DIATONIC PROCEDURES I
|Chapter 12. Transition to the Common Practice Period|
|Chapter 13. Roman Numeral Analysis|
14.1 DEFINING TONIC
TONIC contains ^1 - ^3 - ^5 and is the central harmonic area in any key. Just as ^1 provides focus to a scale, this triad provides the identity of a key. It also provides the ultimate in stability and resolution, in both major and minor keys. The tonic is the beginning, and when there is a move away from tonic, there is always an inevitable return. All other harmonic areas have one primary purpose: to move toward the tonic. The tonic triad is like the king in a game of chess; it is the most important piece but is a relatively inactive one.
In major keys the tonic is major (I); in minor keys it is minor (i).
14.2 DEFINING DOMINANT
DOMINANT contains ^5 - ^7 - ^2 and is the exact opposite of tonic. It provides instability and unrest. It is with dominant that a departure from tonic is facilitated, and it is the means which makes a return back to tonic possible. Most of the power of the dominant comes from ^7 (leading tone) which has the strong tendency to move to ^1. In fact, when ^7 occurs in the prominent outer voices (bass and soprano), it must move by step to ^1.
When ^7 occurs in the middle voices (alto and tenor), it still really wants to resolve to ^1, but might not in order to conform to some other consideration of part writing, such as to create a better line. Under no circumstances should ^7 (as leading tone) be doubled.
In major keys, ^7 is automatically leading tone. There are two forms of ^7 in minor keys, the leading tone and the subtonic, which have completely different functions. Since the dominant function requires a leading tone, an accidental must be used to raise ^7. Note that dominant in parallel keys (C major and C minor, for example) is exactly the same major triad (V).
The form of dominant with the lowered ^7 is called MINOR DOMINANT, and will be discussed in Chapter 19. The minor dominant is never used in place of dominant.
Dominant is crucial in defining the tonic. The dominant is like the queen in a game of chess; it is the strongest and most active piece in the game, and serves to save the king.
The dominant can be made even more intense by expanding into a tetrad with the addition of ^4, creating the DOMINANT 7 chord. This quality of the dominant 7 is a Mm7. The top of the tetrad (the seventh above the root) must always resolve down by step in the same voice to a new chord tone in the next sonority, much like suspensions discussed in Chapter 9. In fact, the top note of ALL tertian tetrads must resolve down by step.
Learn more about the dominant 7th
Be careful to understand the difference between ^7 (leading tone) and the seventh of dominant 7. The former resolves up in a Ti-Do motion, while the latter resolves down by step (Fa-Mi).
14.3 HARMONIC STRUCTURE
Roman numerals are a good way to describe what is happening in the counterpoint. They are like words in a sentence. To analyze the structure, each word is assigned a function such as "subject" or "predicate". In the same manner, each Roman numeral is assigned a function.
The revelation of the meaning of Roman numerals is called HARMONIC STRUCTURE. There are two parts to harmonic structure:
Cadences end every phrase just as punctuation marks end every sentence. The most final sounding cadence is the AUTHENTIC cadence, which evolves from the clausula vera. There are two forms of authentic cadences: the PERFECT and the IMPERFECT (discussed below in 14.10).
The perfect authentic cadence (P.A.C.) requires a ^7 - ^8 (Ti-Do) or ^2 - ^1 (Re-Do) motion in the soprano, supported by a ^5 - ^1 (Sol-Do) motion in the bass. The harmonic motion is dominant to tonic. This cadence functions just like a period at the end of a sentence.
Since there is a likelihood for both the ^7 - ^8 and the ^2 - ^1 motions to occur, the resulting tonic can possibly have three roots (which includes the ^5 - ^1 in the bass). If this happens, the fourth voice must move to ^3 and omit ^5. This is one of the few times an incomplete triad can be found (see 14.3a below). Another solution is to have the middle voice move elsewhere (such as ^7 - ^5 or ^2 - ^3).
An authentic cadence can be cut in half by leaving out the culminating tonic: the soprano will end on ^7 (Ti) or ^2 (Re) and the bass on ^5 (Sol). This is a HALF CADENCE (H.C.). The half cadence functions like a question mark at the end of a sentence. The dominant of a half cadence will be a simple dominant triad, never as a dominant 7.
A prolongation is the expansion of a given harmonic area (frequently tonic) into musical space, ultimately leading to the cadence. Therefore, the most basic harmonic structure looks like the following.
The large tonic Roman numeral followed by the horizontal line represents the prolongation of tonic in musical space, and the large dominant to tonic at the end represents the perfect authentic cadence.
As before, the large tonic Roman numeral followed by the horizontal line shows the tonic prolongation, and the large dominant Roman numeral shows now a half cadence. Please note that the prolonging line stops just before the cadence. Also notice that the structural analysis utilizes uppercase Roman numerals even though it is in a minor key. The symbols for structural analysis describe the concept of tonic rather than identifying a specific harmonic area.
14.4 EXPANDING TONIC
The examples above are extremely limited, since they provide little of interest in the prolongation. But as more harmonic vocabulary is introduced there will be more ways to prolong tonic.
The first inversion of tonic has ^3 in the bass and is not as stable as the root position, but does create a way of expanding tonic:
Notice that the tonic prolongation includes information about the first inversions. As new information is encountered in a prolongation, there must be an explanation of how that new material is affecting the prolongation.
The only exception to this is a lone dominant within a tonic prolongation. When tonic and dominant (with or without the 7th) are alternated, there is no clear linear action created in the bass, so the dominant (only when in root position) requires no further explanation.
14.5 INVERSIONS OF 7TH CHORDS
The inversions of 7th chords are labeled by the location of the dissonance above the bass note. In root position, this is located a 7th above the bass. In first inversion, it is located between the 6th and the 5th above the bass. In second inversion, it is located between the 4th and 3rd above the bass. In third inversion, it is located a 2nd above the bass.
Note that it is easy to remember the positions of 7th chords by simply counting backwards from 7 (7 - 65 - 43 - 2).
14.6 DOMINANT AND DOMINANT 7 IN FIRST INVERSION
The first inversion of dominant has ^7 in the bass. If the bass moves ^1 - ^7 - ^1 (Do-Ti-Do), a neighbor motion is created. Therefore, the first inversion of dominant can prolong tonic as a NEIGHBOR CHORD (N). This works exactly the same with both the dominant triad and tetrad. Leading tone (^7), when located in the bass or soprano, must always resolve by step. When leading tone is in the alto or tenor, this resolution is preferable but not mandatory.
14.7 DOMINANT 7 IN SECOND INVERSION
The second inversion of dominant 7, has ^2 in the bass. This can act as a neighbor chord as well (^1 to ^2 to ^1), but can also prolong tonic as a PASSING CHORD (P), moving in the bass from ^1 to ^3.
The second inversion of dominant 7 can also serve as a neighbor chord to prolong the first inversion of tonic.
Note that Roman numeral for tonic is not repeated at the beginning nor in the middle; the only change is the position, not the harmonic area.
14.8 LEADING TONE TRIAD
The leading tone triad shares three scale degrees with the dominant 7: ^7 - ^2 - ^4. Even without ^5, it easily serves the same function as the dominant 7. Dominants, with or without a 7th, and leading tone triads belong to the general category of harmony called DOMINANCE.
The leading tone triad is diminished, and is traditionally found in first inversion (see Chapter 11). This places ^2 in the bass voice, and in effect serves the same functions as the dominant 7 in second inversion.
On rare occasions the leading tone triad can be found in root position; this generally happens in thinner (2 or 3-voice) instrumental music, and implies dominant 7 in first inversion (minus the root: ^5). It is safe, however, to assume that the "normal" position of the leading tone triad is in first inversion and that root position is "abnormal".
In minor keys be careful not to confuse the leading tone triad (which is diminished) with the subtonic triad (which is major). The subtonic will be discussed in Chapter 19.
14.9 DOMINANT 7 IN THIRD INVERSION
The third inversion of dominant 7 has ^4 in the bass. This scale degree is the 7th of the chord and must resolve down by step to ^3. Another way of saying this is the third inversion of dominant 7 must resolve to tonic in 1st inversion. This position of dominant 7 is frequently used as a neighbor chord to prolong the tonic.
Scale degrees ^7 (leading tone) and ^4 (the 7th of dominant 7) both have strong tendencies to resolve: ^7 up to ^1, and ^4 down to ^3. These are known as ACTIVE SCALE DEGREES. It is possible for the bass to leap into either of these, but they still need to resolve, and to do so with a stepwise motion. These motions share a similarity to the neighbor motions described above: ^1 - ^7 - ^1 and ^3 - ^4 - ^3, but appear to be missing the first part of the neighbor motion. Consequently, they are called INCOMPLETE NEIGHBOR (IN) chords.
Incomplete neighbor chords occur relatively rarely. It is important to spot an active scale degree in the bass, and for that pitch to resolve by step, in order to label this function.
14.10 IMPERFECT AUTHENTIC CADENCE
The imperfect authentic cadence (I.A.C.) is defined by any form of dominance moving to tonic, and is missing one or more parts of a perfect authentic cadence. There are three primary possibilities:
For the moment, perfect authentic cadences should be considered the norm, and should be used in written work. Imperfect authentic cadences will only be observed, in analysis work.
14.11 MORE ABOUT PROLONGATIONS
Passing chords and neighboring chords always occur in the middle of a prolongation, and are exclusively prolonging events. They must occur between two sonorities that have the same (or similar) function.
In a similar manner, incomplete neighbor chords must always move to a chord within the prolonged area.
While it is common to find tonic prolongations that begin with tonic, this is not always the case. It is possible for the tonic to appear later within the prolongation.
In certain circumstances, there might not be a tonic until later in the progression, but might have one at the beginning that is implied. In the example below, ^1 at the beginning of the melody strongly implies a tonic area, even though there is no supporting harmonic action.
Implied tonics will always be enclosed in parentheses, which makes the statement "this harmony is not supported by the counterpoint, but there is compelling evidence that it could be."
14.12 REPEATED ROMAN NUMERALS
As more and more complicated Roman numeral analyses are encountered, it is important to begin showing them in the simplest possible way. Never repeat the same Roman numeral back to back. The statement of a Roman numeral should always indicate that a harmonic change has taken place; if the same harmony is restated, the previous Roman numeral is still in effect.
The only exception to this is when a harmony ends a phrase, and then is also the beginning of the next phrase. In this context of two different phrases, it is appropriate to repeat the Roman numeral.
Even if the sonority changes positions, do not rewrite the Roman numeral each time. A general rule of thumb is to use the lowest, most stable position rather than to show all the position changes. In the example below, the first inversion of tonic on the second beat and the second inversion of dominant 7 on beat 4 do not add any new significant information, and in fact could disguise the large neighbor motion on beat 3.
14.13 DETERMINING THE KEY
The process of Roman numeral analysis requires a clear identification of the key, but that must be arrived at carefully. There is a common misconception that key signature always indicates the key; this is not true. Key signatures reveal the inventory of pitches being used, but that can be expanded with accidentals. There is only one accurate way to determine the key of a piece: locating and defining the cadences.
Up to this point, examples have been in either C major or C minor. In all subsequent chapters, a variety of key areas will be explored.
Authentic and half cadences reveal exactly what the key is since they are set formulas. Authentic cadences must end on tonic and must be preceded by a form of dominance. Half cadences must end on dominant, which must be major and in root position.
In the example below, even though there is a key signature of no accidentals, it is clear that it is not in C major because of all the sharps. Upon examination, the soprano and bass make it clear that it is in the key of E major, and is in fact exactly the same analysis as 14.12 above.
14.14 IMPLIED HARMONIC PROGRESSION
It is possible to determine the chordal motion in a piece of music by examining just the soprano and bass, which is called the IMPLIED HARMONIC PROGRESSION. Scale degrees found in the bass line imply specific harmonic actions, as seen in the vocabulary chart below. The soprano line confirms this, and make it more specific. For example, ^2 in the bass can imply either the leading tone in first inversion or the dominant 7 in second inversion (see below). If the soprano is ^4, that analysis is confirmed; if the soprano is ^5, it is also confirmed and further specified as dominant 7 in second inversion.
As your harmonic vocabulary expands there will be many more options with the implied harmony. Harmonic structure dictates what the best choice are, and eventually there will be multiple choices. The combinations of harmonic progression are almost endless, but they must always follow the logic of the Common Practice Period. This is similar to language studies. The possible combinations of words that form sentences are vast, but these combinations are limited by the logic of grammar.
Beginning with this chapter, your harmonic vocabulary will be summarized in two charts, one for major keys and one for minor keys. The charts present
Note that the minor key chart presents two forms for ^6 and ^7 (lowered and raised).
Provide a Roman numeral and structural analysis, and circle and label all non-chord tones, for the following pieces in Music for Analysis [numbers in brackets indicate placement in the anthology, and the location of recorded excerpts on the accompanying CD]:
Add soprano, alto, and tenor lines to this figured bass, then provide a Roman numeral and structural analysis:
To prepare this writing assignment properly, use the notation guidelines appendix, located at Basic Principles of Music Notation, Semester I.
Links to chapters in this unit:
|Chapter 12. Transition to the Common Practice Period|
|Chapter 13. Roman Numeral Analysis|
Link to previous unit: BASIC RULES FOR SPECIES COUNTERPOINT
Link to next unit: DIATONIC PROCEDURES II: Expanding the Phrase
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