Introduction to Schenkerian Analysis

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.

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.

• Quarter notes represent a primary note in the melody
• Notes without staves represent diminutions and are slurred to their main note
• Dotted slurs can be used to draw connections between notes
• Eight notes are used to represent a main note that has been repeated in a less primary context (ex. as part of a 6-4 suspension)
• When a voice leading is “picked up” in a different octave, arrows can be drawn to show the transfer
• Implied notes are shown in parentheses
• Notes can be beamed together to show progression through the fundamental line, with melody notes accompanied by scale steps (for example, 3̂–2̂–1̂) and the bass notes by roman numerals.
• The fundamental structure is shown in whole notes or half notes
• A crosswise beam coming from the top of a low note and connecting to the bottom of a high note (in either direction) representing the unfolding of an interval into a prolonged line

1. Melodic Diminutions

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

• Arpeggiation inserts notes in between the interval that align with the harmonic structure.
• Consonant skips insert notes that align with the harmonic structure but which do not necessarily lead anywhere
• Passing notes are a stepwise motion from one note to another
• Neighbor notes are stepwise motion centered around a single note

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?

4. Linear Intervallic Patterns

A linear intervallic pattern is a voice-leading design made up of successive recurrent pairs of intervals formed between the descant and bass (outer voices).

The term sequence is sometimes used, incorrectly, to designate what we call the linear intervallic pattern. Properly speaking, the sequence is a melodic pattern in a single voice, which is repeated at differnet transpositions and in immediate succession, over the span of a passage. Such sequences may occur in connection with a linear intervallic pattern [... ] however, the melodic sequence is not a necessary condition for the linear intervallic pattern. There are many instances in the musical literature in which a melodic sequence within a linear intervallic pattern may be terminated, while the linear intervallic pattern itself continues.

The important thing to understand about linear intervallic patterns is that they are fundamentally non-harmonic: the succession of intervals is a function of voice leading and (usually) should not be read as a harmonic progression.

Linear intervallic patterns often connect two harmonies together, or one harmony to itself, though this is a secondary function compared to the voice-leading.

They are notated using numerals between 4 and 10 between the staves.

The book walks through the various common linear intervallic patterns and how they function.

The contituents of a linear intervalic pattern—the intervals formed by the outer voices of a voice-leading design—may be two imperfect consonances (for example, tenths), two perfect consonances (for example, the octave and the fifth), an imperfect and a perfect consonance (for example, the sixth and the fifth), or a dissonance and an imperfect consonance (for example, a seventh and a tenth).

5. Harmonic Relations

Harmony in Schenkerian analsis is overall much simpler: there are tonic and dominant chords, all other chords are substutions for one of these (like Ⅶ for Ⅴ or Ⅲ for Ⅰ) or can be understood as a function of voice leading. For example, predominants can be understood as having a neighbor-note voice leading relationship to the dominant.

Harmony in Schenkerian analysis is often analyzed on a large scale, sometimes wrapping an entire piece of music into a few chords.

The term modulation in the sense of an arbitrary change of key is foreign to the Schenkerian orientation. Though Schenker used the term, especially in his earlier writings, he came to prefer the term tonicization, which refers to the establishment of a diatonic triad as a temporary tonic.

Understanding harmonic progression makes it possible to understand which notes are diminutions are which notes are the main melody.

I recall my teacher telling me that in Schenkerian analysis there is no such thing as the Ⅰ6/4 chord. This chapter explains why: in order for harmonic inversion to be a valid analysis, it needs to be possible to substitute the chord in root position while still preserving the overall harmony (if not the voice leading). Substituting the tonic triad in a progression like Ⅱ - Ⅰ6/4 - Ⅴ - Ⅰ produces the incorrect sound. The chord can instead be understood as a voice-leading neighbor to the dominant chord.

6. Some Secondary Structural Features

Voice Exchanges

The voice exchange is a pattern that involves two and only two voices, a pattern in which the voices literally exchange their pitches.

Some common forms of voice exchange follow.

In the 10-8-6 exchange two voices a third apart move stepwise in contrary motion to replace each other.

In the 10-10-6-6 exchange (or 6-6-10-10), one voice moves stepwise in a single direction, and the other has two pairs of contrary steps broken by a leap.

Voice exchanges have no prescribed function, but tend to “intensify” some of the notes in the melody. They can also cause a voice-leading tradeoff, where the natural voice leading roles can be exchanged before the resolution occurs.

Implied Notes

In the free composition, a note may be implied although not actually present in the music. This is possible because o fthe completion of a voice-leadig connection, the continuation o f a linear intervallic pattern, the complete of a voice exchange, or by the completion of a component of a compound melodic structure (as a special case of a voice-leading connection).

Implied notes are of particular interest when they have structural consequences. This means that the presence of the note plays an important part of the melodic structure of the piece.

Implied notes are often created through substitution, by which the note necesary for the voice-leading of the line is replaced by a different note in the harmony, perhaps in order to complete the harmony, or to begin or end a different sub-voice in a compound melody.

Register Transfer

Register transfer is when a voice is shifted into a different octave. This can result in an exchange of which voice is the descant.

Register transfers can occur in more implied ways: for example, a leap up by a seventh might actually be a neighbor-note motion downwards simultaneous with a register transfer.

7. Basic Axioms

Structural Levels

Schenkerian analysis involves breaking the piece into three layers. “Of these, the one most commonly associated with Schenker is that which often seemed to concern him least: namely, the background.”

The progression from background to foregroun moves from the basic idea to its realization; conversely, analysis involves the progessive reduction of a finished work to its fundamental outline. [...] In broadest terms, the closer we get to the background, the more similar any two pieces are likely to appear; obviously, the more detail we introduce, the more differences we are likely to find.

Models of Fundamental Structure

Schenkerian analysis operates on a simple rule of melodic motion based around the tonic triad: “eventually and usually within the theme itself, one triadic degree in particular—third, fifth, or eight—will assert itself as the primary tone (Kopfton), and a descending fundamental line (Urlinie) from this primary tone to the tonic will be traceable over the span of the piece or movement.”

The bass, on the whole, is easier to interpret than the meldoy. Since a tonal piece or movement normally begins and ends on Ⅰ, and since the end is signaled by an authentic cadence in the tonic key, we can see that the bass at the background level will be framed by the outline Ⅰ … Ⅴ–Ⅰ. In between this initial Ⅰ and the final Ⅴ–Ⅰ, we often find Ⅲ as an intermediate resting place in addition to (or instead of) the more usual secondary goal of Ⅴ. [...] The resul tis the large scale succession Ⅰ–(Ⅲ–)Ⅴ–Ⅰ, or a broken tonic triad. Because of this last feature, Schenker called this progression bass arpeggiation (Bassbrechung).

The combination of fundamental line and bass arpeggiation constitutes the fundamental structure (Ursatz) of a tonal composition, and represents the background level of analysis.

General speaking, foreground analysis is similar to the rhythmic reductions potrayed earlier, middleground analysis involves stripping out rhythm to look at how the fundamental structure plays out on a local scale, and background analysis looks at the fundamental structure of the piece as a whole.

8. The Concept of Prolongation

“Prolongation” refers to the ways in which a musical component—a note (melody prolognation) or a chord (harmonic prolongation) remains in effect without being literally represented at every moment.

Harmonic prolongation occurs when the harmonic structure of a section ultimately revolves around a single harmony/tonality. The main way the tonality is shifted is via secondary dominants, and otherwise it’s easy to read a standard harmonic progression as being a prolongation of the tonic harmony.

Melodic prolongation is when a single note (likely a member of the fundamental line) is prolonged, perhaps via arpeggiation or stepwise motion before, after, or around the note.

9. Prolongation of the Primary Tone: Initial Ascent

The initial ascent is a common (but optional) feature of the fundamental line, where the melody begins with a stepwise ascent up to the primary tone before beginnning the descent.

This is the last chapter that features any of Rudy’s underlining. It certainly made reading more difficult while it lasted, but I’ll admit that the book feels much more lonely from here on out.

10. Prolongation of the Primary Tone: Arpeggiation

First order arpeggiation is similar to the initial ascend, but instead ascends through the tonic triad to the primary tone.

Ascending motion in general, whether linear or arpeggiated, is part of the natural rise and fall of inherent in any complete musical statement. It creates a feeling of expectation, of tension, which the descending motion will presumably resolve.

It’s worth noting that the prolonged ascending line may be much longer than the fundamental line itself!

11. Introduction to Musical Form; Unfolding of Intervals

A quick introduction to binary form: a form with two sections, usually of equal length. Rounded binary form is a binary form where the B section is longer, and features a reminder of the A section.

Unfolding is a process by which a prolonged line can be understood as a vertical interval between the top and the bottom of the line. Unfolding specificially applies only if it is proceeding from or two another interval (vertical or also unfolded). It can only be understood as an unfolding if the voice leading between the successive intervals can be understood as valid voice-leading.

12. Fundamental Structure in Complete Units

Some generalities about the fundamental structure:

1. Though it’s profile will likely be reflected on at least one structural level closer to the surface, the fundamental line as such descends to the tonic (scale degree 1̂) only once.
2. The status of the fundamental line at any given time is determined by the highest currently active degree of the tonic scale. (Usually this means that some kind of prolongation is in force.) A note of the fundamental line is considered “active” until it has appeared for the last time.
3. The final 2̂-1̂ of the fundamental line is accompanied harmonically by the final authentic cadence.
4. The open notes showing the fundamental structure should be used sparingly. This includes the bass as well as the fundamental line.

Coupling of Registers

Sometimes, the fundamental line will be reflected in two different octaves, with a melody that spans a long range. However “Shenker’s principle of obligatory register dictates that the fundamental line should present itself within a single octave. The latter constitutes the primary (“obligatory”) register of the work, while other registers, introduced through coupling, remain subordinate.”

13. The harmonized Chorale

Chorales are “highly compressed in time”, featuring a chord change on most beats and a comparatively simple melodic line. This means that chorales often already resemble the result of a rhythmic reduction.

When looking for a primary tone in a chorale melody, repetition is a good clue: even if a higher note seems like a candidate for primary tone, a repeated lower note might be the proper pick. Another thing to keep in mind is whether each step of the descent is “sufficiently supported harmonically”: if the descent clearly belongs to the tonic harmony, it’s more likely to just be a diminution.

Some discussion is needed concerning the placement of scale degree 3̂ in the fundamental line. [...] Frequently, the third of the tonic scale [...] makes its last appearnace over a cadential 6/4 chord, and is actually part of a double passing-note formation dependant upon Ⅴ. Although it is often necessary to accept this contrapuntal support of 3̂, it is preferable to have this scale degree supported harmonically by a root-position tonic.