Music Theory Voice Leading and Counterpoint Syllabus

What is the primary musical purpose of using first-inversion ($^{6}$) chords in a progression?

To create a smoother, more melodic bass line (stepwise motion), to lighten the sonority, and to allow otherwise weak chords (like vii°) to be usable — vii°$^{6}$ is the standard form of the leading-tone triad.

What are the three common uses (types) of the six-four ($^{6}_{4}$) chord, and why can't it be used freely?

Cadential (V$^{6}_{4}$–$^{5}_{3}$ embellishing V), passing (bass fills a third), and pedal/neighbor (bass sustained). It is treated as a dissonance because the fourth above the bass is unstable, so each use requires a specific resolution; the bass note (the fifth of the chord) is doubled.

In a cadential $^{6}_{4}$, how do the sixth and fourth above the bass resolve?

They resolve down by step over the stationary bass: the sixth falls to the fifth and the fourth falls to the third, producing V (or V$^{7}$). It occurs on a stronger beat than its resolution.

When harmonizing a chorale melody, what is the recommended overall working order?

1) Analyze the key and any modulations; 2) plan the cadences (choose cadence types for each phrase ending); 3) sketch a bass line and harmonic rhythm using functional progressions (T–PD–D–T); 4) fill inner voices following doubling and voice-leading rules; 5) add embellishments/NCTs.

When harmonizing a melody, which harmonic function pattern should the chord choices follow?

The functional cycle tonic → pre-dominant → dominant → tonic (e.g., I–IV/ii–V–I). Retrogressions such as V–IV are avoided in common-practice style.

Name and define the four standard cadence types available when harmonizing a phrase ending.

Authentic (V–I; 'perfect' if both chords are root position and the soprano ends on $\hat{1}$, otherwise 'imperfect'), half (ends on V), plagal (IV–I), and deceptive (V–vi, or V–VI in minor).

In figured bass, what chord positions do the figures (none/5,3), 6, and $^{6}_{4}$ indicate?

No figure (or $^{5}_{3}$) = root-position triad; 6 (short for $^{6}_{3}$) = first-inversion triad; $^{6}_{4}$ = second-inversion triad. Figures give intervals above the bass, not chord roots.

What are the figured-bass symbols for the three inversions of a seventh chord?

$^{6}_{5}$ = first inversion, $^{4}_{3}$ = second inversion, $^{4}_{2}$ (or just 2) = third inversion; a plain 7 indicates root position.

In figured bass, what do an accidental standing alone and a slashed figure (or a figure with a plus) mean?

An accidental alone applies to the third above the bass (e.g., $\sharp$ = raise the third, common for the leading tone in minor). A slash through a figure or a $+$ before it means raise that interval a half step.

What does a horizontal line following a figure in a figured bass indicate?

That the notes above the bass are held (the harmony is sustained) while the bass moves or the figure remains in effect — the upper voices do not change with the new bass note.

In first species counterpoint, what is the rhythmic relationship between the counterpoint and the cantus firmus, and which intervals are allowed?

Note against note (1:1), whole note vs. whole note. Only consonances are allowed: perfect unison, octave, fifth, and imperfect thirds and sixths. No dissonances, and the fourth is treated as a dissonance against the bass.

What are the rules for beginning and ending a first-species counterpoint above a cantus firmus?

Begin on a perfect consonance (unison, fifth, or octave above; if below the cantus, only unison or octave). End on a unison or octave, approached by contrary stepwise motion (leading tone rising, cantus descending $\hat{2}$–$\hat{1}$).

In species counterpoint, what is the rule governing approach to perfect consonances?

Perfect intervals (unison, fifth, octave) must be approached by contrary or oblique motion, never by parallel or similar motion (no parallels; no direct fifths/octaves).

In species counterpoint, which melodic intervals are permitted in a single line, and what should follow a large leap?

Steps and leaps of a 3rd, 4th, 5th, minor 6th (ascending only), and octave; no augmented or diminished intervals or 7ths. After a leap (especially a large one), the line should change direction, usually by step, to recover.

In second species counterpoint (2:1), how are the strong and weak beats treated with regard to consonance and dissonance?

The downbeat (strong half) must be consonant; the weak half may be dissonant only if it is a passing tone approached and left by step in the same direction. Weak-beat consonances may be approached by leap.

How does second species affect the parallel-fifths rule from beat to beat?

Perfect fifths or octaves on successive downbeats are still faulty if the intervening note does not sufficiently break the parallel (a leap of at least a fourth in the counterpoint is traditionally required); afterbeat consonance does not automatically excuse downbeat parallels.

In third species counterpoint (4:1), which dissonant figures are permitted besides the passing tone?

The neighbor tone (upper or lower, on a weak quarter) and the double neighbor/cambiata figure. The nota cambiata is a four-note figure: step down to a dissonance, leap down a third, then step up — the dissonance on the second note is left by leap, an allowed exception.

In third species (four notes against one), which beats of the measure must be consonant?

The first quarter (downbeat) must always be consonant; the other quarters may be dissonant if they form correct passing, neighbor, or cambiata figures — dissonances must be approached and left by step (except in the cambiata).

What is the defining rhythmic-dissonance pattern of fourth species counterpoint?

Syncopation: the counterpoint is tied over the barline so a consonance on the weak beat is held to become a dissonant suspension on the strong beat, which then resolves down by step to a consonance (preparation–suspension–resolution).

Name the standard suspension types above the bass and the one used in the bass, by interval numbers.

Above the bass: 4–3, 7–6, and 9–8 suspensions (dissonance → resolution). In the bass voice: the 2–3 suspension. All resolve down by step except the rare retardation (e.g., 7–8), which resolves up.

What are the three parts of a suspension, and on which beats do they fall?

Preparation (a consonance on a weak beat, tied over), suspension (the dissonance sounding on the following strong beat), and resolution (stepwise descent to a consonance on the next weak beat).

What is fifth species (florid) counterpoint?

A free combination of the first four species against the cantus firmus: mixed note values (halves, quarters, ties, some eighths) using passing tones, neighbors, and suspensions, while obeying each figure's own dissonance rules. It most closely approximates real composed melody.

In fifth species counterpoint, what embellishment of the suspension resolution is permitted?

The resolution may be decorated — e.g., the suspended note moves through an anticipation, an escape tone, or a leap to another consonance before arriving at the true resolution note — as long as the resolution still occurs down by step at the proper time.

What is the difference between imitation and canon?

Imitation is the restatement of a melodic idea in another voice shortly after its first statement (it may be brief or inexact). A canon is strict, continuous imitation: the follower (comes) reproduces the leader (dux) exactly at a fixed time and pitch interval for the whole passage.

Define these canon transformations: canon by inversion, retrograde (crab) canon, and canon by augmentation/diminution.

Inversion: the follower mirrors the leader's intervals upside down (ascending becomes descending). Retrograde (crab/cancrizans): the follower plays the leader backward. Augmentation/diminution: the follower states the melody in proportionally longer/shorter note values (e.g., durations multiplied by $2$ or $\frac{1}{2}$).

What is a two-part invention, and what is its basic formal procedure (as in Bach's inventions)?

A short contrapuntal keyboard piece in two voices built from a single motive (subject). The motive is stated, imitated at the octave in the other voice against a countermotive, developed through sequences and modulations to related keys, and rounded off with cadences and a return to the tonic.

In a fugue exposition, define subject, answer, and countersubject, and distinguish a real answer from a tonal answer.

Subject: the main theme, stated alone in the tonic. Answer: the subject's imitation in the dominant by the second voice. Countersubject: recurring counterpoint sounding against the answer. A real answer is an exact transposition (up a perfect fifth/down a fourth); a tonal answer adjusts certain intervals (typically $\hat{5} \leftrightarrow \hat{1}$) to stay within the key.

In a fugue, what are an episode and a stretto?

An episode is a passage (usually sequential, often modulating) between subject entries that contains no complete subject statement. Stretto is the overlapping of subject entries — a new entry begins before the previous statement finishes — used to intensify, often near the end.

What is invertible counterpoint (double counterpoint)?

Counterpoint written so that its two voices can exchange registers (the upper becomes the lower) and still produce correct counterpoint. When designed for more voices it is triple or quadruple counterpoint.

In invertible counterpoint at the octave, what does each original interval become, and which interval must therefore be treated with special care?

An interval $n$ inverts to $9 - n$: unison↔octave, 2nd↔7th, 3rd↔6th, 4th↔5th. Since a perfect fifth inverts to a perfect fourth (a dissonance), fifths must be treated as dissonances (or avoided on strong beats) in the original. At the tenth the sum is $12 - n$... more precisely intervals sum to $11$ ($n \to 11 - n$), and at the twelfth they sum to $13$ ($n \to 13 - n$), where the sixth becomes the dissonant seventh and thus needs care.