论文标题
使用笛卡尔坐标系优化音乐和弦反演
Optimizing musical chord inversions using the cartesian coordinate system
论文作者
论文摘要
在古典音乐和任何当代音乐类型中，用于播放的音调元素或笔记都是相同的。一件给定实例的和弦的众多可能性使演奏一般而言，非常复杂且高级。该理论听起来很琐碎，但是该应用程序具有广泛的选择，每个选择都导致了不可或缺的结果，其特征是科学和音乐原理。和弦及其重要性是不言自明的。和弦是一起演奏的一堆音符。就科学家而言，这是一组音调频率响起，导致辅音/不和谐声音。众所周知，可以重新排列和弦的音符，以提出相同的和弦的各种声音（1），使作曲家/玩家可以选择最佳的和弦，以传达他们希望传达的情感。尽管有许多可能性，但科学认为，对于特定的音调运动，只有一种适当的声音。在这项研究中，我们试图通过考虑和弦在三维笛卡尔坐标系统中找到最佳声音，并进一步了解音乐理论中对数学的基本理解。
In classical music and in any genre of contemporary music, the tonal elements or notes used for playing are the same. The numerous possibilities of chords for a given instance in a piece make the playing, in general, very intricate, and advanced. The theory sounds quite trivial, yet the application has vast options, each leading to inarguably different outcomes, characterized by scientific and musical principles. Chords and their importance are self-explanatory. A chord is a bunch of notes played together. As far as scientists are concerned, it is a set of tonal frequencies ringing together resulting in a consonant/dissonant sound. It is well-known that the notes of a chord can be rearranged to come up with various voicings (1) of the same chord which enables a composer/player to choose the most optimal one to convey the emotion they wish to convey. Though there are numerous possibilities, it is scientific to think that there is just one appropriate voicing for a particular situation of tonal movements. In this study, we attempt to find the optimal voicings by considering chords to be points in a 3-dimensional cartesian coordinate system and further the fundamental understanding of mathematics in music theory.
