Abstract
This article describes a specific aspect of a broad research project which aims at realization of analytical and compositional approaches theoretically based on the principles of Grundgestalt and developing variation, both elaborated by Arnold Schoenberg. The present study introduces a group of four complementary and sequential modules modeled as genetic algorithms (forming the geneMus complex), employed for the systematical production of variants from a basic musical cell. The description of the interaction and functioning of the four modules is followed by examples of their application in the whole process.
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- 2.
In order to emphasize the importance of Brahms’ derivative practice, Schoenberg presented in 1933 in Frankfurt Broadcast a radio conference entitled Brahms the progressive, celebrating his birth’s centennial. Schoenberg provocatively chose this title as a kind of answer to the common sense that considered Brahms as a conservative composer in comparison to Wagner. That conference was years later transformed in a homonymous essay [4].
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The chromosome M is not employed for variation, being only a transcription of chromosome I. It is necessary in order to provide to the system a melodic result with a compatible cardinality in relation to chromosome R (obviously, a sequence of intervals has always one element less than a sequence of corresponding durations).
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The geno-Theorems may be of two kinds, depending on the respective chromosome: R-gT if referred to chromosome R (or one of this “descendant”), or M-gT, in the alternative case.
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For a detailed description of this vector and of a closing related element, the Gödel-address, see [14].
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The number of six generations was arbitrarily determined and can, of course, be expanded in the future.
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Recently, the four gM’s modules were formatted as computational applications, being available for download in www.musmat.org.
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de Lemos Almada, C. (2015). Genetic Algorithms Based on the Principles of Grundgestalt and Developing Variation. In: Collins, T., Meredith, D., Volk, A. (eds) Mathematics and Computation in Music. MCM 2015. Lecture Notes in Computer Science(), vol 9110. Springer, Cham. https://doi.org/10.1007/978-3-319-20603-5_4
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