Twelve-average rhythmic arithmetic

Zhu Zaiyu's greatest contribution to the world is that he created the law of twelve averages. This is a great revolution in musicology and music physics, and also a great invention in the history of world science. During the development of tonality in ancient China, scholars of all ages have been exploring how to realize tonality in music performance, but by the time of Zhu Zaiyu, no one had reached the peak of success, only Zhu Zaiyu had completely solved this problem, which was inseparable from musical arithmetic.

As a by-product of musical arithmetic, Zhu Zaiyu also solved the conversion method of different decimal places and summarized the related calculation rules. In the history of mathematics, these are great achievements. While studying tonality, Zhu Zaiyu also studied the evolution of weights and measures. He personally did the tired millet experiment to determine what the ancients called foot length. In order to determine the measurement standard, he measured the density of mercury, and the measurement result was quite accurate. He dialectically expounded the relationship between "the same method and the same quantity" in theory, which had a great influence on later generations.