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，簡寫：A4）指音數為3的音程，共有六個半音，是減五度的轉位音程與等音音程，屬於不協和。

英文中的Tritone為三全音之意，簡寫為TT，增四度與減五度的統稱。

基本介紹

File:圖片2.png

兩個呈增四度的正弦波的疊加波型，可見其不和諧之處

File:Notenbeispiel Quarten.gif

(File:Loudspeaker.svg 聆聽) 完全四度 (a), 增四度 (b) 和減四度 (c)

本章節除了有特殊註明，否則增四度一律可以指減五度。

增四度於泛音列第一次出現為第十二-十七泛音。（或是也可以勉強的算為第七-第十泛音）

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

由於純律的比例兩相乘於增四度無法達到完美的2，其缺點因此被凸顯出來。

增四度的音效十分不好，所以中世紀-18世紀經常被稱為魔鬼音^[8]^[9]，甚至在某些宗教還禁止使用。

由於增四度的十二平均律比例為 $\sqrt{2}$ ，所以兩個增四度合起來即為完全八度。嚴格來講，增四度+增四度應為增七度，增四度+減五度才是一個完全八度；但由於增七度與完全八度為等音音程，它們的音效是一樣的。（對於純律而言，以上敘述是不成立的）

常見用途

音階

大調音階中的下屬音-導音，自然小音階中下中音-上主音，和聲小音階下屬音-導音、下中音-上主音皆為增四度。

於旋律小音階上行中，中音-下中音、下屬音-導音（或下主音）為增四度，下行時與自然小音階相同。

解決

File:Dominant seventh tritone resolution.png

簡單的減五度、增四度解決

於和絃進行中，導音必須解決到主音，若有V級7或轉位的和絃（有減五度或增四度包含在內），大部份都被解決到I級。

註：增四度在和絃進行中，是被禁止在同一個聲部連續出現的。

參見

完全四度
音程
完全五度

參考資料

↑ ^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

目录

基本介紹

常見用途

音階

解決

參見

參考資料

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度\音數	0	1/2	1	3/2	2	5/2	3	7/2	4	9/2	5	11/2	6	13/2	7
一度	完全	增	倍增
二度	減	小	大	增	倍增
三度		倍減	減	小	大	增	倍增
四度				倍減	減	完全	增	倍增
五度						倍減	減	完全	增	倍增
六度							倍減	減	小	大	增	倍增
七度									倍減	減	小	大	增	倍增
八度											倍減	減	完全	增	倍增