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Introduction to Schenkerian Analysis

Written March 28, 2021, last changed April 2, 2021

Introduction to Schenkerian Analysis was written in 1982 by Allen Forte and Steven E. Gilbert. It’s intended as a college-level textbook for students who have some basic music theory under them.

The cover of the book. The title is printed on top of a music notation with straight lines drawn between between the notes in the top and bottom lines.

My copy contains copious (and fairly distracting) notes and underlines from Rudy Karl Gartner written in 1998 Chicago, Illinois.

Schenkerian Notation

The book is slowly building towards a complete Schenkarian notation one concept at a time, which I’ll record all in one place here.

1. Melodic Diminutions

A melodic diminution is when an interval between two notes is “broken up” by inserting additional secondary notes.

The note receiving the diminutions need not actually be present in the diminutions; that is, the diminutions represent the note being embellished.

To analyze diminutions, you can write “rhythmic reductions” which maintain traditional notation but remove diminutions. Also introduced is a simplified form of Schenkerian notation, where primary notes are represented with quarter notes, and their dependent notes are staffless and slurred.

Diminutions are fractal in nature: by reducing down to a simpler notation, you can see how the broader movement of the melodic line is its own line with further diminutions.

The Neighbor Note as Motive

The neighbor note differs fundamentally from the passing note in musical function, for it always serves as an adjacency, whether directly contiguous to the main note(s) or presented indirectly because of an intervening consonant skip. Thus, the neighbor note always relates to another single note (the main note), whereas the passing note is a _connective, hence joince two notes.

Neighbor notes can be upper neighbors or lower neighbors to the main note.

Neighbor notes are said to be complete when they both depart from and return to the main note. An incomplete neighbor note is either a prefix or a sufix.

The incomplete neighbor note as prefix or suffix can, theoretically, be either upper or lower neighbor, yielding four possibilities for this species of diminution. However, the incomplete lower neighbor note as suffix occurs very seldom in tonal music.

Many, if not almost all, such incomplete lower neighbor suffixes can be understood as anticipations [often of a note in another line].

The Passing Note as Motive

A chromatic passing note can be inserted between a note and its neighbor to form an indirect neighbor.

A consonant passing note is a passing note that is followed by the bass to produce a stable consonance.

Passing notes are often indirect: for example, an upward passing motion might be ocluded by a consant skip upwards in the middle.

The Arpeggiation as Motive

In Schenkerian terms, structural arpeggiation always involves the arpeggiation of a complete consonant harmony. Hence it is distinct from the consonant skip.

The fundamental types of diminutions do not occur in isolation in well-composed tonal music, but are always combined to form variegated structures.

2. Voice Leading: Counterpoint and Figured Bass

The study of voice leading is the stufy of the principles that govern the progression of the component voices of a composition both separately and in combination.

Schenkerian analytic procedures always give primary consideration to the horizontal dimension of the musical composition.

The Species Counterpoint Model

An overview of species counterpoint. Species counterpoint is “an abstract and idealized world from which many aspects of the free tonal composition are absent.”

In each species you are given a single voice (the cantus firmus) and must add one or more additional voices following certain rules.

In the first species, the voices move together note by note. Only consonances are allowed vertically, no successive perfect intervals are allowed, and horizontal intervals of the seventh or anything larger than an octave aren’t allowed.

In the second species, you place two notes against each cantus firmus note. The second note is allowed to be dissonant if it is a complete passing tone.

In the third species four notes are set against each cantus firmus note. The second, third, and fourth notes are all allowed to be complete passing tones (as long as they lead to another consonance), the ocassional neighbor note is permitted, and also allowed is the cambiata, a skip of a third away from a dissonance to a consance, followed by a step in the opposite direction into another consonance.

In the fourth species, two notes are set against one, but the second note is allowed to be tied to the next. In this case, the first note is allowed to be dissonant if it is tied to the previous, and if it steps downards to a consant on the next note. The result is a chain of suspensions.

Fifth species is a free mixture of all of the species.

These exercises, although they are never intended to be musical compositions, serve a very useful conceptual purpose. Precicely because they represent an abstsract that highlights voice leading, they illuminate the greatly expanded phenomena of voice leading in the free tonal composition and reveal the distinctive role of harmony in large and small.

Figured Bass Notation

In this notation, the bass is regarded as the fundamental voice to which the others relate. Figures (numbers, signs of alteration, and other symbols) specify the intervals formed by the voices above teh bass and, in some cases, the progression of the voices to which the symbols refer. In all cases, a figure represents accurately the local voice-leading situation, indicating required progressions.

Any information figures may carry about chord type (e.g. “diminished 7th”), harmonic root (e.g. Ⅴ⁷), or inversion (e.g. Ⅰ⁶) is entirely ancillary to their main purpose, which has to do with voice leading. Figured bass symbols and roman numerals have, over the years, traditionally appeared together; yet conceptually they are distinct.

Generally speaking, the fifth and the third are assumed, and so no figures implies a 5-3, a 6 implies a 6-3, and a 4 imples a 5-4. 6-5 implies 6-5-3, and 7 implies 7-5-3. Intervals of a second are usually indicated with a 9.

The intervals are implied to be the appropriate diatonic interval for the key, unless given an alteration, so ♯6-4-3 means to play the sixth as sharp instead of natural, and a single ♮ means to play the third as natural instead of flat.

If a 2 is included, it implies that the bass has been displaced, and that you can read it as though the bass were one step lower and each interval one step higher. So, 7-4-2 is a displacement of a (8-)5-3. The exclusive use of the 2 for this purpose (using 9 for other seconds) makes it straightforward to tell when this is happening.

Many figures typically represent suspensions.

It is essential to make a basic observation about the suspension. It represents a rhythmic delay of a voice-leading connection, a temporal displacement; it does not generate a new voice-leading situation but merely intensifies one that has already be set in operation.

This is why suspension is not a kind of diminution! It doesn’t affect the voice leading, it just gives it oomph.

3. Compound Melody

In compound melody, “the melody itself is composed of distinct components of the voice leadings,” and are distinct from arpeggiation as diminution in that “the appegiation is th projection of a single voice through the notes of a consonant triad, compound melody involves arpeggiation and partial arpeggiation in [a] more elaborate sense [...] as conveyors of two or more voices over a longer span of music.”

[There are] two major points about compound melodic structures. First, a compound melody always results in a rhythmic displacement of components that “belong together.” [...] The second major point is this: The component voices of compound melodies always follow the voice-leading pattern; indeed, they are the melodic expression of that pattern, which is contained within a single melodic structure.

Partially compound melodies feature a mixuture of arpegiation alongside vertical harmony.

A key way of differentating whether a particular note is part of a compound melody or is a normal arpeggiation/consonant skip is the idea of “consequences” – does the voice go anywhere?