用数学方法解析巴拉克的扩张序列，揭示其独特的音符排列不变性。
Proliferating series by Jean Barraqué: a study and classification in mathematical terms
- 以音符排列顺序不变为核心，重构序列生成规则。
- 相比传统序列主义，可生成更丰富的音程组合。
- 适合对序列音乐创新感兴趣的作曲家与音乐理论研究者。
巴拉克的扩张序列通过对经典序列主义的重新诠释，引入了一种新的构造不变量：在序列扩展过程中，保持不变的是相邻序列间音符排列的变换方式，而非连续音符间的音程。这一机制为作曲家提供了远超传统序列主义的音程多样性。本文从数学角度深入研究扩张序列中未被探索的可能性，旨在帮助作曲家更全面地理解其结构特征，并推动序列主义向更高层次发展。
原文摘要 · Abstract (English)
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.
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