In the World of Grains – Part 13
Some Notes about Composing with Grains
(= part 17 of all articles about sonic grains)
The role of mathematics:
Before I talk about some ways to implement mathematics in the process of composing – a matter which is not exclusively important when working with sonic grains – I´d like to point out, what Curtis Roads once mentioned (I´ve forgotten when and where, please pardon me): he said, that only humans are able to make “inspired choices” concerning art, choices, which cannot put into fixed rules or algorithms. Let me add a bit of my own, and say: but algorithms call serve well to set the general direction a sonic development has to follow, still leaving a wider or closer scope to make my human choices, or in a multi-stage process, I set this general direction myself, and then let mathematics do their work, only to take further action myself again in the following step and make my “inspired choice” concerning the details.
Well, back to earth. One way to make use of algorithms is to set up a whole bunch of them, each of which with a certain compositional intention, and then chose from this spectrum of algorithms like composers decided which scale they´d use in the olden days.
When setting up those algorithms I may try to make mathematical models of anything, not only of audible goings on, and then apply these models to the parameters and arrangements of grains and clusters. I can use mathematical models of weather events, of traffic, of a tree branch floating on the surface of a river, as well as the spectral development of the sound of a trumpet, when being blown at different intensities.
And arriving at this point, I might think of inventing mathematical models, algorithms, which are completely free and independent from any real world process, purely intellectual contructions, which shall come to audible life, when applied to sonic grains.
Another approach is called “cyclical probability”. Imagine we set up a number of mathematical rules how certain parameters of a grain or a cluster (or a swarm) change and lead to another, to the next grain, cluster (or swarm) with different sonic content, but include a probability switch for each of the parameters individually, a switch, which sometimes sends the parameter, which it is manipulating, back to one of its former states – and sometimes not changing anything at all. The step-to-step development of each parameter is unpredictable to a certain degree then.
And then there is the family of different strictly iterative mathematical strategies, where the composer generates his material from applying the same mathematical operation to a parameter again and again, beginning with the recorded or otherwise generated original grain or cluster, and apllying the algorith to this grain or cluster, then again to the result of the operation, and to the result of the result etc.
The frequency sequence 587 Hz – 685 Hz – 761 Hz – 824 Hz – 879 Hz etc. for example is the result of the function 440+440/3*f iterativeply applied. We can generate these sequences for any sonic parameter of course.
In a second step, let me call it the fine tuning of the parameters, the gained values will undergo a more artful, more human process of making smaller changes, or leaving out certain elements of the sequence.
But iterative processing is not always dependent on mathematics. In chapter 6 “A Sonic Microscope” I describe a quite special example of an iterative strategy to gain new sounds and get detailed insights in “old” ones.
to be continued
to part 1: ("A Short History of Granular Synthesis - Part 1"):https://www.dev.rofilm-media.net/node/340
to part 4: ("A Short History of Granular Synthesis - Part 4"): https://www.dev.rofilm-media.net/node/356
to part 5 ("In the World of Grains - Part 1"): https://www.dev.rofilm-media.net/node/364
to part 6 ("In the World of Grains - Part 2"): https://www.dev.rofilm-media.net/node/373
to part 7 (“In the World of Grains – Part 3”): https://www.dev.rofilm-media.net/node/378
to part 8: (“In the World of Grains – Part 4”): https://www.dev.rofilm-media.net/node/385
to part 9: (“In the World of Grains – Part 5”): https://www.dev.rofilm-media.net/node/390
to part 10: (“In the World of Grains – Part 6”): https://www.dev.rofilm-media.net/node/398
to part 11: https://www.dev.rofilm-media.net/node/407
to part 12: https://www.dev.rofilm-media.net/node/414
to part 13: https://www.dev.rofilm-media.net/node/421
TO PART 14: https://www.dev.rofilm-media.net/node/483
TO PART 15: https://www.dev.rofilm-media.net/node/486
to part 16: https://www.dev.rofilm-media.net/node/489