增四度

File:Augmented fourth on C.png

关于这个音频文件播放十二平均律的增四度^{（帮助·信息）}

增四度（英文：Augmented fourth，简写：A4）指音数为3的音程，共有六个半音，是减五度的转位音程与等音音程，属于不协和。

英文中的Tritone为三全音之意，简写为TT，增四度与减五度的统称。

基本介绍[ | ]

File:图片2.png

两个呈增四度的正弦波的叠加波型，可见其不和谐之处

File:Notenbeispiel Quarten.gif

(File:Loudspeaker.svg 聆听) 完全四度 (a), 增四度 (b) 和减四度 (c)

本章节除了有特殊注明，否则增四度一律可以指减五度。

增四度于泛音列第一次出现为第十二-十七泛音。（或是也可以勉强的算为第七-第十泛音）

增四度的十二平均律比例为 $\sqrt{2}=2^{\frac{1}{2}}\approx 1.41421356237309504880168872421$ ，纯律则有 $\frac{25}{18}$ (音分569)^[1]^[2]、 $\frac{45}{32}$ (音分590)^[3]^[4]^[5]^[6]、 $\frac{10}{7}$ (音分617)^[1]^[3]^[7]。

由于纯律的比例两相乘于增四度无法达到完美的2，其缺点因此被凸显出来。

增四度的音效十分不好，所以中世纪-18世纪经常被称为魔鬼音^[8]^[9]，甚至在某些宗教还禁止使用。

由于增四度的十二平均律比例为 $\sqrt{2}$ ，所以两个增四度合起来即为完全八度。严格来讲，增四度+增四度应为增七度，增四度+减五度才是一个完全八度；但由于增七度与完全八度为等音音程，它们的音效是一样的。（对于纯律而言，以上叙述是不成立的）

常见用途[ | ]

音阶[ | ]

大调音阶中的下属音-导音，自然小音阶中下中音-上主音，和声小音阶下属音-导音、下中音-上主音皆为增四度。

于旋律小音阶上行中，中音-下中音、下属音-导音（或下主音）为增四度，下行时与自然小音阶相同。

解决[ | ]

File:Dominant seventh tritone resolution.png

简单的减五度、增四度解决

于和弦进行中，导音必须解决到主音，若有V级7或转位的和弦（有减五度或增四度包含在内），大部分都被解决到I级。

注：增四度在和弦进行中，是被禁止在同一个声部连续出现的。

参见[ | ]

完全四度
音程
完全五度

参考资料[ | ]

↑ ^1.0 ^1.1 Haluska, Ján (2003). The Mathematical Theory of Tone Systems, Pure and Applied Mathematics Series 262 (New York: Marcel Dekker; London: Momenta), p. xxiii. ISBN 0824747143. "7/5 septimal or Huygens' tritone, Bohlen-Pierce fourth", "10/7 Euler's tritone".
↑ Haluska (2003), p. xxiv. "25:18 classic augmented fourth".
↑ ^3.0 ^3.1 Partch, Harry. (1974). Genesis Of A Music: An Account of a Creative Work, Its Roots and Its Fulfillments, second edition, enlarged (New York: Da Capo Press): p. 69. ISBN 030671597X (cloth); ISBN 030680106X (pbk).
↑ Renold, Maria (2004). Intervals, Scales, Tones and the Concert Pitch C=128Hz, translated from the German by Bevis Stevens, with additional editing by Anna R. Meuss (Forest Row: Temple Lodge): p. 15–16. ISBN 1902636465.
↑ Haluska (2003), p. xxv. "36/25 classic diminished fifth".
↑ Helmholtz, Hermann von (2005). On the Sensations of Tone as a Physiological Basis for the Theory of Music, p. 457. ISBN 1419178938. "Cents in interval: 590, Name of Interval: Just Tritone, Number to an Octave: 2.0. [Cents:] 612, [Name:] Pyth.[agorean] Tritone, [per octave:] 2.0."
↑ Strange, Patricia and Patricia, Allen (2001). The contemporary violin: Extended performance techniques, p. 147. ISBN 0520224094. "...septimal tritone, 10:7; smaller septimal tritone, 7:5;...This list is not exhaustive, even when limited to the first sixteen partials. Consider the very narrow augmented fourth, 13:9....just intonation is not an attempt to generate necessarily consonant intervals."
↑ Drabkin, William. Tritone. Grove Music Online (subscription access). Oxford Music Online. [2008-07-21].
↑ Arnold, Denis (1983) « Tritone » in The New Oxford Companion to Music, Volume 1: A-J,Oxford University Press. ISBN 0-19-311316-3

[Haluska_xxiii-1] 1.0 ^1.1 Haluska, Ján (2003). The Mathematical Theory of Tone Systems, Pure and Applied Mathematics Series 262 (New York: Marcel Dekker; London: Momenta), p. xxiii. ISBN 0824747143. "7/5 septimal or Huygens' tritone, Bohlen-Pierce fourth", "10/7 Euler's tritone".

[Haluska-2] Haluska (2003), p. xxiv. "25:18 classic augmented fourth".

[Partch-3] 3.0 ^3.1 Partch, Harry. (1974). Genesis Of A Music: An Account of a Creative Work, Its Roots and Its Fulfillments, second edition, enlarged (New York: Da Capo Press): p. 69. ISBN 030671597X (cloth); ISBN 030680106X (pbk).

[Renold-4] Renold, Maria (2004). Intervals, Scales, Tones and the Concert Pitch C=128Hz, translated from the German by Bevis Stevens, with additional editing by Anna R. Meuss (Forest Row: Temple Lodge): p. 15–16. ISBN 1902636465.

[Haluska_xxv-5] Haluska (2003), p. xxv. "36/25 classic diminished fifth".

[Helmholtz-6] Helmholtz, Hermann von (2005). On the Sensations of Tone as a Physiological Basis for the Theory of Music, p. 457. ISBN 1419178938. "Cents in interval: 590, Name of Interval: Just Tritone, Number to an Octave: 2.0. [Cents:] 612, [Name:] Pyth.[agorean] Tritone, [per octave:] 2.0."

[Strange-7] Strange, Patricia and Patricia, Allen (2001). The contemporary violin: Extended performance techniques, p. 147. ISBN 0520224094. "...septimal tritone, 10:7; smaller septimal tritone, 7:5;...This list is not exhaustive, even when limited to the first sixteen partials. Consider the very narrow augmented fourth, 13:9....just intonation is not an attempt to generate necessarily consonant intervals."

[8] Drabkin, William. Tritone. Grove Music Online (subscription access). Oxford Music Online. [2008-07-21].

[9] Arnold, Denis (1983) « Tritone » in The New Oxford Companion to Music, Volume 1: A-J,Oxford University Press. ISBN 0-19-311316-3

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增四度

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