Generative Theory Of Tonal Music

Generative Theory of Tonal Music ( GTTM ) is a system for musical analysis of tonal music, the 1983 book of the same by the American composer and music theorist Fred Lerdahl ( b. 1943 ) and the American linguist and clarinetist Ray Jackendoff ( born 1945 ) was published.

The cooperation between teachers Dahl and Jackendoff was inspired by Leonard Bernstein Charles Eliot Norton Lectures in 1973 at Harvard University, in which he exhorted the participants to develop a "musical grammar " that explains the unique human capacity for musical understanding in a scientific way, comparable to Noam Chomsky's revolutionary generative transformational grammar. In contrast to analytical methods that had been developed up to that point, the GTTM tried to be guided by the mental processes through which the listener an unconscious understanding of the music developed (focus on hierarchical structures). They are based on an "ideal " audience with musical understanding and the ability to recognize musical objects and abstract structures. It attempts to achieve a synthesis of the views and methods of contemporary linguistics with the insights of modern music theory.

The GTTM had great influence on the further work of the authors as well as other researchers in the fields of music theory, music perception and cognitive musicology.

• 2.1 The structures 2.1.1 Grouping structure
• 2.1.2 Metrical structure
• 2.1.3 Time - span reduction (TSR )
• 2.1.4 Prolongational reduction (PR )

• 2.2.1 Grouping Structure Rules
• 2.2.2 Metrical Structure Rules
• 2.2.3 Time -Span Reduction Rules
• 2.2.4 Prolongational Reduction Rules

Influences and foundations

Schenker

Heinrich Schenker, an Austrian music theorist and composer, has justified the reduction analysis. According to his hypothesis, some sounds are perceived as more important than others. The " unimportant " (eg, side-notes ) are ornaments, decorations, continuations and connections of the main notes. Through reductions at all levels creates a hierarchical structure of the work. The reduction analysis tried the ostensible notation on a supporting sentence - due in the background - " Ursatz ".

Generative Linguistics

Generative linguistics is an attempt to describe the human understanding of language, and the concomitant ability to understand an infinite number of sentences, even those that you have never heard of before and to form. This ability is learned so early and is so ingrained in our minds that they can not be fully learned by instructions. In linguistics, an attempt is made whole ability, their conscious and subconscious shares, to be described by a formal system of rules dhdurch the grammar.

The relevant for the development of GTTM parallel is the combination of psychological findings with a formal structure of the theory. It should the term " generative " not be misunderstood. It does not mean that one can develop an algorithm for generating speech with this theory, but it is more meant in a mathematical sense, one - to describe quantity with finite formalisms - usually infinite. It is not enumerate therefore also in the GTTM what principle are possible for art, but to create a structural description and analysis for existing plants. Linguistics sees itself as a branch of psychology that attempts to make empirically verifiable statements about language, a complex aspect of human life. Similarly, the primary objective of GTTM is an understanding of musical perception, a psychological phenomenon.

The theory

The GTTM focuses on four systems that are designed to track our musical perceptions. Each of these systems consists of a strict hierarchical structure, contain small subregions in the dominant regions are adjacent to each other like elements within a level.

The structures

Grouping structure

The analysis of the groups is regarded as the basic component of the musical understanding. In this case, a hierarchical segmentation of the piece is performed in motifs phrases periods and even greater ranges.

Metrical structure

The metrical structure represents the regular, hierarchical alternations of ( heavy and light ) blows that connects the listener with musical events. Fundamental distinction: Beat / beat = infinitesimal time Time-Span/Zeitspanne = time of one beat to the next. In the metric structure it comes to beats / beats. Strong Beat: impact on a level L (level ) is also at a higher level a blow. Otherwise: Weak beat.

People do not take too much metrical level simultaneously true. There is usually a dominant plane in which the conductor moves his hands, which listeners with his foot whips, etc. - the " tactus ". ( Renaissance expression, most strongly determined by harmonic rhythm )

Time - span reduction (TSR )

The time spans reductions based on the information of the group, and the metric structure. It creates a tree diagram hierarchically connects the periods at all temporal levels of the work. You start on the smallest level, where the metrical structure divides the music into beats of equal length (or more precisely in attacks, between each of which the same periods is ). From there you go up through all higher levels, which are divided by the Grouping Structure in motives, phrases, periods, and even larger units. Also, a head ( the structurally most important element ) is determined for each time period at all hierarchical levels. The complete TSR analysis is called Time -span Tree.

Prolongational reduction (PR )

The Prolongationsreduktion (PR ) forms from our " psychic" experience of tension and relaxation in a precise structural forms. In the TSR, the hierarchy of elements according to the rhythmic stability is created. In PR, however, the hierarchy is built on the basis of relative stability, which presents itself in the form of continuity and progression, the movement direction of tension or relaxation, and the degree of financial statements. The PR is mainly used because the TSR has two limitations:

In PR, a tree diagram is created or the compounds are presented in a visually compressed, " slur " notation. The tree diagram, there are three types of branches:

• Strong prolongation ( represented by a circle at the branch point ),

• Weak prolongation ( represented by a filled circle ) and

• Progression ( represented by a simple branching without a circle ).

In contrast to all other structures of the theory, the PR is created from top to bottom, ie, from the highest level ( whole plant) to smallest ( single notes ). This is because functions such as voltage formation and degradation have to be shown by the context of a musical object. In TSR tree diagrams there is no such distinction. But there are actually many other helpful comments. At higher structural levels, the two tree diagrams are often very similar, but the further you move down towards musical surface, the more often you will find differences in the branches.

The rules

Each of the four hierarchical systems is created by rules which can be divided into three categories:

The system takes a musical surface as input and generates the structure of the listener perceives as output.

Grouping Structure Rules

In sum, the grouping structure is hierarchical, non-overlapping, recursively, and each group must consist of contiguous elements.

There are basically two types of clues, such as the listener perceives the grouping:

Metrical Structure Rules

Time -Span Reduction Rules

Each period has a head. The TSRWFRs describe how to determine the head. ( And that looks like the tree → Links-/Rechtsverzweigung )

Since the TSRWFR leave open several possibilities in some cases, one needs again preference rules. There are three categories:

• Local rules- are addressing only rhythmic and tonal content of the period. (1,2,3)
• Nonlocal rules - relating to other periods of time. (4,5,6)
• Structural accent rules - refer to the group transitions / limits. (7,8)

Prolongational Reduction Rules

There are two possible notations: tree diagram and slur notation ( at Schenker ajar ). Always the underscore from the more important element just goes on.

Short form: 1 There must be a head. 2 Defined continuations: strong and weak prolongation, as well as progression. 3 Each musical object must be connected to the tree. 4 knots may not cross itself.

Tasks: determine the most important for the prolongation object in a region (ei - ej ) ​​and specify whether it is a prolongation of ei or ej.

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