We study the problem of identifying repetitions under transposition and time-warp invariances in polyphonic symbolic music. Using a novel onset-time-pair representation, we reduce the repeating pattern discovery problem to instances of the classical problem of finding the longest increasing subsequences. The resulting algorithm works in $O(n^2\log n)$ time where n is the number of notes in a musical work. We also study windowed variants of the problem where onset-time differences between notes are restricted, and show that they can also be solved in $O(n^2\log n)$ time using the algorithm.

中文翻译：

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通过最长递增子序列发现和弦音乐中扭曲的重复模式

我们研究了在复调符号音乐中识别移调和时间扭曲不变性下的重复的问题。使用新的起始时间对表示，我们将重复模式发现问题简化为寻找最长递增子序列的经典问题的实例。结果算法适用于$哦(n^2\mathrm{日志}n)$时间，其中n是音乐作品中的音符数。我们还研究了音符之间开始时间差异受到限制的问题的窗口变体，并表明它们也可以在$哦(n^2\mathrm{日志}n)$ 使用算法的时间。