Schenkerian analysis is a method of analyzing tonal music, based on the theories of Heinrich Schenker (1868–1935). The goal is to demonstrate the organic coherence of the work by showing how it relates to an abstract deep structure, the Ursatz. This primal structure is roughly the same for any tonal work, but a Schenkerian analysis shows how, in an individual case, that structure develops into a unique work at the 'foreground', the level of the score itself. A key theoretical concept is that of '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 notes, producing new triads and new tonal spaces, open for further elaborations until the surface of the work (the score) is reached. Schenkerian analysis is a method of analyzing tonal music, based on the theories of Heinrich Schenker (1868–1935). The goal is to demonstrate the organic coherence of the work by showing how it relates to an abstract deep structure, the Ursatz. This primal structure is roughly the same for any tonal work, but a Schenkerian analysis shows how, in an individual case, that structure develops into a unique work at the 'foreground', the level of the score itself. A key theoretical concept is that of '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 notes, producing new triads and new tonal spaces, open for further elaborations until the surface of the work (the score) 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 fundamental structure (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 the reduction, rhythmic signs (open and closed noteheads, beams and flags) show 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 nor always clearly understood. It mainly aims at showing 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,. Schenker was convinced of the superiority of music of the common practice period (especially the music of Johann Sebastian Bach, Carl Philipp Emanuel Bach, Joseph Haydn, Wolfgang Amadeus Mozart, Ludwig van Beethoven, Franz Schubert, Frédéric Chopin, and Johannes Brahms). This led him to seek the key to an understanding of music in the traditional discipline of counterpoint, the type of theory the Masters themselves had studied. Schenker's project was to show that free composition (freier Satz) was an elaboration, a 'prolongation', of strict composition (strenger Satz), by which he meant species counterpoint, particularly two-voice counterpoint. He did this by developing a theory of hierarchically organized levels of elaboration (Auskomponierung), called prolongational levels, voice–leading levels (Stimmführungsschichten), or transformations (Verwandlungen), 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' (Fernhören), a 'structural hearing'. The tonic triad, that from which the work as a whole arises, takes its model in the harmonic series. However, Linking the (major) 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: The basic component of Schenkerian harmony is the Stufe (scale degree, scale-step), 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 which Schenker had followed in the Konservatorium in Vienna.