URrhythm — represent Johnson-Laird beat prototypes for a passage
The URrhythm representation encodes beat "prototypes" (Ur-rhythms) evident in a musical passage. The representation is based on Johnson-Laird’s theory of rhythmic prototypes (see REFERENCES below).
The URrhythm representation characterizes each beat in a passage as belonging to one of three "beat types": Note (N), Syncopation (S), or Other (O). Only principle beats are characterized in this way. Hence, in 3/4 or 9/8 meters, three beats are characterized for each complete measure. Similarly, in 4/2 and 12/16, four beats are characterized for each complete measure. Johnson-Laird’s rhythmic-prototype theory can be applied only to musical passages conforming to regular meters (simple and compound, duple, triple and quadruple).
A "Note" (signified in the output by the letter `N') is defined as a beat that coincides with a note onset.
A metric "Syncopation" (signified by the letter `S') is defined as arising when no note-onset happens on a beat whose metric position is more important than that of the most recent note onset. By way of example, imagine a measure in 4/4 meter containing a quarter-note, followed by a half-note, followed by a quarter-note. The third beat position does not coincide with a note onset. The most recent note onset prior to the third beat occurs on beat two. Since beat three is a more important metric position than beat two, beat three is deemed to be syncopated.
Metrically syncopated beats can happen only after the first note onset; subsequent syncopated moments require another note onset (i.e. two syncopated moments can’t occur in a row without some note onset intervening).
An "Other" (signified by the letter `O') is any beat that is not a Note (N) or a syncopation (S).
Barlines are represented using the "common system" for barlines — see barlines.
It is recommended that files containing predominantly URrhythm data should be given names with the distinguishing `.urr' extension.
The following table summarizes the URrhythm mappings of signifiers and signifieds.
N "note" beat prototype O "other" beat prototype S "syncopation" beat prototype . null token = barline; == double barline 0-9 measure numbers —– ——————————–
Summary of URrhythm Signifiers
A sample document is given below:
**URrhythm *M4/4 *tb8 N . N . S . =1 N . O . S . O . =2 S . S . O . N . *- ————–
The following Humdrum command produces URrhythm data as output:
urrhythm characterize the rhythmic prototypes in a passage – ——————————————- —————————————————
The following tandem interpretations can be used in conjunction with URrhythm:
Tandem interpretations for URrhythm
barlines, **metpos, metpos, urrhythm, **synco, synco, **timebase
Philip Johnson-Laird, "Rhythm and meter: A theory at the computational level," Psychomusicology, Vol. 10 (1991) pp. 88-106.
Jasba Simpson & David Huron, "The perception of rhythmic similarity: A test of a modified version of Johnson-Laird’s theory," Canadian Acoustics, Vol. 21, No. 3 (1993) pp. 89-90.