Voice Leading I
Dominant Cadences
Introduction
A simple way to begin formal part writing is to write cadences in all the major and minor keys. This both develops facility in thinking about harmonic progression within any given key, and also develops good habits for bringing traditional musical statements to an elegant close. Cadences are formulae used to punctuate the syntax of a musical statement. They are places of rest or pause and thus are typically more formulaic than then the other more creative and original portions of musical composition.
Cadences are traditionally labelled according to their harmonic progression, as follows:
- Perfect cadences have the progression V-I. Variations on this progression are V7-I (quite common), viiº - I (usually as we will see, with the viiº in first inversion), or viiº7 - I. This cadence occurs in both the major and minor modes. When in minor, of course, the dominant seventh is given a raised leading tone.
- Plagal cadence. A plagal cadence is the formula IV-I. It is a more gentle progression, due to its possessing the tonic note of the key as a shared tone between the two chords. In terms of harmonic dualism, it is a strongly reciprocal motion, from the subdominant to the tonic. The closing cadence of most Christian church hymns ends with an "Amen," which is almost universally set as a plagal cadence.
- Deceptive cadence. The deceptive cadence has for formula
V-vi in major and V-VI in minor. The V can be a triad or the
dominant seventh type. The "deception" here is that the ear
expects a resolution of the V chord to the tonic triad, and indeed the
leading tone does move up "properly" to the tonic, but the
bass note G, rather than moving down to the tonic, moves instead up to
the submediant. It is best thought of as a dominant chord that resolves
to the relative tonic
rather than to the normal tonic. It is quite a striking progression
and composers have often used it to stunning effect.
- Phrygian cadence. Far less common, but important for the study of both modal and tonal music. This can be thought of as the progression vii-i where the vii chord is spelled as a regular minor triad resolving either to a tonic minor triad or an altered major tonic triad. Thus it makes use of a lowered second scale, and logically takes on the name Phrygian cadence. See the example below to clarify this.
For all the cadences above, they have two variants: authentic and inauthentic. This refers to whether the tonic closing chord has the tonic note in the soprano. If so, it is considered to be an authentic cadence. If the third or fifth is in the soprano, this is considered to be an inauthentic cadence, presumably because the tonic chord does not sound quite as definitive or final if the tonic note is not in the upper voice. This language is a little archaic, but it is a common designation and should be recognized as such.
Let's look at how to voice these various cadences. Learning these formulae will be of great benefit when you begin to write full harmonic progressions. The procedures here can be applied to a great many harmonic situations.
Perfect (Dominant) Cadences
Perfect cadences are cadences where the dominant triad or dominant seventh chord resolves to the tonic triad: "V-I" or "V7-I." The I tonic triad in this case can be either major or minor. Perfect cadences can also be expressed by substituting viiº or viiº7 for the V or V7 chord.
In all of these cases, what unifies the perfect cadence is the presence of the leading tone in the penultimate chord, which has the tendency to rise to the tonic.
1) V-I. In cases where the dominant chord is a simple triad, without the seventh, follow the basic rules of doubling. Be sure to resolve the leading tone (the third) of the dominant triad to the root of the tonic triad whenever possible.
Notice here that when the dominant triad is in first position, the rule for any first inversion triad is to double this voice in the soprano. In order to then avoid parallel motion between the voices, the soprano needs to drop down to the fifth while the leadingtone resolves upwards in the bass. This goes against the natural tendency for the leading tone to resolve upward, but since it doing so in the bass, the ear is satisfied and the soprano is free to resolve downwards.
Similarly, if the leading tone is "buried" in the inner parts, it is also customary to allow the leading tone to fall to the fifth of the tonic triad:
2) V7-I. When the cadence involves a dominant seventh chord, then you must be careful to resolve the tritone according to the following principle:
The seventh of the dominant seventh chord resolves down a step, while the third of the dominant seventh chord resolves up a step. Depending on where you place the pitches, the movement between the two notes of the tritone will either be inward or outward. But the actual movement of the pitches are identical:
3) viiº-i. For diminished triads and diminished seventh chords, the following principle applies:
Diminshed triads can sometimes substitute for a full V7-I cadence. This results in a somewhat lighter and slightly more ambiguous harmonic motion, since the progression lackss the strong V-I root movement. When this occurs, it is almost universally the case that the viiº triad is voiced in first inversion, with the third in the bass. This third is then doubled in another voice. By so doing, one avoids an awkward relationship of a tritone between the bassnote and an upper note, as would occur if one were to voice the chord in root position. This progression sounds very much like a V 4-3 to I progression, since (in the key of C), the D is in the bass in both cases.
Here are some examples of viiº to i. As this progression occurs more often in the minor mode, let's express it in C minor.
Notice that in the last measure, the fifth has been doubled, rather than the third. This is approriate in this context, as long as the third remains in the bass.
4) viiº7 - i. In the case of the fully diminished seventh chord, recall that this chord is the "top part" of a dominant seventh minor ninth chord. There is a chapter in Book 1, if you wish to review this concept.
This chord originally appears in the minor mode, since the Ab is already part of the key of C minor, and the B natural is present in any perfect cadence in minor. So powerful was the sound of this diminished seventh chord, however, that in the common practice period it routinely was used in both major and minor cadences.
The following information is taken from pp. 324 and 325 of Robert Gauldin's Harmonic Practice. It provides a good summary of the principles involved.
First, compare the following two musical passages, which present a simple harmonic back and forth between dominant and tonic triads (in C minor). The first uses dominant seventh chords in a variety of inversions, and the second uses exactly the same voicings, but for the sustitution of the Ab for G. This simple substitution transforms all the dominant seventh chords into diminished seventh chords with exactly the same function. It clearly demonstrates the close relationship between dominant and diminished sevenths.
Listen to the chord progressions and hear the subtle difference between the V7 and the viiº7. In much music, the contrast is more stark; the point of this exercise is to hear how closely the two types of chords can be aligned.
Voice leading with diminished seventh chords
Voice leading with diminished sevenths are a little bit more problematic, due to the existence of the two overlapping tritones. When resolving into a triad with a perfect fifth, there is the possibility of parallel unequal fifths, that is, a tritone resolving in similar motion into a perfect fifth:
The fact is, this is a situation where the "rules" of avoiding parallel motion are set aside in favor of practicality and the desire to employ the diminished seventh triad as a compositional tool. Primarily, one should avoid such parallel unequal fifths between the soprano and the bass, as in the final measure of the next example. Otherwise, composers have freely used voice leading with parallel unequal fifths. The first four measures are all "approved" in a standard text such as Gauldin's.
Notice here that in all cases, the seventh resolves upwards to the root, creating the proper resolution. The other voices then have considerable freedom, with the main consideration being the resultant doublings in the tonic chord. There is always some compromise. The first measure gives a well-voiced final triad, but was arrived at through parallel unequal fifths. The second measure avoids this, but results in a double of the minor third, potentially a difficult chord to tune.
Here are some other possible resolutions of diminished seventh chord voicings, this time in C major.
CONCLUSION ABOUT RESOLVING DIMINISHED SEVENTH CHORDS:
- The leading tone should always go up a step to the tonic.
- The other voices have considerable freedom,
- Beware of resolutions with doubled thirds, but use them if the voice leading is smooth.
- Avoid parallel unequal fifths between soprano and bass.
Using the procedures for perfect cadences with secondary chords.
Once you learn how to properly resolve dominant and diminished triads and sevenths chords to the tonic triad, the same rules can be applied to any secondary dominant passage as well. Thus, by learning these procedures, you can apply them in a lot of other situations where a dominant or diminshed typed chord resolves to a chord other than the tonic.
Since you can now instantly voice V/ii, V/vi, V/iv and V/V in any key by applying the same rules of voice leading. you can then also voice viiº/ii, viiº/vi, and viiº/V, as these chords have the same function. All of the above secondaries can be voiced as either triads or seventh chords, with not change in function but with a richer harmonic color.
Here is an example which packs a lot of these chord progressions into a short time frame. Study it, understand it, maybe transpose this to other keys, and you'll have a complete understand of dominant type chords and their resolutions, both at cadential points and also within a musical phrase.
Listen to this pendantic progression just to observe the way it moves between dominant 7th and diminished 7th resolutions. Notice also how the bassline at the beginning is rather awkward, due to the preponderance of root position chords. But by the middle of measure 2, there is a slow and steady rise of the baseline from low F to high C, made possible through the use of various inversions and dominant/diminished seventh chords.