Wind in the Willows – Generating Music by Means of Tree Transducers

An Algebra for Tree-Based Music Generation

“…In this paper, we have continued the work that was started in [3]. In particular, we have presented an algebra for the tree-based generation of music.…”

“…The language generated by g, called a regular tree language, is given by L(g) = {t ∈ T Σ | S → * R t}. As mentioned in the introduction, our general approach for generating music is adopted from [3]: a tree denoting a musical piece is generated by starting with a very simple tree and then applying to it a sequence of td transducers each of which is responsible for adding a specific musical aspect. However, the ordinary top-down tree transducer (td transducer) is not the ideal device for this purpose, because a td transducer has a finite input alphabet and cannot process input trees that contains other symbols.…”

“…2 This assures that the local notes belong toĉ, and that the complete note sequence respects the chosen chord progression. For a more detailed discussion of this subject, see [3].…”

“…Rather than trying to imitate human composers, we are interested in finding out how and how far the formal structures found in music can be captured using the devices of formal language theory and, in particular, tree-based generators. A precursor of the present paper is [3], where the system Willow is presented. In this system, the tree generator is composed of a regular tree grammar g and a sequence td 1 , .…”

“…To the best of our knowledge, no tree-based approach (in the sense described above) to the generation of music has been proposed earlier (except for the first attempt made in [3]). However, there are some publications, often with a somewhat different focus, that propose other approaches to music generation using techniques from formal language theory.…”