Algorithmen zur Satztechnik und ihre Anwendung auf die Analyse

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Title: Algorithmen zur Satztechnik und ihre Anwendung auf die Analyse
Other Titles: Algorithms for Compositional Technique and their Application to Analysis
Authors: Prey, Stefan
Thesis advisor: Apl. Prof. Dr. Joachim Stange-Elbe
Thesis referee: Prof. Dr. Hartmuth Kinzler
Abstract: In the music from 1500 to 1900 the form of a theme and its imitations depend on each other. The principles of this dependency are determined by algorithms. These algorithms help to analyse works of Josquin, Monteverdi, Bach, Mozart, Brahms, and others. In this context the publications of Zarlino, Taneyev, Rovenko und Mazzola are taken into account. Rules for canons to a given entry scheme are determined by a classification of melodical progressions or progression combinations. The method is enlarged to suspensions and to themes with several strettos. The approach is formalised according to Taneyev. By this formalisation it is proved, that Taneyev's compositional techniques are sufficient to construct all finite and infinite canons in similar motion to a given entry scheme. In the special case of canons with an entry distance of one note the canon rules of Rovenko result from Taneyev's theory. The formalisation makes possible to derive the rules for canons to a cantus firmus. The rules for canons with more than two parts are determined just as for themes with different strettos. Canon rules are represented by graphs. The graphs are constructed by an algorithm, which has been implemented as a computer programme. The three-part basic scheme is derived from criteria for contrapunctically favourable entry schemes. The four-part basic scheme is especially important. In addition to its basic form many variants are discussed: reversed form, overlapping of several canons, alteration of octave positions, parallel fourths, consecutive octaves by contrary motion, five-part canons, syncopical entries. To analyse a canon of Bach's St~John Passion a computer programme is used to determine how to combine a four-part canon on the basic scheme and a chromaticised seventh chord sequence. Thus criteria can be found, according to which Bach's canon can be interpreted as the best possible solution. In connection with sequencing entry schemes canons with the following features are analysed: a seven-part canon, a melody with different chord tones of the same harmony, a canon in quadruple counterpoint, a group canon five in two, and a canon over a seventh chord progression. The principles of the two- to four-part canons by inversion are derived. With the basic graph for the inversion [Basisgraph für die Umkehrung] a feature of the theme of Bach's Kunst der Fuge is explained, namely, why there is a stretto by inversion in simple distance and a stretto by similar motion in double distance. The approach is enlarged to canons with dissonances. Canons by augmentation and diminution are analysed by time structure graphs [Zeitstrukturgraphen]. It is explained, why there are such canons for the theme of Bach's Kunst der Fuge. For two-part canons on a given theme the auxiliary tone method [Hilfstonverfahren] is developed, and the many part scheme [Vielstimmigkeitsschema] for canons with more than two parts. The approach enables the analysis of sequencially interlinked canons. For some themes there are several canons with three or more parts. They are analysed by the entry tree [Einsatzbaum]. The many part scheme is applicated to the Tjulin method. The auxiliary tone method is generalised to the combination of two different themes or harmonic progressions. It is formally proved by concepts of the mathematical music theory according to Mazzola. By the generalised forms the following phenomena are analysed: different tones at the same time, the combination of a melody and a harmony progression, manifold counterpoints of three or more themes, canons with dissonances, canons by inversion, combinatoriality of twelve-note series and a rhythmic canon. Two- to five-part canons on a given harmonic progression of triads and seventh chords are constructed by matter canons [Materialkanons]. Thus several canons are explained, namely on a tonic dominant alternation and on a sequence. Combinations of harmonic or melodic sequences with a given harmonic progression or melody are found by a variant of the auxiliary tone method. This is shown to be relevant for melodic structures of classical themes and sequential structures in Schubert and Bach. The analytical results have the logical structure of a compositional modus ponens [satztechnischer Modus ponens]. The analyses prove that there is a logically necessary dependency between different features of a composition under the conditions of the historical compositional technique. The mathematical music theory is used for the construction, proof and implementation of the algorithms. Musical relevance is founded on the psychology of hearing and even more on musical hermeneutics.
Subject Keywords: Algorithmus; Satztechnik; Analyse
Issue Date: 24-Oct-2012
Type of publication: Dissertation oder Habilitation [doctoralThesis]
Appears in Collections:FB03 - E-Dissertationen

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