律學

樂律學（英語：Musical temperament）音樂學的重要組成部分，研究樂律產生，定量，測量，數學表達及相關自然屬性的交叉學科。以字義來說，西方所謂的「律學」（temperament）其實是為了解決畢式律所產生的不和諧八度所產生的「調整」，本身並沒有「規律」的意義。

範疇及爭議

律學是聲學、數學和音樂學的交叉學科，在中國由於史料不易取得，在《宋史・樂制三》中記載宋神宗言：「樂律絕學」。

西方圍繞着樂律學的爭議，從中世紀開始一直到現代仍然沒有停止。

參見

• 十二平均律
• 十二律
• 五度相生律
• 純律

參考資料

• 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) （頁面存檔備份，存於互聯網檔案館）
• 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. 

外部連結

• 律學的奇妙
• 中國古代科技成果：律學領先世界兩千多年
• 律學新說（明-朱載堉） 在線閱讀
• 用數學的觀點論述研究律學的三種途徑
• 三分損益法與五度相生律之比較 （頁面存檔備份，存於互聯網檔案館）
• 三分損益法和三分損益律猜想 （頁面存檔備份，存於互聯網檔案館）