Figure 2 Schubert, Arpeggione Sonata: pre-metrical grouping of durations. An asterisk denotes a phrase terminator, the grouping being the entire tree subtended from that level’s branches.

The grouping algorithm is initially pre-metrical (i.e. non-metrical) and is hierarchical, proceeding from bottom to top, with the various durations being grouped in ascending order of size. A typical example is illustrated by Figure 2, although the actual program output is in the form of coded numbers, equivalent to the tree-diagram. On each hierarchical level, the shortest timelength (interval between attacks) is found and notes separated by this timelength are connected together. (The timelengths are shown on the left of Figure 2). Notes of the smallest remaining duration value that have been connected in this way to subsequent notes are then eliminated from the analysis, as if replaced by rests, and the procedure is repeated to form the next higher level.