Pitch space is commonly represented using the face of a clock, in which the 12 pitch-classes are mapped onto the elements of ${\mathbb{Z}}_{12}$. Combining this form of representation with modular arithmetic results in the emergence of significant rotationally symmetric patterns, which can be used to generate pitch content and to effect a modulation between closely related collections within a composition. We generalize the situation to rotationally symmetric patterns with any number of intervals, and give necessary and sufficient conditions for when an interval pattern yields an analogous symmetry.

中文翻译：

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间隔周期延长

音调空间通常使用时钟的面来表示，其中12个音调类映射到 ${\mathbb{ž}}_{12}$。将这种形式的表示与模块化算术相结合会导致出现明显的旋转对称模式，该模式可用于生成音高内容并实现构图中紧密相关的集合之间的调制。我们将情况推广到具有任意数量的间隔的旋转对称模式，并为间隔模式何时产生相似对称性提供必要和充分的条件。