Interpreting the Analytical Graphs

These analyses might look a bit daunting at first, but they should be very easy to read and interpret after a little introduction.

If you read them from bottom-to-top you can follow how music is reduced by analysis; if you read them from top-to-bottom, you can understand how a very simple starting design is repeatedly subdivided by layers of structure and fundamental harmony to create a composition. Beyond that, they’re also very pretty to look at.

Foreground:

The foreground section at the bottom of each analysis is the most genuine representation of the original score. It has some major differences, though:

  • Individual cells represent smaller musical units that subdivide a given phrase, and these are grouped into phrases or sub-phrases as appropriate. Any given moment can be easily found on the original score by reference to bar numbers in the top row of this section: “Bb.”;

  • Repetition, and the surface rhythm and/or ‘texture’ of the music is stripped away, leaving chorale-style harmonic reductions of each phrase;

  • These harmonic reductions exclude non-harmonised individual passing or auxiliary notes, but anything beyond that is reduced in painstaking detail, and is detailed using traditional Roman numerals. Passing and auxiliary chords are included;

  • The Roman numeral harmonic analysis in the foreground is always relative to the local tonic specified in the row below. A colour system is used to help notice when this local tonic changes.

Middleground:

Each section of the foreground reduction is now considered as a component of structures that appear within the middleground:

  • Bar ranges that encompass each middleground structural division are again included as the top row of this section;

  • The middleground structural sections are grouped by general function and location as per sonata theory and contemporary studies of form (Formenlehre);

  • Foreground phrases within each middleground section are reduced to their most basic design, and are grouped together accordingly.

  • All Roman numerals in the middleground are written relative to the tonic of the movement. Do not consider the foreground “local tonic” when interpreting the middleground — it has already been translated.

Background:

Background structures are generated by grouping middleground structures. These background structural divisions will also be understood as components (divisions) of a deep-background structure. When put together, the background divisions define the form of the movement.

  • The background is reduced from the middleground in much the same way that the middleground is reduced from the foreground.

  • Bar ranges, labels and brackets that isolate and define background structural sections (based on the middleground choices within each) are again found at the top of this section.

  • The middleground tonal designs and harmonic events (that act as components of the background), are reduced to their skeleton designs, and grouped accordingly.

  • All Roman numerals in the background are written relative to the tonic of the movement. Do not consider the foreground “local tonic” when interpreting the background.

Deep-background:

The deep-background allows us to put the background designs of complete movements side-by-side, to see if there is any overarching tonal or structural coherence that connects the individual movements of a multi-movement work. Just as foreground sections are considered components of the middleground, and as middleground sections are considered as components of the background, the deep-background structure of a multi-movement work is revealed by treating background structures as components of a larger form.

  • Individual ‘movement’ tables only show that respective movement’s contribution to the parent work’s deep-background structure.

  • I believe that deep-background structures of multi-movement sonata and symphony-type works from c.1800 onward are likely to display at least one instance of deep-background tonal resolution, inversion or symmetry that exists to help kickstart the compositional process, and to provide a more profound sense of cohesiveness that connects the movements of a multi-movement work.

Symbols:

There are four types of arrows used within the Roman numeral rows that are used consistently in every dimension of the analysis.

  • “Right arrows”: “→”: denotes perfect cadence (PAC) relationships between two Roman numerals. Not all of these are rhythmically or structurally important;

  • “Interrupted arrows”: “⍆”: denotes an interrupted or deceptive cadence relationship between two chords separated by this arrow. Most commonly manifests as V to bVI, or vi, or VI, also to #i⁰;

  • “Zig-zag arrows”: “⟿”: denotes effective voice-leading between two Roman numerals. In other words, at least two tones are shared between chords separated by this arrow. One might also say that these chords are connected by neo-Riemannian voice-leading relationships;

  • “Curly arrows”: “↝”: denotes a modulatory shift. Roman numerals separated by this arrow are, by definition, the same chord. Read this arrow type as “x is reunderstood as y”.

Square brackets are used to isolate specific groups of Roman numerals, and have no inherent meaning beyond this. Things like “[ ] x2” are also used to denote repetition where it has been removed. In the deeper reductive levels, square brackets are also used to show which groups of chords are divided into smaller units together. If these brackets are used with alternative meaning, it will be specified in the “comments” row of the deep-background.