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What's the difference between generative and transformative algorithms in relation to algorithmic composition of music?

As I understand the basic idea of the algorithms themselves, generative uses past candidate values (output becomes input) as progenitors (parents) for the next output, i.e. by combining them under certain conditions.

Transformative algorithms use environmental factors only to determine how to change the existing input.

However I've read that generative music as created by Brian Eno can use environmental factors and a single candidate input value, transforming it based on stored environmental factors.

I am struggling to understand what the difference is since there seems to be no universal agreement on what constitutes generative.

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Google's Ngram viewer suggests that the term Generative Music may have been around before Eno's popularisation of the term, but in modern usage his meaning seems the predominant one. Eno uses the term in a broad sense, referring in his book A Year with Swollen Appendices to systems where recordings of different lengths are allowed to repeat and overlay each other with continually changing offsets (as in the production of Discreet Music) as early examples of generative music. The product Generative Music 1, using the SSEYO Koan engine, also bore the label, even though the music is produced in a very different way. You can see from the Koan Pro manual that the author is expected to choose whether to specify a great number of rules.

Eno saw generative music as a type of product - one that had perhaps long existed, but was maybe only able to reach its potential through digital technology :

Some very basic forms of generative music have existed for a long time, but as marginal curiosities. Wind chimes are an example, but the only compositional control you have over the music they produce is in the original choice of notes that the chimes will sound. Recently, however, out of the union of synthesisers and computers, some much finer tools have evolved. Koan Software is probably the best of these systems, allowing a composer to control not one, but one-hundred and fifty musical and sonic parameters, within which the computer then improvises (as wind improvises the wind chimes).

The works I have made with this system symbolise, to me, the beginning of a new era of music. Until a hundred years ago, every musical event was unique: music was ephemeral and unrepeatable, and even classical scoring couldn't guarantee precise duplication. Then came the gramophone record, which captured particular performances, and made it possible to hear them identically, over and over again.

But now, there are three alternatives: live music, recorded music, and generative music. Generative music enjoys some of the benefits of both its ancestors. Like live music, it is always different. Like recorded music, it is free of time-and-place limitations — you can hear it when and where you want.

The term 'generative music' seems to include any algorithm or system that essentially makes musical choices through rules or processes, resulting in unpredictable musical output.

Something that is transformative takes an input, and generates an output. There is perhaps an implication that the input should be of the same form as the output - for example, a sequence of notes may be transformed into a harmonising sequence of notes, or a simple rhythm may be filled out to become a denser and more complex rhythm. An arpeggiator could be seen as a simple kind of transformative algorithm.

So you can't really draw a clear line between the meanings of 'generative' and 'transformative'; they're just looking at the behaviour of a system from slightly different perspectives. A transformative algorithm may be a part of a generative system, as you can see from some of the options in the Koan manual. If you remove the need in your definition of 'transformative' for the input to be of the same form as the output (your choice, I think!), you could see any generative system as also transformative, because at some level, even a generative system can't create music completely from scratch; it must have at least two initial inputs : a set of output possibilities, and a means to select between them.

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