等音性的通用方法
A General Approach to Enharmonicism
- University of Missouri - Columbia（密苏里大学哥伦比亚分校）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文在句法音乐理论中提出通用等音性方法，形式化抽象结构，并建议用反射性和最大均匀性判断等音系统的实用性，从抽象数学角度论证标准等音系统的优先性。
AI中文摘要：
我们在句法音乐理论中提出了一种通用的等音性方法；也就是说，我们在不考虑任何声学因素的情况下，形式化了等音性的若干抽象结构。本文关注的结构由全音阶、半音阶和等音阶构成，我们试图提出一种通用的等音理论，该理论建立在Hook于2007年发表的《等音系统：调号、等音等价与全音性理论》中所提出的等音理论基础上。我们还提出，反射性和最大均匀性这两个标准可用于判断任意等音系统在音乐上是否实用。此外，我们认为，从脱离音高考虑和SES的传统声学构造的抽象数学视角来看，可以论证标准等音系统（SES）的优先选择是合理的。
英文摘要：
We propose a general approach to enharmonicism within syntactic music theory; that is, we formalize several abstract structures of enharmonicism without any acoustic considerations. The structures of concern to this paper are constructed from diatonics, chromatics, and enharmonics, and we seek to present a general enharmonic theory that builds upon Hook's enharmonic theory published in "Enharmonic Systems: A Theory of Key Signatures, Enharmonic Equivalence and Diatonicism" (2007). We also propose that the two criteria of reflection and maximal evenness can be used to determine whether an arbitrary enharmonic system is musically practical. Moreover, we argue that preferential treatment of the standard enharmonic system (SES) can be motivated from an abstract mathematical perspective divorced from pitch consideration and conventional acoustic constructions of SES.
