Page 36 - Summer 2007

Fig. 1e. Construction of the DIFFDOT plot formed from the note event time deltas.
Fig. 1f. DIFFDOT plot of the Introduction to “It don’t mean a thing....”
threshold level. This is illustrated in Fig. 1d where the note event in each peak is plotted as a red diamond. Although the algorithm is adequate, it is not ideal since in real music there may be numerous artifacts that can “mislead” the algorithm. This is due to the fact that not all note events are clear, sharp and precise. The notes played by the hi-hat in Fig. 1d can be seen to be precise, but the notes played by the piano are not. In the second and third graphs from the bottom there are collec- tions of two, three or four small ripples at the top of some of the peaks. These may be caused by two, three or four fingers hitting the piano keys that are not precisely synchronized. Meticulous listening of the original recording can reveal the multiplicity of key note events in this frequency range. The first event in such a cluster was chosen as the keynote event. Addressing the question of what was the musician's intention, or whether the choice of note event time location for this study is identical to the perceived time location by a listener calls for further research. In this article, the focus is only on character- izing rhythmic timing and it is believed that our choice, while slightly arbitrary and ambiguous in some cases, is nonetheless
reasonable for the current context. The musical meter and subdivi- sion were marked in a straightforward way on the CHKDOT plots. The black and green vertical lines delineate the start or downbeat of each musical measure. There are eight measures in the introduction. It can be seen that Armstrong, on trumpet, picked up his solo on the eighth measure. Figure 1d shows the breakdown for the hi-hat cymbal and piano/bass parts in It Don’t Mean a Thing. The note events, marked by red diamonds, are placed along the invisible line in the center of the horizontal frequency band that contains the time series graph. In Fig. 1d there is one set of note events for the low frequency band (850 to 1020 Hz) and a second set of note events for the high frequency band (7500 to 22,000 Hz). Notice that some note events are sharp and distinct, e.g., the upper waveform—the hi-hat cymbal—while other time series waveforms have many jagged sections where the precise time of a note event becomes ambigu- ous, e.g., bottom three time series—
piano upper, piano lower, and bass. The less distinct waveforms, espe- cially the bass, are spread out more in time than the sharp events, indicating that the attack envelope of the sound is slower for these events. These note events—actual time locations—may also be imprecise. Often, the piano and bass sounds obscure each other. Separating these overlapping note events would need more sophisticated signal processing techniques than are currently used in this study. Nonetheless, it is fairly easy to identify enough note events to specify the rhythmic timing details. These details
are enough to reveal the Swing.
To mark the musical subdivision, note events that repre-
sent a pulse are first selected to use for the basic beat in the musical sample, such as the downbeat in a musical measure. This main beat can be subdivided in any convenient way, depending on the rhythm to be measured. Because triplets are a common timing feature in Swing, it was decided to sub- divide the main beat by six. These subdivisions are marked with pink lines that provide for the location of a backbeat on the third pink line and triplets on the other pink lines in the same measure.
While triplets can be and often are marked in sheet music, the standard subdivision of “Mozart-Bach” (MB) notation is by factors of 2. This is one reason why notating Swing music is somewhat difficult—triplets do not fit natu- rally into a “subdivide by 2” metaphor. It will be demonstrat- ed later that Swing can also contain subdivisions that are nei-
34 Acoustics Today, July 2007