An Exploration of Mathematical Principles of Musical Temperaments: A Case Study of Why the 12-equal-temperament Is Dominant
- Questioz Editor
- Aug 5, 2024
- 1 min read
Xiaowen A. Zheng
ABSTRACT
Most teen students are simply taught how to play instruments during middle or high school rather than being explained the basic mathematical principles behind the musical temperaments or musical terms like notes, chords, scales, dominant 7th, harmonics, major, minor, and so on. This tends to lead to confusion and frustration. In this article, the mathematical principles are interpreted in an easy-to-understand way to illustrate that the ultimate goal of music is to satisfy the human ear. It is a compromised result of how music originated, evolved, and developed given the physical constraint of human audibility and fundamental sound theory as well as the music-developing trends and demands. By comparing and contrasting the 4 major music temperaments: the Pythagorean tuning, the just intonation, the 1/4 comma meantone, and the 12-equal-temperament in mathematical methods, the article concludes why the 12-equal-temperament is dominant nowadays.
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