Improvement of Piano Tuning in Music Education---Using Classical Temperaments instead of 12 Equal Temperament

12等律有400分的大三度，比纯大三度高14分，听起来没有音乐性，有嘈杂的节拍。本研究旨在改进现代键盘调音的主要三和弦，在对皮塔格拉斯律、意通律、韦克迈斯特律、柯恩伯格律、巴赫-莱曼律和瓦罗蒂-杨律等6种古典律进行理论思考和比较听力测试后，引入了杨律作为古典律中的佼佼者。现代键盘乐器在古典音律中调音的困难在于钢琴弦的不和谐性。基音的音高与较低八度的2^泛音并不严格一致<nd>，理论上相同音符的频率差异会带来不舒服的节拍。经过多次试验，钢琴成功地调整在年轻的气质与最低八度拉伸。钢琴上的扬三和弦声音和谐，并根据音调的变化而变化其颜色。表<th><th>中示出了从A1到最高A7的基本调音八度音阶中的每4^和5^间隔的每秒拍数和泛音百分率（包括不和谐性）。

12 equal temperament has 400 cent major 3rd witch is 14 cent higher than pure major 3rd and sounds unmusically with noisy beats. In this research to improve major triads of the modern keyboard tuning, Young temperament is introduced as the best of the classical others, after the theoretical consideration and comparative hearing tests of the 6 classical temperaments such as Pytagorean, meantone, Werkmaister, Kirnberger, Bach-Lehmann and Varotti-Young temperaments. The difficulty of modern keyboard instruments to tune in classical temperament is inharmonicity of the piano strings. The pitch of the fundamental tone does not strictly coincide with the 2^<nd> overtone of the lower octave and the difference of the frequency of the theoretically same notes brings uncomfortable beats. After many trials the piano was successfully tuned in Young temperament with minimum octave stretch. The Young triad on the piano sounds harmonically and varies its color according to the change of tonality. The number of beats per second of every 4^<th> and 5^<th> intervals in the fundamental tuning octave and overtone cent rate (including inharmonicity), of Al to the highest A7 are showed in the tables.