By a "scheme" of a musical canon, we mean the time and pitch displacement of each entering voice. When the time displacements are unequal, achieving consonant sonorities is especially challenging. Using a first-species theoretical model, we quantify the flexibility of schemes that Renaissance composers used or could have used. We craft an algorithm to compute this flexibility value precisely (finding in the process that it is an algebraic integer). We find that Palestrina consistently selected some of the most flexible schemes, more so than his predecessors, but that he by no means exhausted all feasible schemes. To add support to the model, we present two new compositions within the limits of the style utilizing unexplored canonic schemes. In the Online Supplement (attached via Papers with Code), we provide MIDI realizations of the musical examples and Sage code used in the numerical computations.

翻译：通过“模式”一词，我们指音乐卡农中各声部进入时的时间与音高偏移。当时间偏移量不相等时，实现协和音响效果尤为困难。采用一阶对位理论模型，我们量化了文艺复兴作曲家曾使用或可能使用的模式的灵活度。我们设计了一种算法以精确计算该灵活度值（并在此过程中发现其为一个代数整数）。我们发现帕莱斯特里纳始终选择一些最具灵活度的模式，其灵活度高于其前辈，但他绝未穷尽所有可行模式。为增强模型的可信度，我们创作了两首在风格限定内运用未探索卡农模式的新作品。在在线附录（通过Papers with Code附加）中，我们提供了音乐示例的MIDI实现及数值计算所使用的Sage代码。