Generative theory of tonal music and modality: Research based on the analysis of 44 miniatures for piano by Yannis Constantinidis

The PhD research involves the adaptation and expansion of Lerdahl's & Jackendoff’s Generative Theory of Tonal Music in order to enable its application to the analysis of modal music. The musical grammar rules of the original formulation of the theory (1983) apply to the classical tonal idiom. However, the authors claim that a considerable part of the theory's rules are universal, meaning that the principles of music perception and cognition are the same for all experienced listeners, regardless of the musical idiom in which they are experienced, since they relate to innate and unlearnable processes of human cognition. So, the application of the theory to other musical idioms requires the formulation of the idiom specific well formedness and preference rules and the description of the special tonal hierarchy. These tasks can be accomplished through the analytical study of a considerable amount of music representing the idiom and the description of its characteristics in relation to the four levels of the GTTM methodology (grouping structure, metrical structure, time-span reduction and prolongational reduction). The chosen analytical object - 44 Greek miniatures for piano - represents the musical idiom of the special mixture of Greek modal music and 20th century harmony techniques that constitutes the musical style of the Greek composer Yannis Constantinidis, member of the Greek National School. All of the 44 pieces were studied as part of an inductive methodological process. The research results consist of a detailed description of the stylistic characteristics of the analyzed music and of the formulation of the special well-formedness and preference rules that have been introduced either as new rules to the theory or as adaptations of the existing ones. The Generative Theory of Tonal Music (Lerdahl & Jackendoff 1983) places music theory among the cognitive sciences by examining issues concerning the perception and cognition of musical structure, namely the mental representation of music. The theory, starts from the point that an experienced to a musical idiom listener organizes the musical sounds (musical surface) into coherent mental structures and correlates music cognition with language cognition arriving at the formulation of a musical grammar, a system of rules that construct the hierarchical structure that the experienced listener assigns to a musical surface. There are two basic categories of musical grammar rules: the well-formedness rules, that determine the grammatically correct possible structural descriptions of a piece and the preference rules, that choose from among the possible structures the most coherent and closest to the listener’s mental representation. The analytical theory is reductional, since it presents its analytical results in multiple hierarchical levels of four integrated types (grouping structure, metrical structure, time- span reduction and prolongational reduction) that start from the musical surface (specific level) and progress gradually to the structural skeleton (abstract level). The Generative Theory of Tonal Music in its original form (1983) applied to music belonging to the Western tonal idiom only. However, its authors claim (chap. 11 of GTTM) that a considerable part of the theory’s rules possess universal validity and that by modifying the existing or adding new idiom specific rules the theory could be used for the analysis of music belonging to other musical idioms. Defining musical universals, Lerdahl & Jackendoff refer to the basic principles of music cognition that all experienced listeners use for the organization of perceived musical surfaces, regardless of the musical idiom in which they are experienced. These principles relate to the human cognitive capacity and ability which are mainly innate and independent from cultural, geographical or historical factors.This dissertation research involves the adaptation and expansion of the Generative Theory of Tonal Music in order to enable its application to the analysis of modal music. The modal idiom chosen for the research is Yannis Constantinidis’s musical style as represented by his 44 Greek miniatures for piano and the expected research results include: - The stylistic characteristics of the chosen musical idiom. - The formulation of the new or modified musical grammar rules that correspond to this idiom. 2. Background. The basic principles of the theory, that are considered universal and idiom independent are: • Musical intuitions are organized along four hierarchical dimensions, each including every pitch-event in a piece: grouping, metrical structure, time-span reduction and prolongational reduction. • The structure of a piece in each component is determined by the interaction of well- formedness rules, preference rules and transformational rules. • The four components interrelate as following: - Grouping and meter are independent. - Time-span reduction depends on meter at small levels, grouping at large levels and the combination of the two at intermediate levels. - Time-span reduction depends on a combination of pitch stability and time-span segmentation. - Prolongational regions and prolongational importance are determined largely in terms of time-span importance and stability of pitch connection. • In order for the two reductional components to be completed, there must exist criteria for the relative stability of pitch events. This means that a musical idiom must supply a tonal center for a piece and a scale of distance of other pitch-events from it, namely a tonal hierarchy. • Structural beginnings and endings of groups form significant articulation of a piece’s structure; structural endings are marked by conventional formulas (cadences of some kind). So, extending the use of the theory to idioms other than the Western tonal one - assuming the existence of a tonal center and a tonal hierarchy - needs, apart from the retention of the above universal principles, also: - the formulation of the special conditions that describe the specific idiom in the form of special well-formedness and preference rules and - the formulation of the special tonal hierarchy and the special cadence formulas. These tasks can be accomplished through both the specific and the comparative study of a representative specimen of a musical idiom for the inductive extraction of general conclusions about the idiom and its relation to the four methodological components of the theory. The above conditions apply to the use of the theory for the analysis of Yannis Constantinidis’s (1903-1984) music, whose style is a special mixture of diatonic modality and 20th century compositional techniques. The 44 Greek miniatures for piano, like the rest of Constantinidis’s art music, is based on the processing of authentic Greek folk tunes and dances. Written during the period 1949-51, this three-volume collection of the processing of 44 folk melodies from all Greek territories is among his first mature works and possibly the most decisive for the creation of his compositional style. The most salient characteristic of Constantinidis’s music is that the original tune is strictly unalterable and functions as a type of cantus firmus while the processing occurs in the harmonic and rhythmic domain. The modal system of Greek folk music consists mainly of heptatonic modes, kin but not identical with the Byzantine modes, without excluding cases of tetratonic or pentatonic modes. The heptatonic modes are diatonic (containing major or minor seconds) or chromatic (containing augmented seconds also), consisting of conjunct or disjunct tetrachords and pentachords and include certain characteristic chromatic alterations. The most common structural scale steps are 1ˆ (tonic center), (subtonic, generally one major second below the tonic) and 4 (one perfect fourth above the tonic). Every mode includes characteristic cadential formulas, among which the most typical are 3ˆ— 2ˆ — 1ˆ— 7ˆ — 1ˆ and 4ˆ — 3ˆ — 1ˆ and typical melodic embellishment patterns. […