Not exactly on topic, but I thought I’d offer my picture of what generative means to me.
My take on the term generative is that the material is generated, as opposed to composed or entered. This leaves almost anything where melody or rhythm emerges under that purview. The generation may be deterministic (chaotic or otherwise) or not, and at any level of abstraction: the key is that the material played isn’t composed or entered.
In the deterministic domain, the generator would be Algorithmic, be that a complex function or an iterative mechanism. The key would be that from some given initial state the result would be the same. For algorithms executed in the digital domain the end result of a chaotic dynamical system can remain consistent. An interesting middle ground would be to create a dynamically unstable arrangement of components in the analogue domain (a physical “strange attractor”). In this situation the behaviour is well understood, but divergent meaning the long time behaviour can’t be predicted (as the initial state can’t be sufficiently well reproduced and the system has noise).
In the non deterministic domain we have similarly Algorithmic approaches, where decisions are made based on randomness. Such approaches aren’t reproducible but may be constrained by applying that randomness to a deterministic system (e.g attenuate and quantize sampled and held noise for pitch). Given mechanisms to record snippets of the random stream one may freeze or repeat the behaviour as required.
As for abstraction and the previously mentioned danceability, I’d take a Euclidean rhythm generator as a good example. Rather than temporally random triggers, one can place triggers on some clock. The Euclidean subdivision parameters may be chosen algorithmically but the result always fits a conventional musical model. Combined with a quantizer you can get melody. Another abstraction might be a chord generator. It could generate a random pitch cloud (little harmony or temporal coherence), select a random chromatics (more conventional but not necessarily musical), a random chord type and root note (musical, but with no clear temporal direction), a random diatonic chord (musically well defined and easier to fit with other musical elements), or a random chord progression based on some algorithm (“always musical”). All these elements could be considered generative, but the control comes from the constraints we apply and algorithms we choose (either by programming, patching, or both).
In any case, what I’m driving at, is that generative, to me, is about finding a balance. You balance controllability, reproducibility, temporal coherence, musical structure (harmonic, melodic and rhythmic) and domain of generation against one another. In the end, where in that spectrum you choose to be, depends on your personal technical, artistic and aesthetic preferences.