For the purpose of creating new musical instruments, chaotic dynamical systems can be simulated in real time to synthesize complex sounds. This work investigates a series of discrete-time chaotic maps, which have the potential to generate intriguing sounds when they are adjusted to be on the edge of chaos. With these chaotic maps as studied historically, the edge of chaos tends to be razor-thin, which can make it difficult to employ them for making new musical instruments. The authors therefore suggest connecting chaotic maps with digital waveguides, which (1) make it easier to synthesize harmonic tones and (2) make it harder to fall off of the edge of chaos while playing a musical instrument. The authors argue therefore that this technique widens the razor-thin edge of chaos into a musical highway.