The function theory is the branch of music theory and belongs to the theory of harmony. It describes the relationships between the chords in major -minor tonal music. Hugo Riemann she developed in 1893. It was developed primarily by William Painter and Diether de la Motte and expanded.
The functional theory is used for music analysis. Common, but also unusual harmonic progressions can be determined and described on its basis. It relies listeners maintenance of certain sequences of harmonies advance (for example, cadences and sequences). Also can be viewed with their help, even the outline of longer pieces of music.
The function theory can be applied to the harmony of the music of the Baroque, Classical and Romantic. Also many harmonious relationships within the jazz and pop music can be recorded with the theory of functions. In jazz theory, however predominates the analysis according to the theory of stages and the chord scale theory. In popular music literature individual concepts of functional analysis and theory of stages are often used interchangeably. Both systems are integrated models for the description of harmonic relationships. From the context depends on which method is given preference.
(: 1st stage in the stage theory ) of this section in the function theory, a key, which manifests itself in a certain period of time when the tonic is considered. The dominant ( upper fifth, 5th level) and the subdominant ( fourth or fifth below, 4th level): To her, two other main functions, namely the next quint pure relatives join. The functions themselves are referred to in the theory of functions using letters, with major functions obtained uppercase and lowercase minor functions.
In addition to functions
Then there are the secondary functions that are available in the third interval to the main functions. For symbolic representation of the secondary functions of the main functions, a letter is appended.
The secondary functions include several groups:
- The parallels in Kleinterzabstand to the main function Main function in major: Parallel sound ( minor ) down - Tp, and Main function in a minor key: Parallel sound ( major) up - tp -
- The counter sounds in Großterzabstand Main function in major: Gegenklang ( in minor ) up -Tg, or Main function in a minor key: Gegenklang ( in major) down - tG -
- The mediant in wholesale or Kleinterzabstand up or down, which can not be formed out of gamut own tones and are achieved by Verdurung or Vermollung the main function or adrenal function.
Examples of parallels: Tp in C major is A minor. tP in A minor is C major. Examples of counter- sounds: Tg in C major is E minor. tG in A minor, F major. A mediant E major would be in C major: TG ( the addition function is verdurt ) it is another minor in C minor: tp (main and auxiliary function are vermollt ).
Vermollungen and Verdurungen is also available for each major function. They are always indicated by uppercase or lowercase letters ( the vermollte subdominant in a Dursystem is referred to, for example, with s instead of S).
Cadences, and modulations conclusions
The tonic is strengthened by cadences. The simplest cadences are DT ( authentic circuit) and ST ( plagal circuit). As a basic model for the full cadences cadence TSDT is usually assumed.
A transition from one key to another by diatonic, chromatic or enharmonic modulation in a factory instead of passage, the new key is valid as long as in the analysis as unconfirmed until an authentic, or more rarely, plagal cadence follows. Can a chord not only be understood as a function of the current, but also as a main function of the new key, one speaks of main intermediate functions. These include in particular the secondary dominant, which ever is possible only in the case of diatonic modulations.
Additives in the form of numbers
All symbols can be combined with additives in the form of numbers and letters. Superscript number of additions after the function name indicate additional tones. Written under the function symbol numbers refer to the bass note of the chord in the intervallic relationship to the root note of each function. Triads in normal position be written without additive.
The most common additives:
- On the dominant seventh chord (D7 )
- Seventh chords exist in the normal position ( to a triad occurs seventh) and in three inversions: 1st inversion = Quintsextstellung, 2nd inversion = Terzquartstellung, 3 reverse = Sekundstellung. The names indicate at what intervals to the lowest tone of the chord tones are the two that result in the Sekunddissonanz. In the name by the theory of functions, however, the superscript 7 is maintained, and is called instead the bass relative to the chord root. Thus, for the first reversal of a subscript 3 added because the third of the chord is in her normal position in the bass, for the second reversal a subscript 5 ( fifth in the bass), for the third reversal of a subscript 7 ( seventh in the bass). In the latter case, the seventh is only listed under the function symbol, since it is already clear that there is a seventh chord.
- The function theory knows the possibility that an additional sixth chord is added ( added sixth ajoutée ). This is referred to by 5 and 6 represents high. This chord is usually evaluated in the function theory as a subdominant. According to the stage theory is a seventh chord, stage II in Quintsextstellung.
- In addition, suspensions are noted. The fourth replaces the third of the dominant triad ( = fourth derivative ) and is then dissolved:
- Although the following example is apparently the functional progression T - T5 - D - T, the second chord is, however, interpreted as Quartsextvorhalt for subsequent, real dominant, as it is also resolved as follows:
- In a derivative action None the basic chord is added a ninth, the resolution immediately follows the octave:
Other signs and symbols
Function Harmonic Analysis of a Bach chorale
Although Bach was unaware of the function theory, his chorales can be described (within limits) with her. The following analysis raises (of course) no claim to completeness or accuracy. It is also only an interpretation of the chorale, others are quite possible. Good to see that the composition can be described because of the many small movements in the individual parts are very complicated vertically, so harmonious, which is due to a strong linear component. The function theory is this music really does not do justice as harmonic structures were thought at that time by the General Bass ago. Nevertheless, the functional harmonic analysis is common practice, even though they will quickly reach its limits in terms of clarity and completeness.
Sound sample of the analyzed chorale (Midi )
This analysis, however, is useless if it is not interpreted. Basically, the translation is in function symbols only a generalized view of the composed special case.
A starting point of interpretation is, for example, the description of harmonic drama: The first part modulated ( to repeat sign ) to the dominant, which would be interpreted as a well-known principle of the Sonata and the later sonata form. After the tonic was established at the beginning of the second part first ( the subdominant have a decisive share ), removed the set very far from her, the two condensed interim dominants offer the same train a new sound quality. After the longest break on the achieved Subdominantparallele the tonic re-established, is also striking that the harmonic motion is towards the end of a quiet, and the complete absence of secondary dominants smoothes the way to the final basic sound. Of particular note would be here at the end of the two-time closing phrase TSDT, and an emphasis ( through strong temporal extension ) as the dominant penultimate sound.
Another possible object of observation would be the treatment of reversals, in particular the voice leading of the bass: sevenths are invariably continued with a Sekundschritt down, thirds also have a schrittige environment, etc.
Not all chord relationships and progressions can be grasped with the help of function theory. Harmonic function takes only where it is designed at least in triad harmonies music, which is a key major or minor key basis. Therefore, the function theory is unsuitable as an instrument of analysis in so far as the music does not meet these conditions.
For example, polytonality and atonality in the 20th century music, and the music of the Renaissance with means of function theory are not well detected.
The pre-baroque and late medieval music ( Ars Nova ) works more like melodic or contrapuntal laws. The harmonic curve results from the rules of progression within a voice and the ratio of each two votes each other, not by a higher harmonic structure. However, the resulting sequence of harmonies is the origin of our later-developing harmony feeling.