INTERPRETING RA MODELS OF NOTE-ONSET INTERACTIONS TO DISCERN AND EXPLAIN CLAVE DIRECTION

Mehmet Vurkaç

Abstract


Reconstructability Analysis (RA) was used to generate and evaluate models of sequences of musical note onsets. These sequences were classified into four classes in three musical contexts based on a musical grammar akin to “harmony” but concerning the timing of note events. (Having emerged only in certain societies and from the cultural interactions between Yorùbá, various Angolan peoples, Iberians, and the native peoples of the pre-Columbian Americas, this musical grammar is found only in some of the musics of South America and the Caribbean.)

A variety of search approaches and search criteria were used in the OCCAM 3 modeling engine, including BIC, AIC, and information, to extract classification information from rhythmic sequences. (‘Rhythm’ here refers to the timing of note events, not necessarily to any steady pulse, repetition, or percussive instrumentation.) The models discovered reflect trade-offs between complexity (degrees of freedom) and simplicity in how they prioritize some note-event interactions over others.

These close to 10,800 randomly generated idealized patterns have a 16-dimensional input space and a four-dimensional output space (for a total of 20). By limiting the output classes to whether a certain clave direction was present or not, the search space dropped to 17 dimensions. Hence, it was paramount to develop search trade-offs. The approaches developed for traversing the search space efficiently are detailed in the paper. Interpretation of these models is compared with several criteria for clave-direction determination deduced from systematic observations of four master musicians (and from deep exposure to the underlying musical practice).

BIC was found to be the most beneficial modeling criterion, with information second, and AIC third. The models discovered through RA provide insight into how clave direction arises in all possible rhythm sequences in that they highlight certain rhythmic schemata known to be strong indicators of clave direction while leaving out others as well as highlighting other rhythmic relationships for discerning clave direction that have been discovered through musicological (qualitative) means.

In some cases, models considered in this study show trade-offs suggesting that sufficient musical insight may be gained by considering interactions of fewer note events. In other cases, the interpretation of clave through an analogue to algebraic elimination gains unexpected support through RA modeling.

We thus demonstrate the ability of RA to model an intricate and culturally specific (not broadly accessible) musical construct in terms of discrete note events and their interactions in such a way as to mirror a human understanding of the corresponding musical practice.


Keywords


RA, culture, music, rhythm, clave

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