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Schenkerian graphs use specialized notation (reduction notation with lines, stems, beams, and beaming patterns) to show how musical materials are nested and related across structural levels. Mastering graph notation is essential for communicating reductions and comparing different analytical interpretations systematically.
From your work in Schenkerian levels analysis, you know the core analytical claim: tonal music is organized across multiple structural levels, from the note-by-note foreground to the large-scale background structure (the *Ursatz*). The challenge is how to represent this hierarchy visually. Schenkerian graphs solve this by using a specialized notational system that encodes both the structural level of each note and the voice-leading relationships between notes — all on a single staff.
The most important notational tool is stemming. A note with a stem belongs to a structurally significant level: stems pointing up generally indicate the *Urlinie* (fundamental melodic line), while stems pointing down indicate the bass arpeggiation or important inner voices. A note without a stem is at a lower structural level — it is a neighbor tone, passing tone, or other embellishment elaborating a stemmed note. Beams connect notes of the same structural level that form a coherent linear motion: a descending stepwise line from 3̂ to 1̂ in the Urlinie might be beamed together to show its unity across many measures of surface music. Slurs indicate prolongations — a slur spanning many notes shows that one structural harmony is being prolonged through all the embellishing material beneath it.
The graph is read simultaneously as a pitch reduction and a voice-leading statement. When two notes at the same structural level are connected by a beam, the claim is that these notes are structurally equivalent and that all surface notes between them elaborate the space those structural tones define. The Kopfton — the initial note of the Urlinie, usually 3̂ or 5̂ — appears as the first stemmed note in the graph, and its descent to 1̂ is the organizing melodic arc of the entire piece. The bass arpeggiation from I through V to I mirrors this descent in the bass register. Together they form the *Ursatz*, the background structure from which all foreground detail is understood to derive.
The practical skill is learning to read graphs in both directions: from graph to music (using the graph as a guide for where to listen in the score) and from music to graph (making analytical decisions about which notes warrant stems and how to connect them). Different analysts sometimes produce different graphs of the same piece, and Schenkerian analysis is partly a practice of argumentation about which reductions best explain a work's coherence. The graph is not a description of what the music is; it is a claim about how the music works. Mastering the notation means you can read, produce, and debate those claims with rigor and clarity.
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