Analysis - Resynthesis
Sonic Visualizer
Framework for audio signal analysis.
http://www.sonicvisualiser.org/
LibXtract
Open source, portable, lightweight library of audio feature extraction functions.
http://libxtract.sourceforge.net/
Tapestrae
Analyzes and recomposes sound scenes.
http://taps.cs.princeton.edu/
Modular Synthesis Tools
CSound
Programming language for sound rendering and signal processing.
http://www.csounds.com/
PureData (PD)
Real-time graphical programming environment by Miller Puckette. One of the best prototyping tools.
http://puredata.info/
STK
Open source audio signal processing and algorithmic synthesis classes written in C++ by Perry R. Cook.
http://ccrma.stanford.edu/software/stk/