Alda was originally named after Yggdrasil, the venerated tree of Norse legend which held aloft the mythical nine worlds. Dave thought it to be a fitting name, imagining the realm of sound/music to be an immense tree bearing numerous branches which could represent genres, tonalities, paradigms, etc.
By incredible coincidence, the company Dave works for uses Norse mythology as a theme for naming their software projects, and there was a working project called Yggdrasil. Dave was never totally happy with Yggdrasil as the name for his music programming language (it's a mouthful), so he this as an opportunity to rename it. Alda is Quenya for "tree."
There is a plethora of music software out there, but most of these programs tend to specialize or "reside" in at most one or two different realms -- FamiTracker and MCK are specifically for the creation of NES music; puredata, Csound and ChucK are mostly useful for experimental electronic music; Lilypond, Rosegarden, and MuseScore can be used for more than just classical music, but their standard notation interface suggests a preference for classical music; Guitar Pro is targeted toward the creation of guitar-based music. Why not have one piece of software that can serve as the Great Tree that supports all of these existing worlds?