces an imaginary journey across this projection, using the angle of apparent slope away from the observer of any given plane in the original 3D polygon as the means of defining tempo. It can quickly be understood that the outer 6 panels in the diagram are the most inclined away from the observer in the 3D model, and occur in pairs, while the single central panel is perpendicular to the line of vision. The 3 intermediate panels are inclined slightly way from an observer, but not so inclined as the outer 6. Thus we have three principal tempi, which are defined as mm120, mm.72, and mm. 45. (see diagram 2 at the bottom of the page)
The travel across this 2D projection starts at the outer panel pairs (a & b), at mm.120, and moves across these two mm.120 panels before encountering a mm.72 panel (g), which must be crossed before the next mm.120 pair (c & d) are reached. This continues in circular motion (through h, e, & f ) until the last mm.72 panel (j) has been gained, at which point the direction of travel moves towards the centre of the projection, and to the m.m.50 panel (k). Thus the entire journey resembles a spiral.
This main tempo structure is aurally defined by the running semiquaver line in one hand, initially the right, but moving downwards in pitch following a "drunk walk" path into the left hand, then back up into the right hand. This is meant to be heard as a background layer.
The foreground content comes from what is going on alongside this structure, and can be summed up as sets of 5 dyads which are representative of the boundaries of the planes being crossed. Thus, in crossing the first temporal section at mm120 in which the 2 panels (a &b) are traversed, the boundaries are 5 in number, hence 5 sets of 5 dyads are presented at 3 different speeds (mm.192, mm.137, and mm.320). There are 3 different speeds because there are three different apparent lengths of boundary in the 2D projection; the slower speed is the outer boundary, the faster speed is the shared boundary of the two panels, the middle speed the remaining inner side. Thus, in the case of panels a and b, the speeds in order at which the 5 sets of 5 dyads are heard are mm.192, 137, 320, 137, 192 against a backdrop of movement at mm480. (See Diagram 2)
Diagram 2
Crossing into the first m72 panel (g), since the boundaries are 3 in number, there are 3 instantiations of the 5 dyad sets heard at 2 tempi, one of which, mm.192, we have already met as the boundary between (a) and (j), and (b) and (g). This tempo occurs twice at mm.72, the two occurrences separated by the occurrence of a mm.115 dyad set.
This temporal process continues as described following the path c, d, h, e, f, j, leading to the slowest and climactic statement of three mm.115. 5-dyad sets in k at mm50.
https://drive.google.com/open?id=0Bz4hsX04m-CQRnlLeUdFYVRpVkE
The piece can be heard at https://soundcloud.com/fergusjohnston/piano-study-no-1 . The score can be accessed here
