律学

乐律学（英语：Musical temperament）音乐学的重要组成部分，研究乐律产生，定量，测量，数学表达及相关自然属性的交叉学科。以字义来说，西方所谓的“律学”（temperament）其实是为了解决毕式律所产生的不和谐八度所产生的“调整”，本身并没有“规律”的意义。

范畴及争议

律学是声学、数学和音乐学的交叉学科，在中国由于史料不易取得，在《宋史・乐制三》中记载宋神宗言：“乐律绝学”^[1]。

西方围绕着乐律学的争议，从中世纪开始一直到现代仍然没有停止。

参见

• 十二平均律
• 十二律
• 五度相生律
• 纯律

参考资料

1. 沈冬. 宋代乐议研究——以《宋史．乐志》为中心 （页面存档备份，存于互联网档案馆）. 2021-01-31[2021-06-25]

• Music: a Mathematical Offering (mathematical perspective with two chapters on temperament) by Dave Benson
• Tuning And Temperament A Historical Survey (1951) by J. Murray Barbour
• Essay on Musical Temperament (part 2) by Prof. Fisher (Yale College)
• "Temperament" from A supplement to Mr. Chambers's cyclopædia (1753) （页面存档备份，存于互联网档案馆）
• Theory and practice of just intonation (1850) by Thomas Perronet Thompson
• Elements of musical composition: comprehending the rules of thorough bass and the theory of tuning (1812) by William Crotch
• An essay on temperament (1832) by J. Jousse
• Essay on musical intervals, harmonics, and the temperament of the musical scale, &c (1835) by Wesley Stoker B. Woolhouse
• Harmonics, or The philosophy of musical sounds (1759) by Robert Smith (1689-1768)
• Modern organ tuning : the how and why? by Hermann Smith (1824-1910)
• Piano Tuning: A Simple and Accurate Method for Amateurs by Jerry Cree Fischer
• The organ viewed from within : a practical handbook on the mechanism of the organ, with a chapter on tuning by John Broadhouse
• Construction, Tuning and Care of the Piano-forte (1887) by Edward Quincy Norton
• Regulation and Repair of Piano and Player Mechanism, Together with Tuning as Science and Art (1909) by William Braid White
• Modern piano tuning and allied arts (1917) by William Braid White (1878-1959)
• Biddle, Horace Peters. The Musical Scale. Oliver Ditson & Company. 1867.

外部链接

• 律学的奇妙^{[失效链接]}
• 中国古代科技成果：律学领先世界两千多年^{[永久失效链接]}
• 律学新说（明-朱载堉） 在线阅读
• 用数学的观点论述研究律学的三种途径^{[永久失效链接]}
• 三分损益法与五度相生律之比较 （页面存档备份，存于互联网档案馆）
• 三分损益法和三分损益律猜想 （页面存档备份，存于互联网档案馆）