ABSTRACT
In 1956, Elvis Presley released his own faster and more syncopated version of a slow blues song recorded 4 years earlier by Willie Mae “Big Mama” ornton. For both ornton and Presley, this song, titled Hound Dog, rose to the top of the charts. In Elvis Presley’s rendition, the rhythmic patterns produced by the snare drum, the bass, and the handclaps are typical traditional African rhythms, a common thread that meanders through the rockabilly music of the 1950s.* Less well known is the fact that these rhythms have two interesting mathematical properties: they are all deep, and three of them exhibit what is called the shelling property with respect to the deepness property. e four rhythms that permeate the song are shown in Figure 26.1 along with their inter-onset interval histograms directly underneath each of them. From these histograms, it is clear that the rst three rhythms are deep: they have the property that each interval in the rhythm appears a unique number of times.† e bass pattern on the le is the well-known Cuban tresillo pattern. In “Big Mama” ornton’s version, the less syncopated duration pattern of the bass is [x . . . x . x .]. e clap pattern in Elvis’ version (second from le ), known as the habanera rhythm,‡ is obtained by adding an onset at pulse position ve (here adding refers to replacing a silent pulse with a sounded one). In “Big Mama” ornton’s version, the unsyncopated clap pattern is a straight pulsation given by [. . x . . . x .]. Elvis’ snare-drum pattern, on the right is the signature “backbeat”§ pattern of “rock-n-roll” music, and plays the role of the clap in “Big Mama” ornton’s version. If the snare-drum onset at pulse two
is added to the clapping pattern, then the well-known cinquillo pattern (second from right) is obtained.*
A rhythm admits a shelling, with respect to some property P if there exists a sequence of insertions or deletions of onsets so that, a er each insertion or deletion, the rhythm thus obtained continues to have property P. Again, here and throughout this chapter, the terms “insertions” (or deletions) refer to replacements of a silent (or sounded) pulse with a sounded (or silent) pulse. In the present case, starting with the bass pattern, onsets may be inserted in positions ve and two, in this order, while maintaining the deepness property of the resulting rhythms. Similarly, starting with the cinquillo rhythm and deleting the onsets in the reverse order (two before ve), preserves the deepness property. In fact, since, by convention, a pair of onsets denes just one duration interval corresponding to the shortest circular arc determined by the pair, another onset may be deleted from the bass pattern on the le , while still maintaining the deepness property, albeit at its most elemental level. Deleting the third onset at pulse six yields the Cuban timeline [x . . x . . . .] called the conga,† which at a faster pace becomes the charleston rhythm.‡ Recall that this rhythm, probably the simplest, minimalist, yet eective, electric guitar solo ever used in a rock-n-roll megahit, is played in the middle section of the 1964 song Don’t Worry Baby, by the Beach Boys. eir solo ends by inserting the third onset, thus converting it to the tresillo. Deleting the rst onset of the tresillo yields [. . . x . . x .], also a Cuban rhythm called the conga.§
e 12-pulse ternary timelines used in much sub-Saharan African music provide another example of a family of rhythms that admit shelling with respect to the deepness property. Consider the bembé rhythm and its interval-content histogram shown in Figure 26.2. ere are seven dierent onsets each of which may be deleted to obtain a six-onset rhythm. Each of the seven onsets has a spectrum of six distances determined by the other six onsets. To ensure that the rhythm remains deep when an onset is deleted, the onset to be deleted must contain a spectrum with exactly one instance of every distance present in the histogram of the rhythm before the onset is deleted. In that way, the height of each column of the histogram will be reduced by one unit, thus preserving the deepness property. e spectrum for the onset at pulse 11 is pictured in Figure 26.2 (le ). Note that only the onsets at pulses 5 and 11 have spectra that contain all the distances, and therefore only one of these two onsets may be deleted. If we remove the onset at pulse 11, we obtain the rhythm shown in the middle with its resulting histogram on the right. is rhythm is also a bell timeline used by the Yoruba people of Nigeria. Of the six onsets, only the onset at pulse ve has all ve distances in its spectrum. erefore, only this onset may be deleted next if deepness is to be preserved, and doing so results in the fume-fume rhythm.
