Combining Grammar-Based and Memory-Based Models of Perception of Time Signature and Phase

Neta Spiro's paper Combining Grammar-Based and Memory-Based Models of Perception of Time Signature and Phase describes a method for recovering the time signature from a sequence of notes using a combination of grammar-based and memory-based approach. Interestingly, the only information considered in the algorithm is note-length; actual tones are completely ignored. Results are analyzed for 16 movements of solo string music by Bach, and compared with results from several previously published methods. Sprio's algorithm has two components. The first is a rule based grammar that takes a sequence of note-lengths and generates a time signature hypothesis. Many of the rules are motivated by common rhythmic structures such as dactyl and waltz. A dactyl is a long note followed by two short notes, so one of the rules says that if three notes match that pattern, those three notes' lenghts may add up to make the time signature. Likewise, the waltz rule says that if a note is exactly double or triple the length of the next note, those two notes may make a time signature as well. In any case, for a time signature to be accepted, its length can only have 2 and 3 as prime factors. This would seem to be a shortcoming, as it is not unheard of for a time signature to be of length 5, 7, or even 11. Those cases, however, are by far the exception, so this rule is generally acceptable. The rules are first processed on the initial 32 notes of a piece, producing a set of hypotheses for the time signature. The rest of the piece is then processed as a confirmation stage. Every time a pattern is found that suggests one of the candidate time signatures according to one of the rules, that time signature's score is increased. The details of the scoring system are omitted, which is unfortunate as it makes it difficult to reproduce Sprio's work. The time signature with the highest score is accepted as the correct one. The second component of the algorithm takes the time signature discovered by the rule based grammar and attempts to find the phase, or the place in the music that the first measure begins. This effectively allows the program to insert bar lines correctly between notes. If the first measure starts, say, after the first note and the time signature is _, there should be a bar line after the …