弹性泛音：一种具有‘完美五度’的十二平均音音乐系统
Elastic overtones: an equal temperament 12 tone music system with "perfect" fifths
AI总结：
本文提出一种基于‘完美五度’的十二平均音音乐系统，通过调整谐波结构和八度定义，实现与纯律相似的音乐品质，同时保留十二平均音的灵活性和调制能力。
摘要：
十二等分八度调音的不可行性源于数学事实：2×2^(7/12)≠3，即五度的第二泛音无法精确匹配基音的第三泛音。这进一步源于西方音乐的整数谐波结构，以及八度间隔作为频率倍数的基本性质，这一性质源自乐器振动元件近似为一维的物理特性。在电子音乐时代，可以放松上述假设，构建一个类似的音乐系统，其中标准音乐系统的全部结构特性得以保持，但谐波不再是基频的整数倍，八度也不再是频率的2倍因子。这现在允许构建一个可移植的十二等分音音乐系统，其中五度的第二泛音精确匹配基音的第三泛音。该系统的增强谐波特性在近似程度上恢复了纯律的音乐特性，同时通过构造保留了十二平均音的所有灵活性和调制能力。
英文摘要：
The impossibility of a transposable 12 semitone tuning of the octave arises from the mathematical fact that $2 \times 2^{7/12} \neq 3$ i.e., the second harmonic of the fifth can not exactly match the third harmonic of the fundamental. This in turn, stems from the whole number harmonic structure of western music, and the subsequent fundamental character of the octave interval as multiples of 2 in frequency, a property inherited by our music system from the physics of instruments with vibrating elements being to a good approximation one dimensional. In the current era of electronic music, one can relax the above assumptions to construct an analogous music system where all the structural properties of the standard music system are preserved, but where harmonics are not whole number multiples of the fundamental frequency, and the octave is no longer a factor of 2 in frequency. This now allows to construct a transposable 12 semitone music system where the second harmonic of the fifth exactly matches the third harmonic of the fundamental. The enhanced harmonic qualities of this system recover to a good approximation the musical qualities of Just Intonation, whilst retaining by construction all the versatility and modulating ability of 12TET.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
