中文摘要：

目的剖析古代东西方律学理论创立初期与数学的交互关系，比较其运用数学方法探索音乐规律的过程。方法采用原始文献考证法，运用数理逻辑进行分析。结果古代中国与希腊在律学计算方面具有显著差异：中国古代沿着追求社会和谐的道路，创制了其特有的乐律计算方法——三分损益法，并不断完善与改进这种计算方法以契合音乐实践的需求。古希腊毕达哥拉斯（前570-前496））学派依其“数是万物本原”的模式将音乐转化为数的关系，在追求宇宙和谐的道路上，通过更加深化的对数的关系的研究来揭示音乐声音的本质。结论古代东西方不同文明的音乐体系各拥有不同的价值观，二者虽动机不同，经历了不同路径，但都各自独立创立了乐律计算方法以及分析结果，它们共同反映了数学和声学方面的正确性。

英文摘要：

Aim To analyze the mutual relationship between mathematics and ancient temperament theory in both East and West at the initial period of its creation, point out how to use mathematics method to explore the rules of the temperament theory. Methods Original literature analyzing and researching, and the methods of mathematical logic. Results The calculations of pitch between aicient China and Greece are of significant difference ： in ancient China, the special computing method was created along the way to find the social harmony, continuing to perfect and improve the method to meet the demand of practical music. Following to the idea of ＂the number is the origin of everything＂, ancient Greek Pythagorean transformed the music to the relation of numbers, on the way of finding cosmic harmony, through the research of numbers to reveal the essence of music deeply. Conclusion Music sys- tems between different civilizations have different value positions. Although their aims are different and they experience different ways, all of them create calculation methods of pitch and analysis result, they mirror the modernization the ＂correctness＂ of mathmatics and music. Because of this, the calculation of pitch by ancient Chinese and ancient Greek from different civilizations can be formed and developed independently.