A Quantitative Rule System for Musical Performance

Anders Friberg
KTH - Royal Institute of Technology, Stockholm, Sweden (1995)


A rule system is described that translates an input score file to a musical performance. The rules model different principles of interpretation used by real musicians, such as phrasing, punctuation, harmonic and melodic structure, micro timing, accents, intonation, and final ritard. These rules have been applied primarily to Western classical music but also to contemporary music, folk music and jazz. The rules consider mainly melodic aspects, i. e., they look primarily at pitch and duration relations, disregarding repetitive rhythmic patterns. A complete description and discussion of each rule is presented. The effect of each rule applied to a music example is demonstrated on the CD-ROM. A complete implementation is found in the program Director Musices, also included on the CD-ROM.
The smallest deviations that can be perceived in a musical performance, i. e., the JND, was measured in three experiments. In one experiment the JND for displacement of a single tone in an isochronous sequence was found to be 6 ms for short tones and 2.5% for tones longer than 250 ms. In two other experiments the JND for rule-generated deviations was measured. Rather similar values were found despite different musical situations, provided that the deviations were expressed in terms of the maximum span, MS. This is a measure of a parameter's maximum deviation from a deadpan performance in a specific music excerpt. The JND values obtained were typically 3-4 times higher than the corresponding JNDs previously observed in psychophysical experiments.
Evaluation, i. e. the testing of the generality of the rules and the principles they reflect, has been carried out using four different methods: (1) listening tests with fixed quantities, (2) preference tests where each subject adjusted the rule quantity, (3) tracing of the rules in measured performances, and (4) matching of rule quantities to measured performances. The results confirmed the validity of many rules and suggested later realized modifications of others.
Music is often described by means of motion words. The origin of such analogies was pursued in three experiments. The force envelope of the foot while walking or dancing was transferred to sound level envelopes of tones. Sequences of such tones, repeated at different tempi were perceived by expert listeners as possessing motion character, particularly when presented at the original walking tempo. Also, some of the character of the original walking or dancing could be mediated to the listeners by means of these tone sequences. These results suggest that the musical expressivity might be increased in rule-generated performances if rules are implemented which reflect locomotion patterns.

[BibTex, External Link, Return]