Processing of hierarchical syntactic structure in music

Illustration of stimuli. (A) Original version of J. S. Bach’s chorale Liebster Jesu, wir sind hier (BWV 373). The first phrase ends on an open dominant (see chord with fermata below orange rectangle), and the second phrase ends on a tonic (dotted rectangle). The tree structure above the scores represents a schematic diagram of the harmonic dependencies (for full tree graphs, see Figs. S2 and S3). The two thick vertical lines (separating the first and the second phrase) visualize that the local dominant (V in orange rectangle) is not immediately followed by a resolving tonic chord but implies its resolution with the final tonic (indicated by the dotted arrow). The same dependency exists between initial and final tonic (indicated by the solid arrow). The tree thus illustrates the nonlocal (long-distance) dependency between the initial and final tonic regions and tonic chords, respectively (also illustrated by the blue rectangles). The chords belonging to a key other than the initial key (yellow rectangle) represent one level of embedding. (B) Modified version (the first phrase was transposed downward by the pitch interval of one fourth, red color). The tree structure above the scores illustrates that the second phrase is not compatible with an expected tonic region (indicated by the red dotted line with the red question mark) and that the last chord (a tonic of a local cadence, dotted rectangle) neither prolongs the initial tonic nor closes the open dominant (see solid and dotted lines followed by red question mark). In both A and B, Roman numerals indicate scale degrees. T, S, and D indicate the main tonal functions (tonic, subdominant, dominant) of the respective part of the sequence (such as functional regions in the GSM). Squared brackets indicate scale degrees relative to the local key (in the original version, the yellow rectangle indicates that the local key of C major is a subdominant region of the initial key G major).