论文标题
对“我一生中的谐波结构”的几何分析
A Geometric Analysis Of The Harmonic Structure of "In My Life"
论文作者
论文摘要
在我们的书（数学和音乐：构图，感知和表演）之后，第二版，CRC出版社，2020年---出版了，我们发现了一个引人注目的例子，说明了托尼兹在分析甲壳虫乐队歌曲的谐波结构“我一生中”的重要性。我们的Tonnetz分析将说明歌曲中众多和弦进展的高度结构化的几何逻辑。频谱图为我们提供了一种可视化和弦谐波及其与语音领先的联系的方法。我们还将描述歌曲和弦进步的有趣的谐音节奏。许多谐波节奏都很好地适应了几何描述。
After our book---Mathematics and Music: Composition, Perception, and Performance, 2nd edition, CRC Press, 2020---was published, we found a striking example of the importance of the Tonnetz for analyzing the harmonic structure of The Beatles' song, "In My Life." Our Tonnetz analysis will illustrate the highly structured geometric logic underlying the numerous chord progressions in the song. Spectrograms provide a way for us to visualize chordal harmonics and their connection with voice leading. We shall also describe the interesting harmonic rhythms of the song's chord progressions. A lot of this harmonic rhythm lends itself well to a geometric description.
