Page 37 - Summer 2007

ther factors of 2 nor 3. The approach used in this study avoid- ed the limitations of subdivision that are inherent to MB notation.
The actual note events in the recording are used to deter- mine the musical meter and subdivision of the beat in the CHKDOT diagram (Fig. 1d). Essentially the reverse of play- ing a tune by reading sheet music, note information was extracted from the recording which could be used to generate sheet music. The pulse in Fig. 1d is marked by green and black vertical lines, which correspond to the downbeat of the measure in MB notation (a two measure phrase, one green and one black). Each musical measure was subdivided by six, looking for triplet notes of the classic Jazz Swing pattern and this subdivision was marked by using six pink lines in the CHKDOT diagram. The pink line exactly in the middle between a black and green line represents the time location of the backbeat of the rhythm. Thus it is observed that the piano/bass peaks are on the downbeat and backbeat, with diamond markers on certain backbeats in the third time series up from the bottom of the chart. These events were used to mark the pulse. The hi-hat cymbal note events in the time series at the top occur on the downbeat, backbeat and triplet pickup to the downbeat and backbeat. The triplet tim- ing is indicated by note events on a pink line just ahead of a black or green line.
To analyze Swing rhythm it must be known when the beat occurred, the deviations of the beats of each instrument from their mean, and from each other. This is performed in MATLAB by a second program called DIFFDOT which extracts the time differences (time delta) between note events. Delta corresponds to the length of a musical note in MB notation—1/4 note, 1/2 note, 1/8 note etc. The pulse is used for the master time clock (whole note), and a time delta with length 1/2 of the pulse would be a half-note in MB nota- tion, 1/4 of the pulse length would be a quarter-note and so on. Because the beat can be subdivided by any number that makes sense for a musical sample, triplets can be easily accommodated (divide by 3) or any other note time duration. Since the pulse note event timings have some variation, the minimum, maximum, and mean or average of the time dif- ferences are notated, and the mean value is used as the canonical pulse time to subdivide the beat.
Figure 1e shows the mapping process from a CHKDOT plot to a DIFFDOT plot. The two time series in Fig. 1d that were marked with note events—hi-hat cymbal and piano (upper)—are superimposed over the DIFFDOT plot, Fig. 1e, for the same time range. The elapsed time on the X axis is the same for both forms. A red diamond on the CHKDOT plot maps to a circle on the DIFFDOT plot—red circles for the hi- hat, and green circles for the piano. The X position of match- ing diamond/circle pairs is the same. The Y position of the circles indicates the time from that note event until the next note event in the set. Thus longer notes, such as the pulse, are at the top of the DIFFDOT plot, and shorter notes are in the lower half of the plot.
In Figs. 1e and 1f, the red circles are the hi-hat note events. Notice the first three red circles are fairly evenly timed on the backbeat (1/2) of the pulse. These three time deltas correspond to the first four diamonds in the corre-
sponding time series graph. After four note events, the hi-hat starts to play triplet notes, clearly visible on the pink subdivi- sion lines in the CHKDOT diagram (Fig. 1d) and transferred to the DIFFDOT diagram (Fig. 1f) onto the 1/3 and 1/6— lying between 1/6 and 1/8, really. These note events on the 1/3 and 1/6 lines of Figs. 1e and 1f are the time deltas between the swung notes in Figs. 1e and 1f, and the beats immediate- ly before and after: i.e., 1/2 - 1/3 = 1/6. The slight imprecision of the note timings in this example indicate a somewhat loose rhythmic style for this recording. Later a recording which has a very tight rhythmic style will be analyzed. This is another aspect of the music performance that can be read directly from the DIFFDOT diagram.
Note events are essentially transferred one for one from the CHKDOT to the DIFFDOT plots. CHKDOT plots are more intuitive to read since they parallel standard musical notation. DIFFDOT plots may require careful inspection, but by looking at the spatial patterns it is possible to get an intu- itive sense of how the Swing works.
In addition to the time differences between note events, the DIFFDOT plots can also show the variations in time loca- tions of repetitive musical events extracted from the CHK- DOT plots, such as pulse, backbeat and swung notes. This is not a feature which can be written in MB notation. The DIFFDOT plots also clearly show how on some beats two instruments may not be precisely synchronized—in some cases, the hi-hat plays slightly before the piano note event, and in other cases, the reverse is true. This can be read direct-
Technical Anaylsis of Swing Music 35