Mazzola, Guerino / Noll, Thomas / Lluis-Puebla, Emilio: Perspectives in Mathematical and Computational Music Theory

‘pressed’. At the borders of the event interval the values of $Y '$ are set corresponding to the given velocity of the event. The outside borders of the transition intervals are either defined by an absolute value (if there is no neighbour interval, as it is at the beginning and at the end of the score) or by the transition to the neighbour interval. For example in figure 3 the transitions from the second to the third event (at $t = 2/3$ ) are a change in pitch (the transitions in $X1$ ) and ‘release key’ plus ‘press next key’ for $Y1$ . The transition curves are cubic interpolations of their border values and tangents.

Figure 4:

Symbolic gesture curve for finger 2, with curve parameter $t$ running from 0 to 1 on the horizontal axis.

Figure 4 shows the symbolic gesture curve for finger 2 of our score (c.f. figure 2). Observe the two transitions below and after $t = 1/2$ , where onset time $E2$ remains constant and the finger moves in zero time from one key to the next. Finally note that the curves in figure 3 and figure 4 are not two separate symbolic gesture curves, they build together a single eight-dimensional parametric curve. The same applies when building a curve for all ten fingers, for instance.

4.3 Freezing a Symbolic Gesture Curve

While we have just dealt with the construction of symbolic gesture curves, which was denoted by the ‘thawing’ operation in figure 1, let us add a concluding remark on the reverse process, the ‘freezing’ of symbolic gesture curves. Since the symbolic gesture spaces are similar to the “Note on”, “Note off”, and “Velocity” concepts offered by MIDI, the ‘freezing’ operation in the symbolic domain is easy compared to the construction of a gesture curve: it is basically the transformation of a MIDI