ABSTRACT
While it is difficult to dene precisely what makes a “good” rhythm good, it is not hard to list properties that appear to contribute to a rhythm’s goodness in the presence of other appropriate properties. Given that we know a certain rhythm to be good, we may examine its properties to gain insight into what makes it good. However, such properties are, by themselves, neither necessary nor su cient to make a rhythm good. We have already examined several such properties in previous chapters. Another possible candidate for such a property is that the mirror-symmetric image of a rhythm about some axis of symmetry be equal to its complementary rhythm.* I call rhythms that have this geometric property interlocking reection rhythms. ese rhythms also exhibit the phenomenological property that if the rhythm and its complement are both played simultaneously, and their acoustic properties such as timbre or intensity dier, the listener has the impression that the rhythm is switching roles, sometimes acting as a gure with its complement as a background, or vice versa. is occurrence is analogous to the unstable perception caused by the cubic wireframe shown in Figure 28.1 (le ) that has no depth cues, and which is sometimes perceived as a cube viewed either from the top (center) or from the bottom (right). Such gures are known as Necker cubes.†
is chapter presents, by means of examples, two simple methods to generate rhythms that exhibit the interlocking re ection property: it introduces the notion of rhythmic canons and relates re ection rhythms to rhythmic canons.‡ e rst technique uses the well-known snare drum rudiments called paradiddles.§ ese rudiments form the basis of modern drumming technique, and have been shown to increase speed, control, independence, accuracy, creativity, rhythmic innovation, and uency. ey have roots in African
balafon technique, and have inspired rock drummers as well as modern jazz pioneers.* e reader is warned that the mathematics, theory, and algorithms used in paradiddles are simple. is chapter is more about drumming technique, about le −right independence, and hand−foot independence, than about deep theory. us, the reader is advised to use the hands and feet while studying this chapter. Once the simple technique is mastered and has become automatic, a few simple rules thrown in will cause the emergence of elegant rhythmic complexity.
