Harmonik

Harmonik (von agr. ἁρμονία harmonía „Ebenmaß“, „Harmonie“) ist ein umfassender Begriff aus der Musiktheorie. Sie beschäftigt sich mit der Ordnung des Klangs bzw. der Klangsprache in einem Musikstück oder -werk und berücksichtigt im Unterschied zu den horizontalen (zeitseriellen) Komponenten Rhythmik, Melodik bzw. Tonalität auch die vertikale (zeitgleiche) Komponente der Musik.

Harmonik wird traditionell im Fach Tonsatz an Musikhochschulen (dort als „Harmonielehre“), aber auch an Musikschulen und im Rahmen des Musikunterrichts an Gymnasien unterrichtet.

Begriffsgeschichte

In der Antike deckt sich der Begriff der Harmonik mit der Theorie der Tonsysteme (siehe Philolaos und Aristoxenos). Mit der Entwicklung der Mehrstimmigkeit engte sich die Bedeutung des Begriffs im abendländisch-europäischen Kulturraum mehr und mehr auf den gleichzeitigen Zusammenklang verschiedener Stimmen ein. In dieser engeren Bedeutung umfasst Harmonik alle Formen des Zusammenklangs von Musik, beginnend bei der frühen Mehrstimmigkeit des europäischen Mittelalters über die Musik des 18. Jahrhunderts mit ihrer Nutzung von Dissonanzen und den zunehmenden Gebrauch der Chromatik (zunächst als ausschmückende „Farbtupfer“) bis hin zu Klangstrukturen der Avantgarde. Dort wird Harmonik zum ersten Mal, etwa in der seriellen Musik, nicht mehr über Grundtöne konzipiert; dabei entsteht etwas Neuartiges, weil der Zusammenklang und die Linie aus den gleichen, zugrunde liegenden Reihenstrukturen gewonnen werden. Wird auch nicht-europäische Musik betrachtet, so kann es wünschenswert erscheinen, Einseitigkeiten und Grenzen, die sich in der europäischen Harmonik verfestigt hatten, zu überwinden und andernorts praktizierte Alternativen zu ihr aufzugreifen.

Die systematische Erfassung der Akkordgestalten und des tonalen Klangraumes im Bereich der dur-moll-tonalen Musik des 17. bis 19. Jahrhunderts wird durch die Harmonielehre behandelt.

Etymology and definitions

The term harmony derives from the Greek ἁρμονία harmonia, meaning "joint, agreement, concord", from the verb ἁρμόζω harmozō, "(Ι) fit together, join". Aristoxenus wrote a work entitled Elements of Harmony, which is thought the first work in European history written on the subject of harmony. In this book, Aristoxenus refers to previous experiments conducted by Pythagoreans to determine the relationship between small integer ratios and consonant notes (e.g., 1:2 describes an octave relationship, which is a doubling of frequency). While identifying as a Pythagorean, Aristoxenus claims that numerical ratios are not the ultimate determinant of harmony; instead, he claims that the listener's ear determines harmony.

Current dictionary definitions, while attempting to give concise descriptions, often highlight the ambiguity of the term in modern use. Ambiguities tend to arise from either aesthetic considerations (for example the view that only pleasing concords may be harmonious) or from the point of view of musical texture (distinguishing between harmonic (simultaneously sounding pitches) and "contrapuntal" (successively sounding tones)). According to A. Whittall:

The view that modern tonal harmony in Western music began in about 1600 is commonplace in music theory. This is usually accounted for by the replacement of horizontal (or contrapuntal) composition, common in the music of the Renaissance, with a new emphasis on the vertical element of composed music. Modern theorists, however, tend to see this as an unsatisfactory generalisation. According to Carl Dahlhaus:

Descriptions and definitions of harmony and harmonic practice often show bias towards European (or Western) musical traditions, although many cultures practice vertical harmony. In addition, South Asian art music (Hindustani and Carnatic music) is frequently cited as placing little emphasis on what is perceived in western practice as conventional harmony; the underlying harmonic foundation for most South Asian music is the drone, a held open fifth interval (or fourth interval) that does not alter in pitch throughout the course of a composition. Pitch simultaneity in particular is rarely a major consideration. Nevertheless, many other considerations of pitch are relevant to the music, its theory and its structure, such as the complex system of Ragas, which combines both melodic and modal considerations and codifications within it.

So, intricate pitch combinations that sound simultaneously do occur in Indian classical music – but they are rarely studied as teleological harmonic or contrapuntal progressions – as with notated Western music. This contrasting emphasis (with regard to Indian music in particular) manifests itself in the different methods of performance adopted: in Indian Music, improvisation takes a major role in the structural framework of a piece, whereas in Western Music improvisation has been uncommon since the end of the 19th century. Where it does occur in Western music (or has in the past), the improvisation either embellishes pre-notated music or draws from musical models previously established in notated compositions, and therefore uses familiar harmonic schemes.

Emphasis on the precomposed in European art music and the written theory surrounding it shows considerable cultural bias. The Grove Dictionary of Music and Musicians (Oxford University Press) identifies this clearly:

Yet the evolution of harmonic practice and language itself, in Western art music, is and was facilitated by this process of prior composition, which permitted the study and analysis by theorists and composers of individual pre-constructed works in which pitches (and to some extent rhythms) remained unchanged regardless of the nature of the performance.

Perception

The harmonious major triad is composed of three tones. Their frequency ratio corresponds approximately 6:5:4. In real performances, however, the third is often larger than 5:4. The ratio 5:4 corresponds to an interval of 386 cents, but an equally tempered major third is 400 cents and a Pythagorean third with a ratio of 81:64 is 408 cents. Measurements of frequencies in good performances confirm that the size of the major third varies across this range and can even lie outside it without sounding out of tune. Thus, there is no simple connection between frequency ratios and harmonic function.

A number of features contribute to the perception of a chord's harmony.

Tonal fusion

Tonal fusion contributes to the perceived consonance of a chord, describing the degree to which multiple pitches are heard as a single, unitary tone. Chords which have more coinciding partials (frequency components) are perceived as more consonant, such as the octave and perfect fifth. The spectra of these intervals resemble that of a uniform tone. According to this definition, a major triad fuses better than a minor triad and a major-minor seventh chord fuses better than a major-major seventh or minor-minor seventh. These differences may not be readily apparent in tempered contexts but can explain why major triads are generally more prevalent than minor triads and major-minor sevenths are generally more prevalent than other sevenths (in spite of the dissonance of the tritone interval) in mainstream tonal music.

In organ registers, certain harmonic interval combinations and chords are activated by a single key. The sounds produced fuse into one tone with a new timbre. This tonal fusion effect is also used in synthesizers and orchestral arrangements; for instance, in Ravel's Bolero #5 the parallel parts of flutes, horn and celesta resemble the sound of an electric organ.

Roughness

When adjacent harmonics in complex tones interfere with one another, they create the perception of what is known as "beating" or "roughness". These precepts are closely related to the perceived dissonance of chords. To interfere, partials must lie within a critical bandwidth, which is a measure of the ear's ability to separate different frequencies. Critical bandwidth lies between 2 and 3 semitones at high frequencies and becomes larger at lower frequencies. The roughest interval in the chromatic scale is the minor second and its inversion, the major seventh. For typical spectral envelopes in the central range, the second roughest interval is the major second and minor seventh, followed by the tritone, the minor third (major sixth), the major third (minor sixth) and the perfect fourth (fifth).

Familiarity

Familiarity also contributes to the perceived harmony of an interval. Chords that have often been heard in musical contexts tend to sound more consonant. This principle explains the gradual historical increase in harmonic complexity of Western music. For example, around 1600 unprepared seventh chords gradually became familiar and were therefore gradually perceived as more consonant.

Individual characteristics such as age and musical experience also have an effect on harmony perception.

Neural correlates of harmony

The inferior colliculus is a mid-brain structure which is the first site of binaural auditory integration, processing auditory information from the left and right ears. Frequency following responses (FFRs) recorded from the mid-brain exhibit peaks in activity which correspond to the frequency components of a tonal stimulus. The extent to which FFRs accurately represent the harmonic information of a chord is called neural salience, and this value is correlated with behavioral ratings of the perceived pleasantness of chords.

In response to harmonic intervals, cortical activity also distinguishes chords by their consonance, responding more robustly to chords with greater consonance.

Siehe auch

• Harmonik (Hans Kayser)
• Harmonische Teilung
• Sphärenharmonie

Weblinks

Commons: Harmonik – Sammlung von Bildern, Videos und Audiodateien

Wikiquote: Harmonik – Zitate

• Harmonie und Konsonanz