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Inspired by Spinoza, [6] Taneyev developed a theory which covers and generalizes a wide range of advanced contrapuntal phenomena, including what is known to the english-speaking theorists as invertible counterpoint (although he describes them mainly using his own, custom-built terminology), by means of linking them to simple algebraic procedures.
In music theory, contrapuntal motion is the general movement of two or more melodic lines with respect to each other. [1] In traditional four-part harmony, it is important that lines maintain their independence, an effect which can be achieved by the judicious use of the four types of contrapuntal motion: parallel motion, similar motion, contrary motion, and oblique motion.
The principles of strict counterpoint constitute one of the fundamental components of Schenker's musical theory (see Schenkerian analysis).For Schenker, the study of counterpoint is the study of voice leading; in particular, contrapuntal theory is separate from and independent of harmonic theory, which is concerned with scale-steps (see Harmony).
Voice leading developed as an independent concept when Heinrich Schenker stressed its importance in "free counterpoint", as opposed to strict counterpoint. He wrote: All musical technique is derived from two basic ingredients: voice leading and the progression of scale degrees [i.e. of harmonic roots]. Of the two, voice leading is the earlier ...
Voice exchange is also used in Schenkerian analysis to refer to a pitch class exchange involving two voices across registers, one of which is usually the bass. In this sense, it is a common secondary structural feature found in the music of a wide variety of composers. [12]
Post-tonal music theory is the set of theories put forward to describe music written outside of, or 'after', the tonal system of the common practice period.It revolves around the idea of 'emancipating dissonance', that is, freeing the structure of music from the familiar harmonic patterns that are derived from natural overtones.
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice. Oxford and New York: Oxford University Press. ISBN 978-0-19-971435-3. van den Toorn, Pieter. 1975. "Some Characteristics of Stravinsky's Diatonic Music". Perspectives of New Music 14, no. 1. (Autumn-Winter): 104–138. Waters, Robert Francis. 2008.
In geometry, a point is an abstract idealization of an exact position, without size, in physical space, [1] or its generalization to other kinds of mathematical spaces.As zero-dimensional objects, points are usually taken to be the fundamental indivisible elements comprising the space, of which one-dimensional curves, two-dimensional surfaces, and higher-dimensional objects consist; conversely ...