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Exam review

Exam 1
Final Exam

Harmony

A&S Questions
Figured bass
Four-part
writing
Voice leading
in 4 parts
Dominant
sevenths

This page has a variety of resources for students in Larry Zbikowski's undergraduate harmony course at the University of Chicago, Autumn term 2008.

Edward Aldwell and Carl Schachter, Harmony and Voice Leading, 3rd ed. (Wordsworth, 2003) [Call number: MT50 .A446 2003]

Intervals

• numerical size
• quality of interval (major, minor, perfect, augmented, diminished)
• ascending and descending intervals
• interval inversion (seconds through sevenths, all qualities)

Scales and Modes

• structure of major scales—know the placement of half-steps
• structure of all three forms minor scales can take (natural, harmonic, and melodic)—here you'll need to know not only the placement of half-steps, but also what notes of the scale are altered in the harmonic and melodic forms
• the difference between the subtonic and the leading tone
• all major and minor key signatures through six sharps and six flats
• relative and parallel relationships between major and minor
• names of scale steps (tonic, supertonic, mediant, and so on)
• know how to generate D, E, F, G, A, and C modes

Species Counterpoint

• the rules for melodic writing and the rules governing harmonic writing in two-voice first species; expect to write counterpoint on the test
• the rules governing harmonic writing in two-voice first species
• the four types of motion described by two voices (similar/parallel, oblique, and contrary motion)
• all other style rules for species counterpoint discussed thus far including
  • starting and ending intervals
  • clasula formalis (in all modes)
  • rules governing chromaticism
  • rules about leaps in both voices at the same time
  • be able to provide an in-depth critique of a given melodic line

Triads

• know how to construct each of the four types of triad: major, minor, augmented, and diminished
• know the designations of the elements of a triad (that is, root, third, and fifth), and how to build a triad from any of these
• know the different arrangements of the notes of the triad (root position, first and second inversion), as well as their figured bass designations (detailed figured-bass notation will not be emphasized on the test)
• know the vocal ranges typical for SATB writing, as well as the rules about how the voices should be spaced (e.g., no more than an octave between S and A or A and T)

Seventh chords

• know how to construct the following five types of seventh chord: major seventh, minor seventh, fully-diminished seventh, half-diminished seventh, and dominant seventh
• know the dual-appellation designation of each type of seventh (which identifies the type of triad and seventh that constitute the chord): for instance, a half-diminished seventh would be called a diminished-minor seventh
• know the different arrangements of the notes of the seventh chord (root position, first, second and third inversion), as well as their figured bass designations

Review materials for the final exam will appear here closer to the time of the exam.

Unit 5: Procedures of Four-Part Writing

Are there any strict guidelines for doublings?

How effect does the position of the soprano have on how a chord sounds?

What is the function of the inner voices in a four-part texture (cf. p 69)

What kinds of motion are forbidden in a four-part texture?

When can contrary motion, which is usually the safest bet, cause problems in the voice leading between the outer voices?

What is overlapping?

Unit 6: I, V, and V⁷

How is an imperfect authentic cadence different from a perfect authentic cadence?

What is the relationship between harmony and rhythm (especially meter)? Is it always the case that the one should reinforce the other?

Unit 7: I⁶, V ⁶, and VII⁶

What can a first-inversion harmony be used to expand a root-position harmony? Must the root-position harmony always be first?

What rules, if any, are there for doublings when first-inversion harmonies are used?

What guidelines are there for resolving the tritone within a VII⁶ chord?

What relationship should there be between harmony and meter?

Unit 8: Inversions of V⁷

What should normally happen to scale step 4 as V⁷ or any of its inversions moves to I? What are the exceptions?

Can different inversions of V⁷ be used in succession? What sort of figure typically results in the bass?

Figured bass is a notational shorthand developed in the early seventeenth century for ensemble music. Ensembles of the period consisted (most typically) of a fairly small number of players and singers—perhaps between five and eight (sometimes more, sometimes fewer). At this time, scores (that is, a notation that combines all of the various parts) were still relatively uncommon. Figured-bass notation can be thought of as a proto-score notation. The notation consists of a bass part (played by one or more bass instruments, such as viol, bassoon, theorbo, or organ) together with "figures" (numbers) indicating the intervals that other parts made with the bass. This shorthand was enough to allow players of harmonic instruments (such as harpsichord, lute, guitar, harp, and so on) to create multi-voice parts that would harmonize with the ensemble as a whole.

With few exceptions, figured-bass notation observes octave equivalence. Thus, if the singer's part made a 13th with the bass, it would be notated as a 6th. What exceptions there are almost always involve an octave above the bass—for instance, a 9th above the bass going to an 8ve would not be notated "2-1" (as a strict adherence to octave equivalence would suggest) but "9-8".

Because figured bass was a shorthand, the intervals that were most common above the bass were not notated. For instance, if the singer's part made a 5th above the bass and the violin a 3rd (or some octave-duplicate of those intervals), neither interval would be notated. Thus a bass note with no figure always stood for a "5-3" chord. If there was a 6th and 3rd above the bass, only the 6th would be indicated—3rds were simply too common to deserve notice.

What was included in figured-bass notation, invariably, were any departures from the diatonic (key-based) framework that provided the context for any bass. Any and all departures from the notated key signature were indicated in the bass, even when these applied to intervals (such as 3rds and 5ths) that were normally left out of the figures.

The nuances of figured-bass practice varied over time and from region to region. During the period countless treatises attempted to clarify the practice; modern books explicating the different practices run to many pages and multiple volumes, and even so cannot always give a clear interpretation of a given figured bass. When all is said and done, performers of the time relied on their knowledge of the style to interpret a figured bass, and we must do the same when we encounter this notation. In class, we will use a few standard figures as a shorthand for common inversions and voice-leading strategies. These are best memorized; eventually, they will provide a highly reliable guide, independent of key and texture, to the harmonic texture of a composition.

1. Observe the ranges for each voice. After all, it is vocal writing we're talking about. Taking middle C as C4, the recommended ranges for each voice are as follows.

The range for each voice can be extended above and below by approximately a third, but this should be done with caution.

2. Remember to observe other vocal writing rules (such as those used in counterpoint) within each vocal line. Avoid voice-crossing and voice overlap (at least within our simple exercises). Do not use augmented or diminished intervals, avoid sevenths, and step in the opposite direction after a leap of more than a third or a fourth (depending on the context and what the voice does next).

3. Know the chord components for each chord.

4. Choose a provisional voicing for the first chord (perhaps look ahead to see what might work out).

5. Keeping common tones between chords wherever possible, sketch a few chords (I always work in pencil myself). Perhaps work to a phrase end or other logical stopping point.

6. Check for parallels (octaves and fifths). Remember, you must check between all voice pairs for parallels. A good general rule is that if all the voices move in the same direction between chords parallels are likely. If necessary, go back to #4.

7. Two minor points to remember:

1. Parallels occur where the harmony changes. In certain circumstances, a harmony is repeated. Voice motion is then relatively free.
2. Parallels between phrases may be permitted on occasion, but let's not make a habit of it, okay?

1. The basic rules for voice leading in four parts are taken from two-part species counterpoint:

1. parallel perfect unisons, fifths or octaves between any pair of voices is not permitted
2. similar motion into a perfect unison, fifth, or octave by any pair of voices is not permitted

2. Because the texture of four-part harmony means that individual pairs of voices are less exposed than in two-part practice, the second of these rules (1b) is relaxed somewhat. The guidelines are these:

1. similar motion into a perfect unison, fifth, or octave by a pair of voices is permitted if (i) one of the voices moves by step and (ii) one of the voices is an inner voice
2. similar motion into a perfect unison, fifth, or octave by the outer voices is possible only if one of the voices moves by half-step

Keeping track of all of the voice pairs and their motions can be rather daunting. Remember, however, that voice-leading problems occur when voices are moving in the same direction. When voices make use of contrary or oblique motion, the problems pretty much disappear.

3. Keep in mind that certain notes, in certain contexts, are regarded as tendency tones—that is, they have marked voice-leading tendencies that should be respected:

1. the leading tone (as the third of the V chord or root of the vii chord) has a marked tendency (rehearsed many times in class) to ascend a half-step to the first step of the scale
2. scale-step 4, in major, has a somewhat weaker tendency to descend to scale-step 3. When, however, it occurs together with the leading tone (as it does in the V⁷ and vii chords) it creates the key-defining tritone and thus should lead to scale-step 3 (whether in major or minor)
3. any chromatically altered note (the prime example is the leading tone in minor) should be regarded as a tendency tone

Not only should the tendencies of tendency tones be respected, but tendency tones should not be doubled, since to do so reinforces the obvious and since it can lead to parallel octaves. For instance, if two voices are both on the leading tone and each leading tone progresses as it should (to the first step of the scale), parallel octaves will result.

4. It is possible to omit the fifth from a chord; the result is called an incomplete chord. The third, however, is never omitted in this style. If the seventh is omitted from a chord it becomes a standard three-note chord. If the seventh is required by the figured bass or (less frequently) by context, it may not be omitted.

5. Although chord spacing is not directly related to voice leading, reinforcement of the point seems necessary. As a general practice, each of the upper three voices should stay within an octave of the next adjacent voice. Thus soprano and alto should never be more than an octave apart, and tenor and alto should never be more than an octave apart. Although one can see exceptions to this in four-part chorales, they are generally for expressive purposes. Since we are not currently setting text, we shall not avail ourselves of this resource and, in the interests of greater homogeneity in vocal sound, hew to the stated guidelines for voice spacing.

The dominant seventh (V⁷) is perhaps the most important member of a class of harmonies used in tonal music, and that is the class of dissonant chords. Included in this class are the leading-tone triad (vii°) and half- and fully-diminished seventh chords. Each dissonant harmony contains one or more dissonant intervals. In the case of a root-position V⁷, the intervals are the seventh above the bass, and the tritone that exists between the third and seventh of the chord. The following chart may be useful:

As we shall soon see, V⁷ can occur in different inversions, and so the seventh above the bass may not always be there. The tritone, however, is invariable.

As you know, in both melodic and harmonic contexts the leading tone of a key (7) is a note with a pronounced tendency, and that tendency is to ascend a half-step to tonic (1). (Of course, in minor the leading tone has to be provided, since it isn't in the key signature; this leading tone often has a more marked effect, since it is foreign to the key signature.) In major, the fourth scale step (4) also has a tendency (although much less strong) to descend a half-step to the third step of the scale (3). Combined in the tritone of the V⁷, the tendencies of these two notes become even more pronounced—7 wants to go to 1, and 4 wants to go to 3.

It is the usual practice in treating the voice-leading of each V⁷ chord to respect these tendencies—to ignore them is to ignore how the chord functions (as a dissonant chord) and to turn a deaf ear towards a particularly compelling aspect of musical syntax. The tendencies of 7 and 4 also dictate how they should be treated in four-part textures. Since both are "charged" notes, they should not be doubled—there should be only one 7 and one 4 amongst the four voices. Given the richness of the V⁷ chord, the fifth of the chord (2) is often left out, especially where it will create voice-leading problems. The root of the chord (5) is then doubled at the unison or octave.

Because V⁷ is a dissonant chord that bundles all these various tendencies (together with either explicit or implicit fourth/fifth root motion to tonic), it is completely ineffective to introduce V⁷ and then follow it with V. In general, once V⁷ is introduced it should proceed to tonic (or to some tonic substitute, as we shall see)—anything else is just lame.