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Unless you're familiar with stochastic composition, I recommend reading and checking out the sound examples that explain the basics of some techniques of musical composition using randomness here:
gemini://thrig.me/blog/2023/09/23/random-melody-generation.gmi
I have also touched on this topic in the last section of a recent post titled Three variations on a feedback theme.
"The computer as psychoanalyst" was the title of some paper circulated by one of my composition teachers. By delegating choices to the machine you get to reflect on the appropriateness of its choices, which means you gain insight into your own musical preferencecs. In particular, this is the case with randomness as musical material.
The reason for resorting to random decisions may be that it seems to be a technique of composition in its own right, and one that promises an objective music liberated from personal taste. However, all the crucial choices are usually taken before the employment of randomness, and corrections may be applied afterwards.
But what parameters do we apply randomness to? Pitch is typically the first thing to come up, then perhaps durations and possibly dynamics, and if you are schooled in serialist thinking you surely go on to apply random numbers to whatever else there is that can be formalised and treated as numerical parameters.
I heard of a rather original approach to making "random pieces" from someone on a music forum. He would throw dice with six, twelve, or twenty faces and use the outcomes to decide the time signature, key, instrumentation, and maybe a few more global parameters before going on to compose the piece more or less intuitively and without the aid of randomness at the level we normally think of as musical composition.
When you have decided to apply randomness to pitches, it may strike you that pure randomness doesn't fix the problem of making music, or melodic lines in this case, that sound good or convincing. The decision to restrict oneself to a diatonic pitch set, as chosen in many of the examples in the post at thrig.me, is understandable in this regard. A well known problem with randomly picked notes from the full chromatic set is that it often sounds atonal, but not enough so. Sometimes a major or minor chord or a run of a diatonic scale slips through, which sounds out of place in that context. Tenney's algorithm fixes that problem by updating the probability distribution and making it impossible or unlikely to repeat a recently occuring outcome.
So there your preferences enter and incentivise you to search for better stochastic models of music. Many options have been explored since the early days of computers, by the likes of Lejaren Hiller and Iannis Xenakis. Weighted probability distributions applied to pitch series can generate a kind of modal music, because what characterises a modus is that there is a root note which is emphasised by being more common than other notes, and there are rare notes only used in modulations or chromatic alterations. But still, the arbitrary order of notes produces pure gibberish unless one uses a Markov chain. And with Markov chains comes the problem of potential over-fitting; that is, if a high order transition table is used it will capture the analysed corpus and its output will not be very original. Exactly the same weakness that haunts generative AI models.
John Cage of course is famous for his extensive use of chance operations. But he was trying to escape his own taste, or at least that is the story we are often told. As all the examples of stochastic techniques show, it is very difficult to escape your own preferences simply by resorting to chance, and often that is not the goal at all. Therefore, Cage went further and introduced indeterminacy in his compositions, meaning that the scores could be interpreted in innumerable ways. Decisions were handed to the musicians, but if they chose to play fragments of a Wiener Waltz Cage wasn't at all happy about that.
Thus far I have used chance sparingly in my own music, but I'm currently working on something in several movements built on a single random series of notes. I literally threw a twelve-sided die over a hundred times and interpreted the numbers as pitch classes. The various movements or variations consist of layered melodic lines playing through the list of notes. Two pieces use acoustic instruments such as guitar, melodica, and voice, on the other ones I use a modular synthesizer. The randomness actually makes the material robust against mistakes, and I do allow many of my mistakes to be a part of the piece. In two of the variations the series is played forward and backwards simultaneously, and in another variation I diminished all intervals so that the chromatic twelve tone scale becomes a quarter tone scale.
Repetition is the antithesis of chance. By repeating a random sequence it becomes familiar, its arbitrariness takes on sigificance.
... jamais n'abolira le hasard.