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偏差音 .
音樂上的偏差音 (inharmonicity)是樂器的本性,代表樂器發出的泛音 頻率偏離其基本頻率 整數倍的特性。
Railsback曲線 鋼琴調音(調律)中,所有平均律 都需要微調,因為琴弦的剛性(stiffness)會產生偏差音。
1943年,Schuck和Young兩位科學家首次測得鋼琴的偏差音。相對於平均律的鋼琴偏差音見Railsback曲線圖[ 1] 。圖中顯示偏差音向鋼琴左右兩端擴大,偏離平均律的最大值約±30音分 ,差不多是一個半音的1/3。理論物理學家費曼 在1961年的書信中描述金屬線的剛性與琴弦頻率偏移之間的關係如下式。真實的頻率等於
f
(
1
+
π
2
E
A
2
μ
T
2
f
2
)
{\displaystyle f\left(1+{\frac {\pi }{2)){\frac {EA^{2}\mu }{T^{2))}f^{2}\right)}
其中f 是基頻;T 是弦的張力;A 是弦的截面積;E 是鋼的楊式模數 ;μ 是單位長度鋼的質量7.8 g/cm乘以單位截面積(單位是cm²)[ 2] 。這說明琴弦天生具有泛音偏高的本性。偏高的泛音導致鋼琴調音師調高了高音域的音高,同時調低了低音域的音高,而不按平均律[ 3] [ 4] 。
1962年,Harvey Fletcher等人表示:偏差音的重要性在於,它讓琴音聽起來更像鋼琴,帶有溫暖的特質。實驗也顯示:多數的演奏者較滿意憑聽覺調出的音。用儀器調出的音,聽起來感到高音域偏低,低音域又偏高。這是屬於人聽覺上的共同習慣性[ 3] 。
^ D.W. Martin and W.D. Ward (1961). Subjective evaluation of musical scale temperament in pianos, J. Acoust. Soc. Am. , v. 33, 582-585.
^ Bryner, J. C. (2009). Stiff-string theory: Richard Feynman on piano tuning, Phys. Today , v. 62, no. 12, p. 46.
^ 3.0 3.1 劉客養,初探鋼琴十二平均律調音 (页面存档备份 ,存于互联网档案馆 ).
^ 引用错误:没有为名为ref4
的参考文献提供内容
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