Ardour
Ardour is a free open source DAW (Digital Audio Workstation) with capabilities similar to other commercial products like Pro-Tools or Reaper.
Real Time Kernel
Although not mandatory, for optimal performance it is recommended to install Ardour in a Linux Kernel with the Real Time feature enabled.
Real time means that the actions are executed by the CPU as they are received, thus avoiding lags in the sound. On the other side, a non-rt kernel usually stacks the actions and makes selective choices about in which order they will be executed. This optimizes general computer performance, but can cause delays and glitches when working with sounds.
Even without a RT kernel, Puppy Linux's all-in-Ram philosophy guarantees brilliant performance.
A Puppy version with the RT enabled is Puppy Studio. It also includes an out of the box old Ardour version (sadly this distro is no longer maintained).
Ardour standalone package (for Puppy Precise): http://murga-linux.com/puppy/viewtopic.php?search_id=1974496821&t=92471
Ardour project site: http://ardour.org/