Matching the rule parameters of PHRASE ARCH to performances of "Träumerei": a preliminary study

In music performance a basic principle is the marking of phrases, which often seems to be achieved by means of tone durations. In our grammar for music performance the rule PHRASE ARCH, has been formulated to model this eflect. A technical description of the rule is presented. Also presented is an attempt to match the diflerent parameters of this rule to the duration data fiom 28 performances of the Jirst 9 bars of Robert Schumann 's Traumerei as measured by Bruno Repp (1992). The optimisation was based on relative duration measured in percent. On average 44% of the total variation was accounted for by PHRASE ARCH. The discrepancies were mostly at the note level and were mostly associated with small musical gestures. Introduction The KTH performance rules translate scores to music performances. These rules have been described in several previous papers (e.g. Friberg, 1995; Sundberg, 1993). We will focus here on the rule PHRASE ARCH. The aim is two-fold: to provide a complete technical description and to see if the rule can be traced in real performances. PHRASE ARCH is a rule that is particularly suited to romantic classical music, performing the phrases with an initial accelerando and a subsequent ritardando. The definition of the rule was inspired by Neil Todd's phrase model (Todd, 1985, 1989), see also Friberg et al. (1994) and Friberg (1995). The existing measurements by Repp (1992) on 28 performances of Robert Shumann's "Traumerei" were well suited for testing the validity of the rule. It is clearly a romantic piece with often very pronounced tone duration changes. Many artists and recordings spanning several decades ensured that much of individual plausible variation was exposed in this data. An interesting question was how much of the variation seen in these performances could be explained by varying the parameter values in the rule. A complete technical description of the rule will be given below which includes both timing and sound-level variations. The following parameter matching is, however, only done with regard to the timing information. In this preliminary study, the matching was limited to the first nine measures of "Triiumerei". Also appearing in Friberg A & Sundberg J, eds, Proceedings of the KTH Symposium on Grammars for Music Performance, May 27, 1995.