mathematics and music theory share the elements of abstract languages, consisting of semantics and syntax. mathematical models can be used to analyze and to create musical structures. in the domain of digital art and of electronic music different programs are used, mainly for live performing. here some applications are presented that can be used for ear training, for practicing improvisation and for composing.

- catch the note, an application to learn to recognize single notes, intervals and little melodies
- chord trainer, an application to learn chords, diatonic and chromatic
- zzound (work in progress), an application to generate harmonic progressions. it can be used for improvisation, arranging and composing

catch the note and chord trainer are written in pd (pure data), zzound is a java application. these tools are work in progress and will be available on request.