Variable functions |
Variable functions (secondary, local functions) – modal functions, “contradictory to the main modal setting” (Yu. N. Tyulin). During the development of music prod. the tones of the mode (including the fundamental tones of the chords) enter into diverse and complex relationships with each other and with a common tonal center. At the same time, any quartic-fifth ratio of tones distant from the center generates a local modal cell, where the tone connections imitate the tonic-dominant (or tonic-subdominant) connections of the main. fret cell. Remaining subordinate to the common tonal center, each of the tones can temporarily take on the function of a local tonic, and the one lying a fifth above it can, respectively, be dominant. A chain of secondary modal cells arises, in which contradictory fundamentals are realized. fret installation of gravity. The elements of these cells perform P. f. So, in C-dur, the tone c has a main. stable modal function (prima tonic), but in the process of harmonic. shift can become both a local (variable) subdominant (for the tonic g) and a local dominant (for the variable tonic f). The emergence of a local function of a chord can affect its melodic character. figuration. The general principle of P. f .:
Yu. N. Tyulin calls all local supports (in the diagram – T) side tonics; gravitating to them P. f. (in the diagram – D) – respectively, side dominants, extending this concept to diatonic. chords. Unstable P. t. can be not only dominant, but also subdominant. As a result, all tones are diatonic. the fifth series form complete (S – T – D) modal cells, except for the edge tones (in C-dur f and h), since the reduced-fifth ratio only under certain conditions is likened to a pure-fifth. The complete scheme of the main and P. t. see column 241 above.
In addition to the aforementioned harmonies P. f., melodic is formed in the same way. P. f. With diatonic introductory tones, complication and enrichment occurs due to
changes in the value of tones adjacent to the given above and below:
(for example, the sound of the III degree can become the introductory tone to II or IV). With alteration introductory tones, characteristic elements of related keys are introduced into the system of the main key:
Theory of P. f. expands and deepens the understanding of the connections of chords and keys. Following. excerpt:
J. S. Bach. The Well-Tempered Clavier, Volume I, Prelude es-moll.
the culminating Neapolitan harmony, on the basis of the variability of functions, also performs the local function of the Fes-dur tonic. This makes it possible to bring into es-moll the melody that is absent in this key. moves ces-heses-as (es-moll should be ces-b-as).
Secondary dominant (ko II st.) a-cis-e (-g) in C-dur from the standpoint of the theory of P. f. turns out to be alteration-chromatic. pure diatonic variant. secondary dominant (to the same degree) a-c-e. As a variable-functional strengthening of the multidimensionality of the harmonic. structure, the origin of polyfunctionality, polyharmony and polytonality is interpreted.
The origins of the theory of P. f. date back to the 18th century. Even J.F. Rameau put forward the idea of ”imitation of the cadence”. So, in a typical sequential sequence VI – II – V – I, the first binomial, according to Rameau, “imitates” the turnover V – I, that is, the cadence. Subsequently, G. Schenker proposed the term “tonicization” of a non-tonic chord, designating with it the tendency of each of the steps of the mode to turn into a tonic. M. Hauptmann (and after him X. Riemann) in the analysis of harmonics. cadences T – S – D – T saw the desire of the initial T to become dominant for S. Riemann’s inattention to functional processes on the modal periphery – beings. the omission of the functional theory, a cut and caused the need for the theory of P. f. This theory was developed by Yu. N. Tyulin (1937). Similar I. V. Sposobin also expressed ideas (distinguishing between “central” and “local” functions). Theory of P. f. Tyulin reflects the psychological. features of perception: “Evaluation of perceived phenomena, in particular chords, changes all the time depending on the context being created.” In the process of development, there is a constant reassessment of the previous in relation to the present.
References: Tyulin Yu. N., Teaching about harmony, v. 1, L., 1937, M., 1966; Tyulin Yu. H., Rivano N. G., Theoretical Foundations of Harmony, L., 1956, M., 1965; them, Textbook of harmony, M., 1959, M., 1964; Sposobin I. V., Lectures on the course of harmony, M., 1969.
Yu. N. Kholopov
