Schenkerian analysis
Schenkerian analysis is a method of analyzing tonal music based on the theories of Heinrich Schenker. The goal is to demonstrate the organic coherence of the work by showing how the "foreground" relates to an abstracted deep structure, the Ursatz. This primal structure is roughly the same for any tonal work, but a Schenkerian analysis shows how, in each individual case, that structure develops into a unique work at the foreground. A key theoretical concept is "tonal space". The intervals between the notes of the tonic triad in the background form a tonal space that is filled with passing and neighbour tones, producing new triads and new tonal spaces that are open for further elaborations until the "surface" of the work is reached.
The analysis uses a specialized symbolic form of musical notation. Although Schenker himself usually presents his analyses in the generative direction, starting from the Ursatz to reach the score and showing how the work is somehow generated from the Ursatz, the practice of Schenkerian analysis more often is reductive, starting from the score and showing how it can be reduced to its fundamental structure. The graph of the Ursatz is arrhythmic, as is a strict-counterpoint cantus firmus exercise. Even at intermediate levels of reduction, rhythmic signs display not rhythm but the hierarchical relationships between the pitch-events.
Schenkerian analysis is an abstract, complex, and difficult method, not always clearly expressed by Schenker himself and not always clearly understood. It mainly aims to reveal the internal coherence of the work – a coherence that ultimately resides in its being tonal. In some respects, a Schenkerian analysis can reflect the perceptions and intuitions of the analyst.
Fundamentals
Goals
Schenker intended his theory as an exegesis of musical "genius" or the "masterwork", ideas that were closely tied to German nationalism and monarchism. The canon represented in his analytical work therefore is almost entirely made up of German music of the common practice period, and he used his methods to oppose more modern styles of music such as that of Max Reger and Igor Stravinsky. This led him to seek the key to an understanding of music in the traditional disciplines of counterpoint and figured bass, which was central to the compositional training of these composers. Schenker's project was to show that free composition was an elaboration, a "prolongation", of strict composition, by which he meant species counterpoint, particularly two-voice counterpoint. He did this by developing a theory of hierarchically organized levels of elaboration, called prolongational levels, voice-leading levels, or transformations, the idea being that each of the successive levels represents a new freedom taken with respect to the rules of strict composition.Because the first principle of the elaboration is the filling in of the tonal space by passing notes, an essential goal of the analysis is to show linear connections between notes which, filling a single triad at a given level, remain closely related to each other but which, at subsequent levels, may become separated by many measures or many pages as new triads are embedded in the first one. The analyst is expected to develop a "distance hearing", a "structural hearing".
Harmony
The tonic triad, that from which the work as a whole arises, takes its model in the harmonic series. However,the mere duplication of nature cannot be the object of human endeavour. Therefore... the overtone series... is transformed into a succession, a horizontal arpeggiation, which has the added advantage of lying within the range of the human voice. Thus the harmonic series is condensed, abbreviated for the purposes of art".
Linking the triad to the harmonic series, Schenker merely pays lip service to an idea common in the early 20th century. He confirms that the same derivation cannot be made for the minor triad:
Any attempt to derive even as much as the first foundation of this system, i.e., the minor triad itself, from Nature, i.e., from the overtone series, would be more than futile.... The explanation becomes much easier if artistic intention rather than Nature herself is credited with the origin of the minor mode.".
The basic component of Schenkerian harmony is the Stufe, i.e. a chord having gained structural significance. Chords arise from within chords, as the result of the combination of passing notes and arpeggiations: they are at first mere embellishments, mere voice-leading constructions, but they become tonal spaces open for further elaboration and, once elaborated, can be considered structurally significant: they become scale-steps properly speaking. Schenker recognizes that "there are no rules which could be laid down once and for all" for recognizing scale-steps, but from his examples one may deduce that a triad cannot be recognized as a scale-step as long as it can be explained by passing or neighboring voice-leading.
Schenkerian analyses label scale-steps with Roman numerals, a practice common in 19th- and 20th-century Vienna, developed by the theoretic work of Georg Joseph Vogler and his student Gottfried Weber, transmitted by Simon Sechter and his disciple Anton Bruckner, the classes of whom Schenker had followed in the Konservatorium in Vienna.
Schenker's theory is monotonal: the Ursatz, as the diatonic unfolding of the tonic triad, by definition cannot include modulation. Local "tonicisation" may arise when a scale-step is elaborated to the point of becoming a local tonic, but the work as a whole projects a single key and ultimately a single Stufe.
Counterpoint, voice-leading
Two-voice counterpoint remains for Schenker the model of strict writing. Free composition is a freer usage of the laws of strict counterpoint. One of the aims of the analysis is to trace how the work remains subject to these laws at the deepest level, despite the freedom taken at subsequent levels.One aspect of strict, two-voice writing that appears to span Schenker's theory throughout the years of its elaboration is the rule of "fluent melody", or "melodic fluency". Schenker attributes the rule to Luigi Cherubini, who would have written that "fluent melody is always preferable in strict counterpoint." Melodic fluency, the preference for conjunct motion, is one of the main rules of voice leading, even in free composition. It avoids successive leaps and produces "a kind of wave-like melodic line which as a whole represents an animated entity, and which, with its ascending and descending curves, appears balanced in all its individual component parts". This idea is at the origin of that of linear progression and, more specifically, of that of the Fundamental Line.
Ursatz
Ursatz is the name given by Schenker to the underlying structure in its simplest form, that from which the work as a whole originates. In the canonical form of the theory, it consists of the Urlinie, the "fundamental line", supported by the Bassbrechung, the "arpeggiation of the bass". The fundamental structure is a two-voice counterpoint and as such belongs to strict composition. In conformity with the theory of the tonal space, the fundamental line is a line starting from any note of the triad and descending to the tonic itself. The arpeggiation is an arpeggiation through the fifth, ascending from I to V and descending back to I. The Urlinie unfolds the tonal space in a melodic dimension, while the Bassbrechung expresses its harmonic dimension.The theory of the fundamental structure is the most criticized aspect of Schenkerian theory: it has seemed unacceptable to reduce all tonal works to one of a few almost identical background structures. This is a misunderstanding: Schenkerian analysis is not about demonstrating that all compositions can be reduced to the same background, but about showing how each work elaborates the background in a unique, individual manner, determining both its identity and its "meaning". Schenker has made this his motto: Semper idem, sed non eodem modo, "always the same, but never in the same manner".