标题： 让·巴拉克的繁殖系列：数学术语中的研究与分类 显示英文标题

标题： Proliferating series by Jean Barraqué: a study and classification in mathematical terms

摘要： 巴拉克的扩展系列通过对经典序列主义概念的有趣转变，当构建序列时创造了一种新的不变量：而不是连续音符之间的音程，所保持不变的是在两个连续序列之间发生的音符排列，也就是说，序列中音符顺序的变换。 鉴于这种方法得到的音程多样性远大于经典序列主义，这为对序列方法感兴趣的作曲家提供了新的可能性。 在本文中，我们将从数学角度研究扩展系列提供的一些未被探索的可能性，这将使作曲家对它们更加熟悉，并可能促成将序列主义推向更高层次的作品的创作。 显示英文摘要

摘要： Barraqué's proliferating series give an interesting turn on the concept of classic serialism by creating a new invariant when it comes to constructing the series: rather than the intervals between consecutive notes, what remains unaltered during the construction of the proliferations of the given base series is the permutation of the notes which happens between two consecutive series, that is to say, the transformation of the order of the notes in the series. This presents new possibilities for composers interested in the serial method, given the fact that the variety of intervals obtained by this method is far greater than that of classic serialism. In this manuscript, we will study some unexplored possibilities that the proliferating series offer from a mathematical point of view, which will allow composers to gain much more familiarity with them and potentially result in the creation of pieces that take serialism to the next level.