協和音と不協和音
出典: フリー百科事典『ウィキペディア（Wikipedia）』
協和音（きょうわおん）、および不協和音（ふきょうわおん）とは、和音を響きの安定度で分類するときに用いられる音楽用語である。もっとも単純には、協和音は「きれいな和音」、不協和音は「濁った和音」と説明される。たびたび見受けられる誤解が、不協和音を「不快な」和音として理解することである。今日最も一般的に聴かれている不協和音は、決して「不快な」和音ではない。特に「不快な」和音を表す言葉に、「カコフォニー」という別の専門用語がある。
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[編集] 協和音
協和音の定義にはさまざまな説がある。
- 周波数比：ピタゴラスによると、和音を構成する音の周波数の比が簡単な整数比（またはその近似値）であれば協和音であるとされる。
- 倍音の一致：ヘルムホルツによると、より多くの倍音が一致する音同士からなる和音は協和音である。この定義に従えば、和音を構成する音の音程のみならず、音波のスペクトルや、音量、音価なども協和音の定義にかかわることになる。
- Fusion or pattern matching: fundamentals may be perceived through pattern-matching of the separately analyzed partials to a best-fit exact-harmonic template (Gerson & Goldstein, 1978) or the best-fit subharmonic (Terhardt, 1974). Or harmonics may be perceptually fused into one entity, with consonances being those intervals which are more likely to be mistaken for unisons, the perfect intervals, because of the multiple estimates of fundamentals, at perfect intervals, for one harmonic tone (Terhardt, 1974). By these definitions inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams, 1983). For some of these definitions neural-firing supplies the data for pattern-matching, see directly below (e.g., Moore, 1989; pp.183-187; Srulovicz & Goldstein, 1983).
- Period length or neural-firing coincidence: with the length of periodic neural-firing created by two or more wave-forms, lower simple numbers creating shorter or common periods or higher coincidence of neural-firing and thus consonance (Patternson, 1986; Boomsliter & Creel, 1961; Meyer, 1898; Roederer, 1973, p.145-149). Pure tones cause neural-firing exactly with the period or some multiple of the pure tone.
- Critical band: Consonances are pitches farther apart than their critical bands.
古典的であり、なおかつ現代でも最も広く受け入れられている音楽理論に従えば、以下の音程が協和音程と呼ばれる。
不完全協和音程は、かつては不協和音に分類されている時代があった。 協和音は強拍、弱拍を問わず、また準備をする必要もなく、自由に使うことができる。
Polyphonic cadences, requiring at least two voices, were created by successive dyads, the first an imperfect consonance on a weak beat, the second a perfect consonance on a strong beat, such as a major sixth moving to an octave (for instance, the major (imperfect) sixth D-B followed by the perfect octave C-C').
[編集] 参考文献
- Burns, Edward M. (1999). "Intervals, Scales, and Tuning", The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0122135644.
[編集] 不協和音
古典的な音楽理論では、不協和音とは「不安定」な状態であり、「安定」した協和音への解決が必要だとされる。 調和・不調和の語は両方とも和声、和音、音程に用いられ、メロディ、調性に拡張され、リズムと拍子にも用いられる。調和・不調和についての考え方を理解するのには、物理的・神経学上の事実が重要であるが、不調和の定義は文化的に条件付けられる。すなわち、調和・不調和の定義、および不調和と関係する音楽上の約束事は、音楽様式、伝統および文化により大きく異なる。しかしながら、不調和・調和・解決の根本概念は、メロディー・和声・調性の概念を持っているすべての音楽の伝統に存在する。
ミュージシャンや作家達が不協和音やそれに類する言葉を厳格もしくは神経質に定義づけた意味で使いつつも、しばしば非公式的または隠喩的(例えば「リズム的な不協和音」など)に用いることもまた混乱を生み易い理由といえる。多くのミュージシュンや作曲家にとって、不協和音とその解決に対する根本的な考え方というのものは、彼らの音楽に対する様々な考え方そのものを強く示すような重大な物である。
Despite the fact that words like "unpleasant" and "grating" are often used to explain the sound of dissonance, in fact all music with a harmonic or tonal basis — even music which is perceived as generally harmonious — incorporates some degree of dissonance. The buildup and release of tension (dissonance and resolution), which can occur on every level from the subtle to the crass, is to a great degree responsible for what many listeners perceive as beauty, emotion, and expressiveness in music.
Brief audio (MIDI) musical examples of the interaction and effect of consonance and dissonance upon each other can be found here: "The effect of context on dissonance'" and here: The role of harmony in music".
[編集] 不協和音と音楽様式
ある音楽様式を理解するためには、その様式の中ではどのような和音が不協和音と定義されているか、またその不協和音はどのように扱われているかを検討することが、きわめて有意義である。For instance, in the common practice period, harmony is generally governed by chords, which are collections of notes generally considered to be consonant (though even within this harmonic system there is a hierarchy of chords, with some considered relatively more consonant and some relatively more dissonant). Any note that does not fall within the prevailing harmony is considered dissonant. Particular attention is paid to how dissonances are approached (approach by step is less jarring, approach by leap more jarring), even more to how they are resolved (almost always by step), to how they are placed within the meter and rhythm (dissonances on stronger beats are considered more forceful and those on weaker beats less vital), and to how they lie within the phrase (dissonances tend to resolve at phrase's end). In short, dissonance is not used willy-nilly but is used in a very careful, controlled, and well circumscribed way. The subtle interplay of different levels of dissonance and resolution is vital to understanding the tonal and harmonic language of this period.
[編集] 西洋音楽における不協和音の歴史
不協和音は、伝統、文化、スタイル、時代によってさまざまな捉らえられ方をしている。
ルネサンス音楽の時代にあっては、完全四度は強い不協和音とみなされ、直ちに解決されるべきだとされた。不完全協和音程はregola delle terze e seste （三度と六度の規則）により、各々の声部の順次進行によって完全音程に解決されるべきとされた。(ダールハウス 1990, p.179). Anonymous 13 allowed two or three, the Optima intorductio three or four, and Anonymous 11 (15th century) four or five successive imperfect consonances. By the end of the 15th century imperfect consonances where no longer "tension sonorities" but, as evidence by the allowance of their successions argued for by Adam von Fulda, but independent sonorities, according to Gerbert (vol.3, p.353), "Although older scholars once would forbid all sequences of more than three or four imperfect consonances, we who are more modern allow them." (ibid, p.92)
In the common practice period all dissonances were required to be prepared and then resolved, occurring on weak beats and quickly giving way or returning to a consonance. There was also a distinction between melodic and harmonic dissonance. Dissonant melodic intervals then included the tritone and all augmented and diminished intervals. Dissonant harmonic intervals included:
このように、西洋音楽の歴史は、きわめて限られた少数の協和音を定義するところから、やがてその定義をより広く広げていく歴史だった、と見ることができる。初期の西洋音楽では、低次倍音のみが協和音程とされた。時代が進むと、より高次の倍音も協和音程とみなされるようになった。この結果、アルノルト・シェーンベルクら20世紀の作曲家達の言うところの、「不協和音の解放」という概念に至ることとなった。20世紀前半のアメリカの作曲家ヘンリー・カウウェルは、トーン・クラスターは高次の倍音の集合体であるとみなしていた。
Despite the fact that this idea of the historical progression towards the acceptance of ever greater levels of dissonance is somewhat oversimplified and glosses over important developments in the history of western music, the general idea was attractive to many 20th-century modernist composers and is considered a formative meta-narrative of musical modernism.
One example of imperfect consonances previously considered dissonances in Guillaume de Machaut's "Je ne cuit pas qu'onques":
Xs mark thirds and sixths. Guillaume de Machaut's "Je ne cuit pas qu'onques".（英語版のフェアユース画像による楽譜）
バロック時代の不協和音の例:
A sharply dissonant chord in Bach's Well-Tempered Clavier, Vol. I (Preludio XXI)（英語版のフェアユース画像による楽譜）
古典時代の不協和音の例:
Dissonance in Mozart's Adagio and Fugue in C Minor, K. 546.（英語版のフェアユース画像による楽譜）
One example of modernist dissonance:
[編集] 不協和音の客観的原理
Musical styles are similar to languages, in that certain physical, physiological, and neurological facts create bounds that greatly affect the development of all languages. Nevertheless, different cultures and traditions have incorporated the possibilities and limitations created by these physical and neurological facts into vastly different, living systems of human language. Neither the importance of the underlying facts, nor the importance of the culture in assigning a particular meaning to the underlying facts, should be minimized.
例えば、同時に同じ音色でわずかに異なった周波数の2つの音が鳴ると、ワウワウワウというようなビート音がはっきり聞こえる。 ある音楽では、これが好ましくない(「はずれている」)と考えて、この効果を排除するために多大な努力を払う。 他の音楽では、この音が魅力的な音色であると考えて、このちょっとした「荒さ」を特徴として持つ楽器を作成するために同様の努力を払う。
Here are some of the physical, physiological, and neurological facts that influence the idea of dissonance in all musical languages:
- In general, for two pitches that are quite close in frequency, the closer the frequencies of two pitches the more "roughness" there is in the resulting composite waveform. As two pitches approach each other they begin to produce beat oscillations, which are caused when the two pitches cause interference, or reinforce and cancel each others amplitudes. Most listeners experience these beat oscillations and interference as a roughness in the sound that is unpleasant or dissonant. The roughness increases to a certain point as frequencies of the two pitches become closer together, reaching a high point of roughness, then decreasing as the frequencies become perceptually indistinguishable.
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- Two pitches moving from the interval of a Major 2nd to a unison：This file illustrates the roughness and beat oscillations that gradually reduce as the interval moves towards the unison.
- うまく聞けない場合は、サウンド再生のヒントをご覧ください。
- Frequency ratios: ratios of higher simple numbers are more dissonant than those which are lower (Pythagoras).
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- Two diverging sinusoid-like tones：The sinusoidal-like tones are filtered triangle waves, which have strong fundamentals, no even overtones (at 2x the fundamental frequency, 4x, 6x, and so on) and highly attenuated odd overtones (at 3x, 5x, 7x, and so on).
- うまく聞けない場合は、サウンド再生のヒントをご覧ください。
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- Two diverging tones with sawtooth waveform：The sawtooth wave has strong overtones, both even and odd, which make some points of dissonance and consonance more audible.
- うまく聞けない場合は、サウンド再生のヒントをご覧ください。
The physical basis for Pythagoras's observation can be seen in the spectral analysis above and heard in the accompanying sound file. At the points where the ratios of the frequencies of the tones are more simple (indicated by arrows near the top of the graph), the overtones as observed in the spectral analysis are more ordered and simple. Most listeners perceive the tone of the interval at these points to be more "pure" or "harmonious".
By contrast, when the ratios of the frequencies are not simple, the overtone situation appears complex and chaotic in the spectral analysis. Most listeners perceive the intervals at these points to be "rougher" or more "disharmonious".
In human hearing, the varying effect of these different ratios may be perceived by one of these mechanisms:
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- Fusion or pattern matching: fundamentals may be perceived through pattern-matching of the separately analyzed partials to a best-fit exact-harmonic template (Gerson & Goldstein, 1978) or the best-fit subharmonic (Terhardt, 1974) or harmonics may be perceptually fused into one entity, with dissonances being those intervals which are less likely to be mistaken for unisons, the imperfect intervals, because of the multiple estimates, at perfect intervals, of fundamentals, for one harmonic tone (Terhardt, 1974). By these definitions inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams, 1983). For some of these definitions neural-firing supplies the data for pattern-matching, see directly below (e.g., Moore, 1989; pp.183-187; Srulovicz & Goldstein, 1983).
- Period length or neural-firing coincidence: with the length of periodic neural-firing created by two or more wave-forms, higher simple numbers creating longer periods or lesser coincidence of neural-firing and thus dissonance (Patternson, 1986; Boomsliter & Creel, 1961; Meyer, 1898; Roederer, 1973, p.145-149). Pure tones cause neural-firing exactly with the period or some multiple of the pure tone.
- Dissonance is also then defined by the amount of beating between non-common harmonics or partials (collectively overtones) (Helmholtz, 1877/1954). Terhardt (1984) calls this "sensory dissonance". By this definition dissonance is dependent not only on the quality of the interval between two notes, but the harmonics and thus sound quality (timbre) of those notes themselves.
- Dissonances are pitches that fall within each other's critical bands.
The strongest homophonic (harmonic) cadence, the authentic cadence, dominant to tonic (D-T, V-I or V7-I), is in part created by the dissonant tritone created by the seventh, also dissonant, in the dominant seventh chord which precedes the tonic.
[編集] 関連項目
[編集] 参考文献
- Burns, Edward M. (1999). “Intervals, Scales, and Tuning”, The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0122135644.
- Dahlhaus, Carl. Gjerdingen, Robert O. trans. (1990). Studies in the Origin of Harmonic Tonality. Princeton University Press. ISBN 0691091358.
[編集] 外部リンク
- Atlas of Consonance
- Babies react: Tonality and dissonance/consonance — News clipping
- Tonalsoft Encyclopaedia of Tuning
- Consonance and Dissonance — Index to Notes by David Huron at Ohio State University School of Music
- The Keyboard Tuning of Domenico Scarlatti
- Natural forces in the evolution of the Scale
- Role of the drone in the evolution of counterpoint & harmony
- Stages in the Evolution of Music
[編集] 参考文献
- Sethares, W. A. (1993). "Local consonance and the relationship between timbre and scale". Journal of the Acoustical Society of America, Vol. 94, Pt. 1, p. 1218. (A non-technical version of the article is available at [1])
- Tenney, James. (1988). A History of "Consonance" and "Dissonance". White Plains, NY: Excelsior, 1988; New York: Gordon and Breach, 1988.
- Readings & Essays: On the Origin of Music, New 2004 Book — Bob Fink. Reviews; Review chapters available: green@webster.sk.ca — One of only 3 full-length English books on music origins) ISBN 0912424141.
