When we refer to the key of a piece, we generally speak of a single key: Bach's Mass in B minor, Mozart's "Jupiter" symphony in C major, Beethoven's Fifth Symphony in C minor. Although we speak about pieces of music that way, we are of course aware that they are not in just a single key; other keys occur as well. Several related keys reinforce the global key through their close relationship to it.
Large-scale forms in tonal music are based on arrangements of related keys. This is not to say that themes, their number and placement are unimportant formal elements. They are important. However, themes are the individualized aspects of a composition, specially composed for a piece, while its key scheme is the generalized aspect. The structural keys in a composition are ordered in a limited number of conventional plans. In short, themes are organized within a group of structural keys rather than the structural keys being organized around the themes.
It is easy to identify the global key of a piece; check the key signature, the last few chords, and final cadence. But it is not always easy to determine where the various related keys in a work are located, i.e., where a prevailing key yields to a new one (modulation), and becomes fully established. Further, we must distinguish between modulations to structural keys on the one hand and, on the other, tonicizations, which are brief, passing references to related keys, and may appear at any time. The following paragraphs offer hints for making that distinction, and for determining what and where the structural keys are.
2. Knowing What to Expect
As mentioned above, large-scale form in tonal music depends on an arrangement of related, structural keys. Given a particular global tonic, the related keys are predictable, and even their arrangement (succession) follows certain conventions. After determining the global tonic, knowing which structural keys to expect and in what order to expect them helps a lot in determining where they are.
Composition teachers of the eighteenth-century wrote about key relationships and the arrangement of structural keys. Joseph Riepel, for instance, pointed out in 1755 that the first movement of a symphony or concerto required only three main keys, I, V, and vi. Other keys might appear to support the main ones, but only briefly. He mentions the following scheme as a possible ordering of keys: I - V - vi - iii - IV - ii - I.[1] In a miniature piece for illustrating a conventional succession of structural keys, Riepel casts each key as an imaginary person in a household in order to specify the relative structural importance of each one. In this imaginary (and humorous) tonal story, the landowner (Meyer) is cast as tonic, the chief servant (Oberknecht) as dominant, chief maid (Obermagd) as submediant (vi), maid's assistant (Untermagd) as mediant (iii), day laborer (Taglohner) as subdominant, and the transient female worker (Unterläufferin) as supertonic (ii).[2]
Another composition teacher, Johann Philipp Kirnberger, who studied briefly with J.S. Bach, gives the same structural keys (in 1771), and goes further than Riepel by specifying the relative duration of each key in order to show the relative structural weight of each in the overall key plan. Tonic and dominant are highest in structural order, vi and iii lower, ii and IV lowest.[3]
Summary: The keys to expect in eighteenth-century works (and, to a large extent, in those from the early nineteenth century) are, aside from tonic, the keys V and vi, as well as IV and ii, if less frequently and to a lesser degree than V and vi. Knowing what to expect will help in identifying the structural keys in a piece.
3. What Key am I In?
As explained above, knowing what keys to expect in a piece is helpful in narrowing down the possibilities, but there still remains the detailed analytical work of figuring out which key is in effect, and distinguishing between an established key and a passing tonicization. The following paragraphs give some guidelines for figuring out the local key, and for distinguishing structural keys from subordinate tonicizations.
First, a warning: don't rely on accidentals as a way of determining the key. It is of course important to be aware of accidentals since they do appear within a local key. But altered tones are generally found throughout a piece, as members of applied dominants and as chromatic embellishments in the melody and harmony, and are not dependable for determining the key. Consider accidentals as supporting evidence for a key you've identified based on other, more reliable factors, and not as the main evidence.
The best way of determining the local key is to check the music for typical cadential gestures such as those found in PAC's. That is to say, check the harmony, bass line, and associated melody for typical PAC components. A bass line coupled with an upper part as illustrated in the following example (see immediately below) indicates a full-fledged cadence signaling the establishment of a key, possibly a structural key.
Example 1
Look at the bass line, E-F-G-C, supporting a clearly cadential progression I6 - IV - V6/4-5/3 - I, and ending in a PAC. The coupling of the strong cadential bass with a clear arrival on scale degree 1 in the treble are unmistakble signs of the establishment of a key.
After locating a cadence of this sort, a quick review of the possible structural keys for the piece should tell whether the key in question is structural or not. If not, it may be only a brief tonicization. If the key is potentially structural, the next step is to examine the music leading up to and following the cadence to see if the bass line, melody, and harmonies confirm that same key. If so, and if the key is either V or vi, it is clearly a structural key in the large-scale sense. If not, it may be either a tonicization (see below for more) or a subsidiary, passing key on the way to a structurally more important one. For determining structural keys, then, follow these three steps:
- Locate PAC's
- Is the key on the list of primary structural keys?
- Yes: proceed to step 3.
- No: this is possibly a passing tonicization with limited formal significance.
- Is the music leading up to and, possibly, following the PAC all in the same key?
- Yes: This may well be a structural key, especially if the passage in the key is lengthy, including complete thematic statements.
- No: This may be a subsidiary key, especially of the passage in the key is relatively brief.
4. Tonicization or Modulation?
As Aldwell and Schachter point out in their textbook, Harmony and Voice Leading, there is no fixed boundary between tonicization and modulation: "we cannot percisely determine where one stops and the other begins."[4] One way to distinguish between the two
is to check for a PAC in the vicinity. Tonicizations often do not involve PAC's, while modulations routinely do. Further, the tonicized chord, as a temporary, local tonic, does not generally remain in effect very long. By contrast, a structural key reached through modulation does. Finally, tonicized chords ordinarily occur in tonally unstable sections, e.g. in transitions, where thematic material is not presented in full. By contrast, modulations establish a local tonic that remains stable, and thematic material (often new material) is presented in full. Still, even with these guidelines it may not always be possible to decide. Ultimately, the most important issue is how much influence a key exerts over the piece as a whole.
Long before Aldwell and Schachter's text, Kirnberger recognized the difference between these two possibilities of tonal shift, although he did not use the modern term tonicization. "Although thirds taken from outside the scale of a given key...usually indicate a modulation, this is not always the case. Often no modulation takes place....For if one does not actually go to the announced key, or if one abandons it immediately, no modulation has occurred." Kirnberger provides an example of such a situation, where some of the chords involving altered thirds are what we today call applied dominants, used in tonicizations.[5]
Summary: Tonicizations operate locally and thus have small-scale influence, while modulations operate globally and have large-scale influence.
5. Half Cadence on V or Authentic Cadence in V?
Beginning students in analysis often become confused when phrases end on V. Is the chord: a) a dominant (V) in the prevailing key; or is it b) a local tonic (I) in a new key? The answer to this question is crucial. Answering it incorrectly leads to misinterpreting the local context and, sometimes, to misidentifying the work's large-scale structure.
Therefore, note well:
- If the chord is a dominant (case a above), the phrase has ended on a V, at a half cadence in the prevailing key.
- If the chord is a tonic (case b above), the phrase has ended on a I, at an authentic cadence (perfect or imperfect) in a new key.
For example, if near the beginning of a piece a phrase ends with a dominant chord, the music is most likely on the dominant chord in the tonic key, at a half cadence. The bass line will most likely be 2-5, 4-5, or #4-5 supporting a progression from a dominant preparation chord (ii, IV, or V/V) leading to the dominant. The bass line, melody, and harmonic progression leading into the phrase ending will not be those of an authentic cadence--that is, harmonically neither ii-V-I nor IV-V-I, with the bass line 4-5-1 or 2-5-1 featured in authentic cadences.
However, if further on in the piece (e.g. at a repeat sign) a phrase ends with a dominant chord, and the harmonic progression and bass line are those characteristic of an authentic cadence, then the music is most likely in the dominant key on a tonic chord, at an authentic cadence (probably a PAC).
Summary: To distinguish tonally between phrases that end on a V chord in the tonic key and those that end in the key of V on a tonic chord, examine the cadence closely (melody, harmony, bass line) to determine whether it is a HC, or a PAC or IAC.
1. Joseph Riepel, Anfangsgründe zur musicalischen Setzkunst, vol. 2, Grundregeln zur Tonordnung (Frankfurt and Leipzig, 1755), 67.
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2. Riepel, Grundregeln zur Tonordnung, 66. Leonard Ratner discusses Riepel's ideas on tonal form and includes the musical example in Classic Music: Expression, Form, and Style (New York: Schirmer, 1980), 49-50.
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3. Kirnberger, The Art of Strict Musical Composition, trans. David Beach and
Jurgen Thym (New Haven: Yale University Press, 1982), 126. Kirnberger's Table 7.1 (p. 124) shows the structural keys, and the example on p. 126 schematically shows the relative durations of the keys.
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4.Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 2nd ed. (New York: Harcourt, Brace, Jovanovich), 196.
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5. Kirnberger, The Art of Strict Musical Composition, 128-29n. See also the example on p. 120 and the accompanying discussion. There, all the chords involved are applied dominants involved in tonicizations.
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